WO2025064706A1 - Detecting the presence of a tumor based on methylation status of cell-free nucleic acid molecules - Google Patents

Abstract

In implementations described herein, methylation information is determined with respect to classification regions of a reference genome that are related to the presence of a tumor in a subject. The methylation information can be analyzed using a number of computational techniques to provide metrics related to the presence or absence of a tumor in a given subject. In one or more examples, the methylation information can be analyzed using one or more computational models that generate output corresponding to an indication of a tumor being present in a subject. The one or more computational models can be trained using training data selected from a subset of available training data according to one or more criteria.

Description

DETECTING THE PRESENCE OF A TUMOR BASED ON METHYLATION STATUS OF CELL-FREE NUCLEIC ACID MOLECULES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority of US Provisional Application No. 63/583,748 filed September 19, 2023 and US Provisional Application No. 63/588,679 filed October 6, 2023, each of which is incorporated by reference herein in its entirety for all purposes.

BACKGROUND

[0002] Cancer is a major cause of disease worldwide. Each year, tens of millions of people are diagnosed with cancer around the world, and more than half eventually die from it. In many countries, cancer ranks the second most common cause of death following cardiovascular diseases. Early detection is associated with improved outcomes for many cancers.

[0003] Cancer can be caused by the accumulation of genetics variations within an individual's normal cells, at least some of which result in improperly regulated cell division. Such variations commonly include copy number variations (CNVs), single nucleotide variations (SNVs), gene fusions, insertions and/or deletions (indels), epigenetic variations including 5-methylation of cytosine (5-methylcytosine) and association of DNA with chromatin and transcription factors.

[0004] Cancers are often detected by biopsies of tumors followed by analysis of cells, markers or DNA extracted from cells. But more recently it has been proposed that cancers can also be detected from cell-free nucleic acids in body fluids, such as blood or urine. Such tests have the advantage that they are noninvasive and can be performed without identifying suspected cancer cells in biopsy. However, such tests are complicated by the fact that the amount of nucleic acids in body fluids is very low and what nucleic acids are present are heterogeneous in form (e.g., RNA and DNA, single-stranded and double- stranded, and various states of post-replication modification and association with proteins, such as histones).

[0005] Thus, there is a need for improved systems and methods for improved cancer detection using liquid biopsy assays. Therefore, it is an object of the disclosure to provide computer-implemented systems and methods that have improved capability to classify a sample as containing tumor-derived DNA with heightened sensitivity.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain implementations, and together with the written description, serve to explain certain principles of the methods, computer readable media, and systems disclosed herein. The description provided herein is better understood when read in conjunction with the accompanying drawings which are included by way of example and not by way of limitation. It will be understood that like reference numerals identify like components throughout the drawings, unless the context indicates otherwise. It will also be understood that some or all of the figures may be schematic representations for purposes of illustration and do not necessarily depict the actual relative sizes or locations of the elements shown.

[0007] Figure 1 is a diagrammatic representation of an example environment 100 that identifies nucleic acids that correspond to classification regions of a reference sequence, where the classification regions have at least a threshold number of CpGs.

[0008] Figure 2 is a diagrammatic representation of an example architecture to determine tumor metrics based on one or more models that analyze methylation status of cell free nucleic acid molecules, according to one or more implementations.

[0009] Figure 3 is a diagrammatic representation of an example architecture to train one or more machine learning models to determine cancer metrics based on methylation status of cell-free nucleic acid molecules, according to one or more implementations.

[0010] Figure 4 is a diagrammatic representation of a framework for generating training data for use in training a computational model that determines indications of cancer being present in subjects, in accordance with one or more example implementations.

[0011] Figure 5 is a diagrammatic representation of a framework of a training process for a computational model that produces indications of cancer being present in one or more subjects, in accordance with one or more example implementations.

[0012] Figure 6 is a diagrammatic framework of a process to train a computational model using biological sample data and in silico training data, in accordance with one or more example implementations. [0013] Figure 7 is a flow diagram of an example process to determine tumor metrics related to levels of methylation of classification regions of a reference sequence, according to one or more implementations.

[0014] Figure 8 is a flowchart of an example method to train a computational model that generates one or more indications of tumors being present in one or more subjects, according to one or more implementations.

[0015] Figure 9 is a block diagram illustrating components of a machine, in the form of a computer system, that may read and execute instructions from one or more machine- readable media to perform any one or more methodologies described herein, in accordance with one or more example implementations.

[0016] Figure 10 is block diagram illustrating a representative software architecture that may be used in conjunction with one or more hardware architectures described herein, in accordance with one or more example implementations.

[0017] Figure 11 shows the limits of detection in relation to the tumor fraction for the first version of a regression model and the second version of the regression model.

[0018] Figure 12 shows the sensitivity for three models in relation to specificity. The bottom line shows results from a first model that does not implement regression model techniques described herein. The middle line shows results from a second model that corresponds to the first version of the regression model and the top line shows results from a third model that corresponds to the second version of the regression model.

Figure 13 shows the limits of detection in relation to the tumor fraction for the first version of the model and the second version of the model with respect to the detection of lung cancer and breast cancer.

SUMMARY

[0019] In one or more aspects, a method includes obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples, analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtaining a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[0020] In one or more aspects, a method includes analyzing, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected. In one or more aspects of the methods, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0021] In one or more aspects, the methods may also include analyzing the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determining, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0022] In one or more aspects, the method may also include obtaining third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples. In one or more aspects of the method, the training process for the second computational model includes a second iteration that includes determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0023] In one or more aspects, the methods may also include determining, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determining a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determining that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modifying the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0024] In one or more aspects, the methods may also include determining, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determining, forthe training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0025] In one or more aspects of the methods, the second computational model is trained using a loss function.

[0026] In one or more aspects of the methods, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0027] In one or more aspects of the methods, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the method includes determining a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and performing training processes for the plurality of computational models using the plurality of groupings of the training data. [0028] In one or more aspects, the methods may also include analyzing the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identifying one or more first samples from among the additional subset of the plurality of samples, and identifying one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0029] In one or more aspects of the methods, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0030] In one or more aspects of the methods, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0031] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects includes a first result indicating a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0032] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0033] In one or more aspects of the methods, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the method includes analyzing the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyzing the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determining a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0034] In one or more aspects of the methods, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content. [0035] In one or more aspects of the methods, the training process for the second computational model includes; performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0036] In one or more aspects of the methods, the second computational model comprises a linear regression model.

[0037] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

[0038] In one or more aspects of the methods, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

[0039] In one or more aspects of the methods, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0040] In one or more aspects, a computing apparatus includes a processor. The computing apparatus also includes a memory storing instructions that, when executed by the processor, configure the computing apparatus to obtain training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determine, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples, analyze the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determine a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtain a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, perform a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyze, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[0041] In one or more aspects, a computing apparatus includes a processor. The computing apparatus also includes a memory storing instructions that, when executed by the processor, configure the computing apparatus to analyze, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected.

[0042] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determine, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0043] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to obtain third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples.

[0044] In one or more aspects of the computing apparatuses, the training process for the second computational model includes a second iteration that includes determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0045] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determine a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determine that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modify the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0046] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor. [0047] In one or more aspects of the computing apparatuses, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0048] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0049] In one or more aspects of the computing apparatuses, the second computational model is trained using a loss function.

[0050] In one or more aspects of the computing apparatuses, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0051] In one or more aspects of the computing apparatuses, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and perform training processes for the plurality of computational models using the plurality of groupings of the training data. [0052] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identify one or more first samples from among the additional subset of the plurality of samples, and identify one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0053] In one or more aspects of the computing apparatuses, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0054] In one or more aspects of the computing apparatuses, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0055] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects includes a first result indicate a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0056] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0057] In one or more aspects of the computing apparatuses, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyze the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine- guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determine a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0058] In one or more aspects of the computing apparatuses, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

[0059] In one or more aspects of the computing apparatuses, the second computational model comprises a linear regression model.

[0060] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

[0061] In one or more aspects of the computing apparatuses, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject. [0062] In one or more aspects of the computing apparatuses, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0063] In one or more aspects of the computing apparatuses, the training process for the second computational model includes: performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0064] In one or more aspects, a non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to obtain training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determine, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples, analyze the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determine a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtain a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, perform a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyze, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects. [0065] In one or more aspects, a non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to analyze, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected.

[0066] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0067] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to analyze the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determine, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0068] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to obtain third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples.

[0069] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a second iteration that includes determine a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0070] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to determine, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determine a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determine that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modify the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0071] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0072] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to determine, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0073] In one or more aspects of the non-transitory computer-readable storage media, the second computational model is trained using a loss function.

[0074] In one or more aspects of the non-transitory computer-readable storage media, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0075] In one or more aspects of the non-transitory computer-readable storage media, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the non-transitory computer-readable storage medium stores additional instructions that when executed by a computer, cause the computer to determine a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and perform training processes for the plurality of computational models using the plurality of groupings of the training data.

[0076] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to analyze the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identify one or more first samples from among the additional subset of the plurality of samples, and identify one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0077] In one or more aspects of the non-transitory computer-readable storage media, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0078] In one or more aspects of the non-transitory computer-readable storage media, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0079] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects includes a first result indicate a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0080] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0081] In one or more aspects of the non-transitory computer-readable storage media, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the non- transitory computer-readable storage medium stores additional instructions that when executed by a computer, cause the computer to analyze the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyze the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determine a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0082] In one or more aspects of the non-transitory computer-readable storage media, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

[0083] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes; performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0084] In one or more aspects of the non-transitory computer-readable storage media, the second computational model comprises a linear regression model.

[0085] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value. [0086] In one or more aspects of the non-transitory computer-readable storage media, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

[0087] In one or more aspects of the non-transitory computer-readable storage media, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0088] Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims.

DEFINITIONS

[0089] In order for the present disclosure to be more readily understood, certain terms are first defined below. Additional definitions for the following terms and other terms may be set forth through the specification. If a definition of a term set forth below is inconsistent with a definition in an application or patent that is incorporated by reference, the definition set forth in this application should be used to understand the meaning of the term.

[0090] As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Thus, for example, a reference to “a method” includes one or more methods, and/or steps of the type described herein and/or which will become apparent to those persons of ordinary skill in the art upon reading this disclosure and so forth.

[0091] It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only, and is not intended to be limiting. Further, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. In describing and claiming the methods, computer readable media, and systems, the following terminology, and grammatical variants thereof, will be used in accordance with the definitions set forth below.

[QQS2] About. As used herein, “about” or “approximately” as applied to one or more values or elements of interest, refers to a value or element that is similar to a stated reference value or element. In certain implementations, the term “about” or “approximately” refers to a range of values or elements that falls within 25%, 20%, 19%, 18%, 17%, 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1 %, or less in either direction (greater than or less than) of the stated reference value or element unless otherwise stated or otherwise evident from the context (except where such number would exceed 100% of a possible value or element).

[0093] Administer: As used herein, “administer” or “administering” a therapeutic agent (e.g., an immunological therapeutic agent) to a subject means to give, apply or bring the composition into contact with the subject. Administration can be accomplished by any of a number of routes, including, for example, topical, oral, subcutaneous, intramuscular, intraperitoneal, intravenous, intrathecal and intradermal.

[0094] Adapter: As used herein, “adapter” refers to a short nucleic acid (e.g., less than about 500 nucleotides, less than about 100 nucleotides, or less than about 50 nucleotides in length) that can be at least partially double-stranded and used to link to either or both ends of a given sample nucleic acid molecule. Adapters can include nucleic acid primer binding sites to permit amplification of a nucleic acid molecule flanked by adapters at both ends, and/or a sequencing primer binding site, including primer binding sites for sequencing applications, such as various next-generation sequencing (NGS) applications. Adapters can also include binding sites for capture probes, such as an oligonucleotide attached to a flow cell support or the like. Adapters can also include a nucleic acid tag as described herein. Nucleic acid tags can be positioned relative to amplification primer and sequencing primer binding sites, such that a nucleic acid tag is included in amplicons and sequence reads of a given nucleic acid molecule. The same or different adapters can be linked to the respective ends of a nucleic acid molecule. In some implementations, the same adapter is linked to the respective ends of the nucleic acid molecule except that the nucleic acid tag differs. In some implementations, the adapter is a Y-shaped adapter in which one end is blunt ended or tailed as described herein, for joining to a nucleic acid molecule, which is also blunt ended or tailed with one or more complementary nucleotides. In still other example implementations, an adapter is a bell-shaped adapter that includes a blunt or tailed end for joining to a nucleic acid molecule to be analyzed. Other examples of adapters include T-tailed and C-tailed adapters. [0095] Alignment. As used herein, “alignment” or “align” refers to determining whether at least two sequence representations have at least a threshold amount of homology. In one or more examples, the threshold amount of homology can be at least about 90%, at least about 91%, at least about 92%, at least about 93%, at least about 94%, at least about 95%, at least about 96%, at least about 97%, at least about 98%, at least about 99%, at least about 99.5%, or at least about 99.9%. In situations where two sequence representations have at least the threshold amount of homology, the two sequence representations can be referred to as being “aligned.”

[0096] Amplify: As used herein, “amplify” or “amplification” in the context of nucleic acids refers to the production of multiple copies of a polynucleotide, or a portion of the polynucleotide, starting from a small amount of the polynucleotide (e.g., a single polynucleotide molecule), where the amplification products or amplicons are generally detectable. Amplification of polynucleotides encompasses a variety of chemical and enzymatic processes.

[0097] Barcode: As used herein, “barcode” or “molecular barcode” in the context of nucleic acids refers to a nucleic acid molecule comprising a sequence that can serve as a molecular identifier. For example, individual "barcode" sequences can be added to each DNA fragment during next-generation sequencing (NGS) library preparation so that each read can be identified and sorted before the final data analysis.

[0098] Cancer Type: As used herein, “cancer type” refers to a type or subtype of cancer defined, e.g., by histopathology. Cancer type can be defined by any conventional criterion, such as on the basis of occurrence in a given tissue (e.g., blood cancers, central nervous system (CNS), brain cancers, lung cancers (small cell and non-small cell), skin cancers, nose cancers, throat cancers, liver cancers, bone cancers, lymphomas, pancreatic cancers, bowel cancers, rectal cancers, thyroid cancers, bladder cancers, kidney cancers, mouth cancers, stomach cancers, breast cancers, prostate cancers, ovarian cancers, lung cancers, intestinal cancers, soft tissue cancers, neuroendocrine cancers, gastroesophageal cancers, head and neck cancers, gynecological cancers, colorectal cancers, urothelial cancers, solid state cancers, heterogeneous cancers, homogenous cancers), unknown primary origin and the like, and/or of the same cell lineage (e.g., carcinoma, sarcoma, lymphoma, cholangiocarcinoma, leukemia, mesothelioma, melanoma, or glioblastoma) and/or cancers exhibiting cancer markers, such as Her2, CA15-3, CA19-9, CA-125, CEA, AFP, PSA, HCG, hormone receptor and NMP-22. Cancers can also be classified by stage (e.g., stage 1 , 2, 3, or 4) and whether of primary or secondary origin.

[0099] Carrier Signal: As used herein, “carrier signal” refers to any intangible medium that is capable of storing, encoding, or carrying transitory or non-transitory instructions 902 for execution by the machine 900, and includes digital or analog communications signals or other intangible medium to facilitate communication of such instructions 902. Instructions 902 may be transmitted or received over the network 934 using a transitory or non-transitory transmission medium via a network interface device and using any one of a number of well-known transfer protocols.

[00100] Cell-Free Nucleic Acid: As used herein, “cell-free nucleic acid” refers to nucleic acids not contained within or otherwise bound to a cell or, in some implementations, nucleic acids remaining in a sample following the removal of intact cells. Cell-free nucleic acids can include, for example, all non-encapsulated nucleic acids sourced from a bodily fluid (e.g., blood, plasma, serum, urine, cerebrospinal fluid (CSF), etc.) from a subject. Cell-free nucleic acids include DNA (cfDNA), RNA (cfRNA), and hybrids thereof, including genomic DNA, mitochondrial DNA, circulating DNA, siRNA, miRNA, circulating RNA (cRNA), tRNA, rRNA, small nucleolar RNA (snoRNA), Piwi- interacting RNA (piRNA), long non-coding RNA (long ncRNA), and/or fragments of any of these. Cell-free nucleic acids can be double-stranded, single-stranded, or a hybrid thereof. A cell-free nucleic acid can be released into bodily fluid through secretion or cell death processes, e.g., cellular necrosis, apoptosis, or the like. Some cell-free nucleic acids are released into bodily fluid from cancer cells, e.g., circulating tumor DNA (ctDNA). Others are released from healthy cells. CtDNA can be non-encapsulated tumor-derived fragmented DNA. A cell-free nucleic acid can have one or more epigenetic modifications, for example, a cell-free nucleic acid can be acetylated, 5-methylated, ubiquitylated, phosphorylated, sumoylated, ribosylated, and/or citrullinated.

[00101] Cellular Nucleic Acids: As used herein, “cellular nucleic acids” means nucleic acids that are disposed within one or more cells at least at the point a sample is taken or collected from a subject, even if those nucleic acids are subsequently removed as part of a given analytical process.

[00102] Classification Region: As used herein, “classification region” refers to a genomic region that may show sequence-independent changes in neoplastic cells (e.g., tumor cells and cancer cells) or that may show sequence-independent changes in cfDNA from subjects having cancer relative to cfDNA from subjects in which cancer is not present. Examples of sequence-independent changes include, but are not limited to, changes in methylation rate (increases or decreases), nucleosome distribution, CTCF binding, transcription start sites, and regulatory protein binding regions. In one or more examples, sequence-independent changes in a classification region can indicate the presence of a single form of cancer in a subject. In one or more additional examples, sequence-independent changes in a classification region can correspond to the presence of multiple forms in a subject. The classification region can be enriched by one or more probes. In addition, the classification region can be defined by a pair of primer binding sites. Further, the classification region can be defined by a predetermined beginning genomic locus and a predetermined ending genomic locus. The classification region can include from about 25 nucleotides to about 250 nucleotides, from about 50 nucleotides to about 200 nucleotides, or from about 75 nucleotides to about 150 nucleotides. For instance, classification region can be a differentially methylated region. “Differentially methylated region” or “DMR” refers to a region of DNA having a detectably different degree of methylation in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type; or having a detectably different degree of methylation in at least one cell or tissue type obtained from a subject having a disease or disorder relative to the degree of methylation in the same region of DNA in the same cell or tissue type obtained from a healthy subject. In some embodiments, a differentially methylated region has a detectably higher degree of methylation (e.g., a hypermethylated region/hypermethylated target region) in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, a differentially methylated region has a detectably lower degree of methylation (e.g., a hypomethylated region/hypomethylated target region) in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and/or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, the classification regions comprise hypermethylated target regions and/or hypomethylated target regions.

[00103] Communications Network. As used herein, “communications network” refers to one or more portions of a network 114, 1034 that may be an ad hoc network, an intranet, an extranet, a virtual private network (VPN), a local area network (LAN), a wireless LAN (WLAN), a wide area network (WAN), a wireless WAN (WWAN), a metropolitan area network (MAN), the Internet, a portion of the Internet, a portion of the Public Switched Telephone Network (PSTN), a plain old telephone service (POTS) network, a cellular telephone network, a wireless network, a Wi-Fi® network, another type of network, or a combination of two or more such networks. For example, a network 114, 1034 or a portion of a network may include a wireless or cellular network and the coupling may be a Code Division Multiple Access (CDMA) connection, a Global System for Mobile communications (GSM) connection, or other type of cellular or wireless coupling. In this example, the coupling may implement any of a variety of types of data transfer technology, such as Single Carrier Radio Transmission Technology (1xRTT), Evolution- Data Optimized (EVDO) technology, General Packet Radio Service (GPRS) technology, Enhanced Data rates for GSM Evolution (EDGE) technology, third Generation Partnership Project (3GPP) including 3G, fourth generation wireless (4G) networks, Universal Mobile Telecommunications System (UMTS), High Speed Packet Access (HSPA), Worldwide Interoperability for Microwave Access (WiMAX), Long Term Evolution (LTE) standard, others defined by various standard setting organizations, other long range protocols, or other data transfer technology.

[00104] Confidence Interval. As used herein, “confidence interval” means a range of values so defined that there is a specified probability that the value of a given parameter lies within that range of values.

[00105] Control Sample: As used herein, “control sample” or “reference sample” refers to a sample obtained from individuals without known copy number variation. [00106] Coverage. As used herein, “coverage” or “coverage metrics” refer to the number of nucleic acid molecules or sequencing reads that correspond to a particular genomic region of a reference sequence.

[00107] Deoxyribonucleic Acid or Ribonucleic Acid: As used herein, “deoxyribonucleic acid” or “DNA” refers to a natural or modified nucleotide which has a hydrogen group at the 2'-position of the sugar moiety. DNA can include a chain of nucleotides comprising four types of nucleotide bases: adenine (A), thymine (T), cytosine (C), and guanine (G). As used herein, “ribonucleic acid” or “RNA” refers to a natural or modified nucleotide which has a hydroxyl group at the 2'-position of the sugar moiety. RNA can include a chain of nucleotides comprising four types of nucleotides: A, uracil (U), G, and C. As used herein, the term “nucleotide” refers to a natural nucleotide or a modified nucleotide. Certain pairs of nucleotides specifically bind to one another in a complementary fashion (called complementary base pairing). In DNA, adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G). In RNA, adenine (A) pairs with uracil (U) and cytosine (C) pairs with guanine (G). When a first nucleic acid strand binds to a second nucleic acid strand made up of nucleotides that are complementary to those in the first strand, the two strands bind to form a double strand. As used herein, “nucleic acid sequencing data”, “nucleic acid sequencing information”, “sequence information”, “sequence representation”, “nucleic acid sequence”, “nucleotide sequence”, “genomic sequence”, “genetic sequence”, “fragment sequence”, “sequencing read”, or “nucleic acid sequencing read” denotes any information or data that is indicative of the order and identity of the nucleotide bases (e.g., adenine, guanine, cytosine, and thymine or uracil) in a molecule (e.g., a whole genome, whole transcriptome, exome, oligonucleotide, polynucleotide, or fragment) of a nucleic acid such as DNA or RNA. It should be understood that the present teachings contemplate sequence information obtained using all available varieties of techniques, platforms or technologies, including, but not limited to: capillary electrophoresis, microarrays, ligation-based systems, polymerase-based systems, hybridization-based systems, direct or indirect nucleotide identification systems, pyrosequencing, ion- or pH-based detection systems, and electronic signature-based systems. [00108] Differentially Methylated Region: As used herein, differentially methylated region” refers to a region of DNA having a detectably different degree of methylation in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type; or having a detectably different degree of methylation in at least one ceil or tissue type obtained from a subject having a disease or disorder relative to the degree of methylation in the same region of DNA in the same cell or tissue type obtained from a healthy subject. In some embodiments, a differentially methylated region has a detectably higher degree of methylation (e.g., a hypermethylated region) in at least one cell or tissue type, such as at least one immune cell type, relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and/or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, a differentially methylated region has a detectably lower degree of methylation (e.g., a hypomethylated region) in at least one cell or tissue type, such as at least one immune cell type, relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and/or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject.

[00109] Driver Mutation. As used herein, “driver mutation” means a mutation that drives cancer progression.

[00110] Epigenetic Target Regions. As used herein, “epigenetic target regions” refers to target regions that may show sequence-independent differences in different cell or tissue types (e.g., different types of immune cells) or in neoplastic cells (e.g., tumor cells and cancer ceils) relative to normal cells; or that may show sequence- independent differences (i.e., in which there is no change to the nucleotide sequence, e.g., differences in methylation, nucleosome distribution, or other epigenetic features) in DNA, such as cfDNA, from different cell types or from subjects having cancer relative to DNA, such as cfDNA, from healthy subjects, or in cfDNA originating from different cell or tissue types that ordinarily do not substantially contribute to cfDNA (e.g., immune, lung, colon, etc.) relative to background cfDNA (e.g., cfDNA that originated from hematopoietic ceils). Examples of sequence-independent changes include, but are not limited to, changes in methylation (increases or decreases), nucleosome distribution, cfDNA fragmentation patterns, CCCTC-binding factor ("CTCF") binding, transcription start sites (e.g., with respect to any one of more of binding of RNA polymerase components, binding of regulatory proteins, fragmentation characteristics, and nucieosomal distribution), and regulatory protein binding regions. Epigenetic target region sets thus include, but are not limited to, hypermethylation target region sets, hypomethylation target region sets, and fragmentation variable target region sets, such as CTCF binding sites and transcription start sites. For present purposes, loci susceptible to neoplasia-, tumor-, or cancer- associated focal amplifications and/or gene fusions may also be included in an epigenetic target region set because detection of a change in copy number by sequencing or a fused sequence that maps to more than one locus in a reference genome tends to be more similar to detection of exemplary epigenetic changes discussed above than detection of nucleotide substitutions, insertions, or deletions, e.g., in that the focal amplifications and/or gene fusions can be detected at a relatively shallow depth of sequencing because their detection does not depend on the accuracy of base calls at one or a few individual positions. An epigenetic target region set is a set of epigenetic target regions.

[00111] Hypermethylation: As used herein, “hypermethylation” refers to an increased level or degree of methylation of nucleic acid molecule(s) relative to the other nucleic acid molecules within a population (e.g., sample) of nucleic acid molecules from the same genomic locus. In some embodiments, hypermethylated DNA can include DNA molecules comprising at least 1 methylated cytosine, at least 2 methylated cytosines, at least 3 methylated cytosines, at least 5 methylated cytosines, or at least 10 methylated cytosines.

[00112] Hypomethylation: As used herein, “hypomethylation” refers to a decreased level or degree of methylation of nucleic acid molecule(s) relative to the other nucleic acid molecules within a population (e.g., sample) of nucleic acid molecules from the same genomic locus. In some embodiments, hypomethylated DNA includes unmethylated DNA molecules. In some embodiments, hypomethylated DNA can include DNA molecules comprising 0 methylated cytosine, at most 1 methylated cytosine, at most 2 methylated cytosines, at most 3 methylated cytosines, at most 4 methylated cytosines, or at most 5 methylated cytosines. [00113] Immunotherapy. As used herein, “immunotherapy” refers to treatment with one or more agents that act to stimulate the immune system so as to kill or at least to inhibit growth of cancer cells, and preferably to reduce further growth of the cancer, reduce the size of the cancer and/or eliminate the cancer. Some such agents bind to a target present on cancer cells; some bind to a target present on immune cells and not on cancer cells; some bind to a target present on both cancer cells and immune cells. Such agents include, but are not limited to, checkpoint inhibitors and/or antibodies. Checkpoint inhibitors are inhibitors of pathways of the immune system that maintain self-tolerance and modulate the duration and amplitude of physiological immune responses in peripheral tissues to minimize collateral tissue damage (see, e.g., Pardoll, Nature Reviews Cancer 12, 252-264 (2012)). Example agents include antibodies against any of PD-1 , PD-2, PD-L1 , PD-L2, CTLA-40, 0X40, B7.1 , B7He, LAG3, CD137, KIR, CCR5, CD27, or CD40. Other example agents include proinflammatory cytokines, such as IL- 10, IL-6, and TNF-a. Other example agents are T-cells activated against a tumor, such as T-cells activated by expressing a chimeric antigen targeting a tumor antigen recognized by the T-cell.

[00114] Indel: As used herein, “indel” refers to a mutation that involves the insertion or deletion of nucleotides in the genome of a subject.

[00115] Limit of Detection (LoD): As used herein, “limit of detection” means the smallest amount of a substance (e.g., a nucleic acid) in a sample that can be measured by a given assay or analytical approach.

[00116] Machine-Readable Medium: As used herein, “machine-readable medium” refers to a component, device, or other tangible media able to store instructions 902 and data temporarily or permanently and may include, but is not limited to, random-access memory (RAM), read-only memory (ROM), buffer memory, flash memory, optical media, magnetic media, cache memory, other types of storage (e.g., erasable programmable read-only memory (EEPROM)) and/or any suitable combination thereof. The term “machine-readable medium” may be taken to include a single medium or multiple media (e.g., a centralized or distributed database, or associated caches and servers) able to store instructions 902. The term “machine-readable medium” shall also be taken to include any medium, or combination of multiple media, that is capable of storing instructions 902 (e.g., code) for execution by a machine 900, such that the instructions 902, when executed by one or more processors 904 of the machine 900, cause the machine 900 to perform any one or more of the methodologies described herein. Accordingly, a “machine-readable medium” refers to a single storage apparatus or device, as well as “cloud-based” storage systems or storage networks that include multiple storage apparatus or devices. The term “machine-readable medium” excludes signals per se.

[00117] Maximum MAF. As used herein, “maximum MAF” or “max MAF” refers to the maximum MAF (mutant allele fraction) of all somatic variants in a sample.

[00118] Methylation: As used herein, “methylation” or “DNA methylation” refers to addition of a methyl group to a nucleotide base in a nucleic acid molecule. In some embodiments, methylation refers to addition of a methyl group to a cytosine at a CpG site (cytosine-phosphate-guanine site (i.e., a cytosine followed by a guanine in a 5' 3’ direction of the nucleic acid sequence). In some embodiments, DNA methylation refers to addition of a methyl group to adenine, such as in N⁶-methyladenine. In some embodiments, DNA methylation is 5-methylation (modification of the 5^th carbon of the 6- carbon ring of cytosine). In some embodiments, 5-methylation refers to addition of a methyl group to the 5C position of the cytosine to create 5-methylcytosine (5mC). In some embodiments, methylation comprises a derivative of 5mC. Derivatives of 5mC include, but are not limited to, 5-hydroxymethylcytosine (5-hmC), 5-formylcytosine (5-fC), and 5- caryboxylcytosine (5-caC). In some embodiments, DNA methylation is 3C methylation (modification of the 3^rd carbon of the 6-carbon ring of cytosine). In some embodiments, 3C methylation comprises addition of a methyl group to the 3C position of the cytosine to generate 3-methylcytosine (3mC). Methylation can also occur at non CpG sites, for example, methylation can occur at a CpA, CpT, or CpC site. DNA methylation can change the activity of methylated DNA region. For example, when DNA in a promoter region is methylated, transcription of the gene may be repressed. DNA methylation is critical for normal development and abnormality in methylation may disrupt epigenetic regulation. The disruption, e.g., repression, in epigenetic regulation may cause diseases, such as cancer. Promoter methylation in DNA may be indicative of cancer. [00119] Methylation-Dependent Nuclease: As used herein, “methylation- dependent nuclease” refers to a nuclease that preferentially cuts methylated DNA relative to unmethylated DNA. For example, a methylation-dependent nuclease may cut at or near a recognition sequence such as a restriction site in a manner dependent on methylation of at least one of the nucleobases in the recognition sequence, such as a cytosine. In some embodiments, the nucleolytic activity of the methylation-dependent nuclease is at least 10, 20, 50, or 100-fold higher on a methylated recognition site relative to an unmethylated control in a standard nucleolysis assay. Methylation-dependent nucleases include methylation-dependent restriction enzymes.

[00120] Methylation-Dependent Restriction Enzyme: As used herein, “methylation-dependent restriction enzyme” or “MDRE” refers to a restriction enzyme that is dependent on methylation of the DNA (e.g., cytosine methylation) i.e., the presence or absence of methyl group in a nucleotide base alters the rate at which the enzyme cleaves the target DNA. In some embodiments, the methylation dependent restriction enzymes do not cleave the DNA if a particular nucleotide base is unmethylated at the recognition sequence. For example, MspJI is a methylation dependent restriction enzyme with a recognition sequence “mCNNR(N9)” and it does not cleave DNA if the absence of the methylated cytosine (mC) in the recognition sequence.

[00121] Methylation-Sensitive Nuclease: As used herein, “methylation-sensitive nuclease” refers to a nuclease that preferentially cuts unmethylated DNA relative to methylated DNA. For example, a methylation-sensitive nuclease may cut at or near a recognition sequence such as a restriction site in a manner dependent on lack of methylation of at least one of the nucleobases in the recognition sequence, such as a cytosine. In some embodiments, the nucleolytic activity of the methylation-sensitive nuclease is at least 10, 20, 50, or 100-fold higher on an unmethylated recognition site relative to a methylated control in a standard nucleolysis assay. Methylation-sensitive nucleases include methylation- sensitive restriction enzymes.

[00122] Methylation Sensitive Restriction Enzyme: As used herein, “methylation sensitive restriction enzyme” or “MSRE” refers to a restriction enzyme that is sensitive to the methylation status of the DNA (e.g., cytosine methylation) i.e., the presence or absence of methyl group in a nucleotide base alters the rate at which the enzyme cleaves the target DNA. In some embodiments, the methylation sensitive restriction enzymes do not cleave the DNA if a particular nucleotide base is methylated at the recognition sequence. For example, Hpall is a methylation sensitive restriction enzyme with a recognition sequence “CCGG” and it does not cleave DNA if the second cytosine in the recognition sequence is methylated.

[00123] Methylation rate: As used herein, “methylation rate” refers to the probability, likelihood, or percentage that a given base (for example: cytosine residue in a CpG) is methylated on a DNA molecule at a particular genomic region analyzed in the sample. In some embodiments, the methylation rate may be applied to a defined region that comprises one or more potentially methylated bases. In some embodiments, the methylation rate refers to the percentage of CpG residues methylated in a DNA molecule. In some embodiments, the methylation rate refers to the percentage of CpG residues methylated in molecules aligned to particular genomic position or genomic region. Methylation rate can be measured by a variety of methods including, but not limited to, either using bisulfite sequencing (any single base resolution like TAPS, EM-SEQ, etc.) or using partitioning (DNA molecule resolution). Methylation rate can be measured in different ways. One estimation can be by counting how many DNA fragments end up in each methylation dependent partition or by counting the number of converted CpGs per fragment in the case of bisulfite sequencing or any other base-level resolution sequencing methods. In addition, in the case of methylation dependent partitioning, the rate calculation can be normalized using a set of predefined regions with known methylation state (i.e. , positive control regions and/or negative control regions) or spiked- in synthetic DNA with known methylation state, deriving rate-parametrized partition distributions and estimating the rate using a maximum likelihood approach. In one or more examples, the methylation rate can be determined by determining an abundance of sequencing reads that correspond to a portion of a genomic region. The portion of the genomic region can include a number of genomic locations of the genomic region for which at least a threshold number of sequencing reads overlap.

[00124] Methylation Status: As used herein, “methylation status” or “methylation state” can refer to the presence or absence of methyl group on a DNA base (e.g., cytosine) at a particular genomic position in a nucleic acid molecule. It can also refer to the degree of methylation in a nucleic acid sequence (e.g., highly methylated, low methylated, intermediately methylated or unmethylated nucleic acid molecules). The methylation status can also refer to the number of nucleotides methylated in a particular nucleic acid molecule.

[00125] Modified Nucleotide Specific Binding Reagent: As used herein, refers to a binding reagent that is specific for, or targets, modified nucleotides. For example, a modified nucleotide can be a nucleotide that has been methylated, thus, the binding reagent can be specific for a methylated nucleotide. Examples of binding reagents include, but are not limited to, a methyl binding domain (MBD) of a methylation binding protein (“MBP”) or variants thereof, an antibody (and antibody variants e.g., single chain antibodies), aptamers, or combinations thereof. Thus, as disclosed throughout, the use of MBD can be exchanged for any other modified nucleotide specific binding reagent, provided the modified nucleotide specific binding reagent has the desired specificity and affinity for the specific modified base of interest in the selected implementation.

[00126] Mutant Allele Fraction. As used herein, “mutant allele fraction”, “mutation dose,” or “MAF” refers to the fraction of nucleic acid molecules harboring an allelic alteration or mutation at a given genomic position in a given sample. MAF is generally expressed as a fraction or a percentage. For example, an MAF can be less than about 0.5, 0.1 , 0.05, or 0.01 (i.e., less than about 50%, 10%, 5%, or 1%) of all somatic variants or alleles present at a given locus.

[00127] Mutation. As used herein, “mutation” refers to a variation from a known reference sequence and includes mutations such as, for example, single nucleotide variants (SNVs), copy number variants or variations (CNVs)Zaberrations, insertions or deletions (indels), gene fusions, transversions, translocations, frame shifts, duplications, repeat expansions, and epigenetic variants. A mutation can be a germline or somatic mutation. In some examples, a reference sequence for purposes of comparison is a wildtype genomic sequence of the species of the subject providing a test sample, typically the human genome.

[00128] Mutation Caller. As used herein, “mutation caller” means an algorithm (embodied in software or otherwise computer implemented) that is used to identify mutations in test sample data (e.g., sequence information obtained from a subject). [00129] Mutation Count. As used herein, “mutation count” or “mutational count” refers to the number of somatic mutations in a whole genome or exome or targeted regions of a nucleic acid sample.

[00130] Negative Control Region: As used herein, “negative control region”, refers to a genomic region that is expected to be unmethylated or hypomethylated in essentially all samples, regardless of whether the DNA is derived from a cancer cell or a normal cell. [00131] Neoplasm: As used herein, the terms “neoplasm” and “tumor” are used interchangeably. They refer to abnormal growth of cells in a subject. A neoplasm or tumor can be benign, potentially malignant, or malignant. A malignant tumor is referred to as a cancer or a cancerous tumor.

[00132] Next Generation Sequencing: As used herein, “next generation sequencing” or “NGS” refers to sequencing technologies having increased throughput as compared to traditional Sanger- and capillary electrophoresis-based approaches, for example, with the ability to generate hundreds of thousands of relatively small sequencing reads at a time. Some examples of next generation sequencing techniques include, but are not limited to, sequencing by synthesis, sequencing by ligation, and sequencing by hybridization.

[00133] Nucleic Acid Tag: As used herein, “nucleic acid tag” refers to a short nucleic acid (e.g., less than about 500 nucleotides, about 100 nucleotides, about 50 nucleotides, or about 10 nucleotides in length), used to distinguish nucleic acids from different samples (e.g., representing a sample index), or different nucleic acid molecules in the same sample (e.g., representing a molecular barcode), of different types, or which have undergone different processing. The nucleic acid tag comprises a predetermined, fixed, non-random, random or semi-random oligonucleotide sequence. Such nucleic acid tags may be used to label different nucleic acid molecules or different nucleic acid samples or sub-samples. Nucleic acid tags can be single-stranded, double-stranded, or at least partially double-stranded. Nucleic acid tags optionally have the same length or varied lengths. Nucleic acid tags can also include double-stranded molecules having one or more blunt-ends, include 5’ or 3’ single-stranded regions (e.g., an overhang), and/or include one or more other single-stranded regions at other locations within a given molecule. Nucleic acid tags can be attached to one end or to both ends of the other nucleic acids (e.g., sample nucleic acids to be amplified and/or sequenced). Nucleic acid tags can be decoded to reveal information such as the sample of origin, form, or processing of a given nucleic acid. For example, nucleic acid tags can also be used to enable pooling and/or parallel processing of multiple samples comprising nucleic acids bearing different molecular barcodes and/or sample indexes in which the nucleic acids are subsequently being deconvolved by detecting (e.g., reading) the nucleic acid tags. Nucleic acid tags can also be referred to as identifiers (e.g., molecular identifier, sample identifier). Additionally, or alternatively, nucleic acid tags can be used as molecular identifiers (e.g., to distinguish between different molecules or amplicons of different parent molecules in the same sample or sub-sample). This includes, for example, uniquely tagging different nucleic acid molecules in a given sample, or non-uniquely tagging such molecules. In the case of non-unique tagging applications, a limited number of tags (i.e., molecular barcodes) may be used to tag each nucleic acid molecule such that different molecules can be distinguished based on their endogenous sequence information (for example, start and/or stop positions where they map to a selected reference sequence, a sub-sequence of one or both ends of a sequence, and/or length of a sequence) in combination with at least one molecular barcode. A sufficient number of different molecular barcodes are used such that there is a low probability (e.g., less than about a 10%, less than about a 5%, less than about a 1%, or less than about a 0.1% chance) that any two molecules may have the same endogenous sequence information (e.g., start and/or stop positions, subsequences of one or both ends of a sequence, and/or lengths) and also have the same molecular barcode.

[00134] Partitioning. As used herein, “partitioning” refers to physically separating or fractionating a mixture of nucleic acid molecules in a sample based on a characteristic of the nucleic acid molecules. The partitioning can be physical partitioning of molecules. Partitioning can involve separating the nucleic acid molecules into groups or sets based on the level of epigenetic feature (for e.g., methylation). For example, the nucleic acid molecules can be partitioned based on the level of methylation of the nucleic acid molecules. In some embodiments, the methods and systems used for partitioning may be found in PCT Patent Application No. PCT/US2017/068329, which is hereby incorporated by reference in its entirety. [00135] Partitioned set: As used herein, “partitioned set” or “partition” refers to a set of nucleic acid molecules partitioned into a set or group based on the differential binding affinity of the nucleic acid molecules or proteins associated with the nucleic acid molecules to a binding agent. A partitioned set may also be referred to as a subsample. The binding agent binds preferentially to the nucleic acid molecules comprising nucleotides with epigenetic modification. For example, if the epigenetic modification is methylation, the binding agent can be a methyl binding domain (MBD) protein. In some embodiments, a partitioned set can comprise nucleic acid molecules belonging to a particular level or degree of epigenetic feature (for e.g., methylation). For example, the nucleic acid molecules can be partitioned into three sets - one set for highly methylated nucleic acid molecules (first subsample, hyper partition, hyper partitioned set or hypermethylated partitioned set), a second set for low methylated nucleic acid molecules (second subsample, hypo partition, hypo partitioned set or hypomethylated partitioned set), and a third set for intermediate methylated nucleic acid molecules (third subsample, intermediate partitioned set, intermediately methylated partitioned set, residual partition, or residual partitioned set). In another example, the nucleic acid molecules can be partitioned based on the number of methylated nucleotides - one partitioned set can have nucleic acid molecules with nine methylated nucleotides, and another partitioned set can have unmethylated nucleic acid molecules (zero methylated nucleotides).

[00136] Polynucleotide: As used herein, “polynucleotide”, “nucleic acid”, “nucleic acid molecule”, “polynucleotide molecule”, or “oligonucleotide” refers to a linear polymer of nucleosides (including deoxyribonucleosides, ribonucleosides, or analogs thereof) joined by internucleosidic linkages. A polynucleotide can comprise at least three nucleosides. Oligonucleotides often range in size from a few monomeric units, e.g., 3-4, to hundreds of monomeric units. Whenever a polynucleotide is represented by a sequence of letters, such as “ATGCCTG,” it will be understood that the nucleotides are in 5’ -> 3’ order from left to right and that in the case of DNA, “A” denotes deoxyadenosine, “C” denotes deoxycytidine, “G” denotes deoxyguanosine, and “T” denotes deoxythymidine, unless otherwise noted. The letters A, C, G, and T may be used to refer to the bases themselves, to nucleosides, or to nucleotides comprising the bases, as is standard in the art. [00137] Positive Control Region. As used herein, As used herein, “positive control region”, refers to a genomic region that is expected to be methylated or hypermethylated in essentially all samples, regardless of whether the DNA is derived from a cancer cell or a normal cell.

[00138] Probe: As used herein, “probe” refers to a polynucleotide comprising a functionality. The functionality can be a detectable label (fluorescent), a binding moiety (biotin), or a solid support (a magnetically attractable particle or a chip). Probes can include single-stranded DNA/RNA polynucleotides or double stranded DNA polynucleotides that hybridize to target nucleic acid sequences (e.g., SureSelect® probes, Agilent Technologies). Sequence capture using probes generally depends, in part, on the number of consecutive nucleotides in at least a portion of the target nucleic acid sequence that is complementary (or nearly complementary) to the sequence of the probe. In some examples, probes can correspond to driver mutations.

[00139] Processing: As used herein, the terms “processing”, “calculating”, and

“comparing” can be used interchangeably. In certain applications, the terms refer to determining a difference, e.g., a difference in number or sequence. For example, gene expression, copy number variation (CNV), indel, and/or single nucleotide variant (SNV) values or sequences can be processed.

[00140] Processor: As used herein, “processor” refers to any circuit or virtual circuit (a physical circuit emulated by logic executing on an actual processor) that manipulates data values according to control signals (e.g., “commands,” “op codes,” “machine code,” etc.) and which produces corresponding output signals that are applied to operate a machine. A processor may, for example, be a CPU, a RISC processor, a CISC processor, a GPU, a DSP, an ASIC, a RFIC or any combination thereof. A processor may further be a multi-core processor having two or more independent processors (sometimes referred to as “cores”) that may execute instructions contemporaneously.

[00141] Promoter Region As used herein, “promoter region” refers to a DNA sequence recognized by the synthetic machinery of the cell, or introduced synthetic machinery, required to initiate the specific transcription of a gene.

[00142] Quantitative Measures: As used herein, “quantitative measures” refers to an absolute or relative measure. A quantitative measure can be, without limitation, a number, a statistical measurement (e.g., frequency, mean, median, standard deviation, or quantile), or a degree or a relative quantity (e.g., high, medium, and low). A quantitative measure can be a ratio of two quantitative measures. A quantitative measure can be a linear combination of quantitative measures. A quantitative measure may be a normalized measure.

[00143] Reference Sequence: As used herein, “reference sequence” refers to a known sequence used for purposes of comparison with experimentally determined sequences. For example, a known sequence can be an entire genome, a chromosome, or any segment thereof. A reference sequence can include at least about 20, at least about 50, at least about 100, at least about 200, at least about 250, at least about 300, at least about 350, at least about 400, at least about 450, at least about 500, at least about 1000, or more nucleotides. A reference sequence can align with a single contiguous sequence of a genome or chromosome or can include non-contiguous segments that align with different regions of a genome or chromosome. Example reference sequences, include, for example, human genome reference sequences, such as, hG19 and hG38.

[00144] Sample: As used herein, “sample” means anything capable of being analyzed by the methods and/or systems disclosed herein.

[00145] Sensitivity: As used herein, “sensitivity” means the probability of detecting the presence of a single nucleotide variant, an insertion, and a deletion at a given MAF and coverage and the probability of detecting the presence of a copy number variant at a given tumor fraction and coverage.

[00146] Sequencing: As used herein, “sequencing” refers to any of a number of technologies used to determine the sequence (e.g., the identity and order of monomer units) of a biomolecule, e.g., a nucleic acid such as DNA or RNA. Example sequencing methods include, but are not limited to, targeted sequencing, single molecule real-time sequencing, exon or exome sequencing, intron sequencing, electron microscopy-based sequencing, panel sequencing, transistor-mediated sequencing, direct sequencing, random shotgun sequencing, Sanger dideoxy termination sequencing, whole-genome sequencing, sequencing by hybridization, pyrosequencing, capillary electrophoresis, duplex sequencing, cycle sequencing, single-base extension sequencing, solid-phase sequencing, high-throughput sequencing, massively parallel signature sequencing, emulsion PCR, co-amplification at lower denaturation temperature-PCR (COLD-PCR), multiplex PCR, sequencing by reversible dye terminator, paired-end sequencing, near- term sequencing, exonuclease sequencing, sequencing by ligation, short-read sequencing, single-molecule sequencing, sequencing-by-synthesis, real-time sequencing, reverse-terminator sequencing, nanopore sequencing, 454 sequencing, Solexa Genome Analyzer sequencing, SOLiD™ sequencing, MS-PET sequencing, and a combination thereof. In some implementations, sequencing can be performer by a gene analyzer such as, for example, gene analyzers commercially available from Illumina, Inc., Pacific Biosciences, Inc., or Applied Biosystems/Thermo Fisher Scientific, among many others.

[00147] Single Nucleotide Variant: As used herein, “single nucleotide variant” or “SNV” means a mutation or variation in a single nucleotide that occurs at a specific position in the genome.

[00148] Somatic Mutation: As used herein, “somatic mutation” means a mutation in the genome that occurs after conception. Somatic mutations can occur in any cell of the body except germ cells and accordingly, are not passed on to progeny.

[00149] Specifically binds: As used herein, “specifically binds” in the context of an probe or other oligonucleotide and a target sequence means that under appropriate hybridization conditions, the oligonucleotide or probe hybridizes to its target sequence, or replicates thereof, to form a stable probe:target hybrid, while at the same time formation of stable probemon-target hybrids is minimized. Thus, a probe hybridizes to a target sequence or replicate thereof to a sufficiently greater extent than to a non-target sequence, to enable capture or detection of the target sequence. Appropriate hybridization conditions are well-known in the art, may be predicted based on sequence composition, or can be determined by using routine testing methods (see, e.g., Sambrook et al., Molecular Cloning, A Laboratory Manual, 2^nd ed. (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1989) at §§ 1.90-1.91 , 7.37-7.57, 9.47-9.51 and 11.47- 11.57, particularly §§ 9.50-9.51 , 11.12-11.13, 11.45-11.47 and 11.55-11.57, incorporated by reference herein).

[00150] Subject: As used herein, “subject” refers to an animal, such as a mammalian species (e.g., human) or avian (e.g., bird) species, or other organism, such as a plant. More specifically, a subject can be a vertebrate, e.g., a mammal such as a mouse, a primate, a simian or a human. Animals include farm animals (e.g., production cattle, dairy cattle, poultry, horses, pigs, and the like), sport animals, and companion animals (e.g., pets or support animals). A subject can be a healthy individual, an individual that has or is suspected of having a disease or a predisposition to the disease, or an individual that is in need of therapy or suspected of needing therapy. The terms “individual” or “patient” are intended to be interchangeable with “subject.”

[00151] For example, a subject can be an individual who has been diagnosed with having a cancer, is going to receive a cancer therapy, and/or has received at least one cancer therapy. The subject can be in remission of a cancer. As another example, the subject can be an individual who is diagnosed of having an autoimmune disease. As another example, the subject can be a female individual who is pregnant or who is planning on getting pregnant, who may have been diagnosed of or suspected of having a disease, e.g., a cancer, an auto-immune disease.

[00152] Target Region. As used herein, “target region” refers to a genomic locus targeted for identification and/or capture, for example, by using probes (e.g., through sequence complementarity). A Target region set” or “set of target regions" refers to a plurality of genomic loci targeted for identification and/or capture, for example, by using a set of probes (e.g., through sequence complementarity).

[00153] Threshold: As used herein, “threshold” refers to a predetermined value used to characterize experimentally determined values of the same parameter for different samples depending on their relation to the threshold.

[00154] Tumor Fraction: As used herein, “tumor fraction” refers to the estimate of the fraction of nucleic acid molecules derived from a tumor in a given sample. For example, the tumor fraction of a sample can be a measure derived from the max MAF of the sample or pattern of sequencing coverage of the sample or length of the cfDNA fragments in the sample or any other selected feature of the sample. In some instances, the tumor fraction of a sample is equal to the max MAF of the sample.

[00155] Variant: As used herein, a “variant” can be referred to as an allele. A variant is usually presented at a frequency of 50% (0.5) or 100% (1 ), depending on whether the allele is heterozygous or homozygous. For example, germline variants are inherited and usually have a frequency of 0.5 or 1. Somatic variants; however, are acquired variants and usually have a frequency of < 0.5. Major and minor alleles of a genetic locus refer to nucleic acids harboring the locus in which the locus is occupied by a nucleotide of a reference sequence, and a variant nucleotide different than the reference sequence respectively. Measurements at a locus can take the form of allelic fractions (Afs), which measure the frequency with which an allele is observed in a sample.

DETAILED DESCRIPTION

[00156] Cancer is usually caused by the accumulation of mutations within genes of an individual’s cells, at least some of which result in improperly regulated cell division. Such mutations can include single nucleotide variations (SNVs), gene fusions, insertions, transversions, translocations, and inversions. These mutations can also include copy number variations that correspond to an increase or a decrease in the number of copies of a gene within a tumor genome relative to an individual’s noncancerous cells. An extent of mutations present in cell-free nucleic acids and an amount of mutated cell-free nucleic acids of a sample can be used as biomarkers to determine tumor progression, predict patient outcome, and refine treatment choices. In various examples, the extent of mutations present in cell-free nucleic acids can be indicated by tumor cells copy number and tumor fraction for a given sample.

[00157] Additionally, cancer can be indicated by non-sequence modifications, such as methylation. Examples of methylation changes in cancer include local gains of DNA methylation in the CpG islands at the TSS of genes involved in normal growth control, DNA repair, cell cycle regulation, and/or cell differentiation. This increased amount of methylation can be associated with an aberrant loss of transcriptional capacity of involved genes and occurs at least as frequently as point mutations and deletions as a cause of altered gene expression.

[00158] Thus, DNA methylation profiling can be used to detect aberrant methylation in DNA of a sample. The DNA can correspond to certain genomic regions (“differentially methylated regions” or “DMRs”) that are normally hypermethylated or hypomethylated in a given sample type (e.g., cfDNA from the bloodstream) but which may show an abnormal degree of methylation that correlates to a neoplasm or cancer, e.g., because of unusually increased contributions of tissues to the type of sample (e.g., due to increased shedding of DNA in or around the neoplasm or cancer) and/or from extents of methylation of the genome that are altered during development or that are perturbed by disease, for example, cancer or any cancer-associated disease.

[00159] Some methods of measuring DNA methylation, can make accurately determining an amount of methylation of DNA difficult. The accuracy with which DNA methylation is determined can impact the accuracy of estimates of tumor fraction for samples. Since tumor fraction can be used to determine whether a sample is derived from a subject in which a tumor is present or not, the accuracy of determination of tumor fraction estimates can impact diagnosis and/or treatment decisions for individuals.

[00160] The methods and systems described herein are directed to accurately generating information indicating the amounts of methylation of nucleic acids using data that indicates an amount of binding of nucleic acids to methyl binding domain (MBD). In various examples, the application is directed to systems and processes to determine an estimate for tumor fraction of a sample. In one or more examples, amounts of methylation of nucleic acids can be determined based on a strength of binding by the nucleic acids to methyl binding domain (MBD). The nucleic acids can be partitioned according to the strength of binding to MBD. Additionally, a number of cytosine-guanine (CG) regions for the nucleic acids can be determined. Amounts of methylation of classification regions of the nucleic acids can be determined based on the partition information associated with the nucleic acids and the number of cytosine-guanine regions of the nucleic acids. The classification regions can have differing amounts of methylation in tumor cells and non- tumor cells. The estimate for tumor fraction of the sample can be determined according to the amounts of methylation of the classification regions.

[00161] In at least some implementations, the methods, systems, techniques, and architectures can implement models that are configured to have at least one of parameters or weights that can be modified to more accurately fit to the methylation data provided to the models. The methods, systems, techniques, and architectures are also directed to implementing a number of optimization procedures during the training of the models to generate models that more accurately predict metrics indicating the presence or absence of tumors than other systems, methods, techniques, and architectures. Further, the methods, techniques, and processes used to generate the information used to produce the methylation data reduce the amount of noise present in the methylation data that leads to more accurate predictions of metrics that indicate the presence or absence of tumors than other methods, techniques, and processes.

[00162] The processes, systems, techniques, methods, frameworks, and architectures described herein are directed to analyzing data generated from biological samples. The amounts of data derived from the biological samples and that corresponds to detectable signals related to the biological samples can be relatively small in relation to the total amount of data derived from the biological samples. Thus, it can be challenging to produce computational models that can reliably detect signals that correspond to one or more biological conditions when the amount of data derived from a sample that can be identified by the computational models as being indicative of a biological condition is relatively small. The importance of producing reliable computational models indicating the presence or absence of a biological condition is high, especially in situations where the biological condition can be detrimental to the health of a subject and/or in situations where healthcare practitioners are making treatment decisions, at least in part, based on the output of the computational models. In many instances, the training process used to produce computational models can have an impact on the accuracy and reliability of the output produced by the computational models. However, training computational models to identify features that are indicative of a biological condition from a relatively small amount of data and/or using data derived from a small number of samples can be challenging. In many typical situations, the amount of data used to train computational models is increased with the intent to increase the accuracy and reliability of the computational models. Yet, simply increasing the amount of data used to train a computational model does not guarantee that the reliability and/or accuracy of the computational model will be improved over versions of the computational model trained with less data.

[00163] At least a portion of the implementations described herein are directed to training computational models using data derived from a relatively small number of biological samples and/or using data with a relatively small proportion that indicates features of the presence of a biological condition within a subject. In various examples, the implementations described herein are directed to identifying one or more subsets of training data from amongst the total data derived from biological samples to produce a computational model that can provide accurate and reliable results indicating the presence or absence of a biological condition within a subject. In one or more examples, training data can be obtained that includes training sequencing reads derived from a plurality of samples of a first plurality of subjects in which a tumor is detected. In at least some examples, the training sequencing reads can correspond to molecules derived from the samples that have at least a threshold amount of methylation in one or more genomic regions. The threshold amount of methylation can correspond to methylated cytosines. Additionally, the training process can use a first computational model and the training data to determine individual values of a quantitative measure for individual samples of the plurality of samples. In one or more illustrative examples, the quantitative measure can indicate an amount of mutant alleles present in nucleic acids derived from the individual samples. For example, the quantitative measure can correlate with the number of mutant alleles present if a mutation is present. In one or more additional illustrative examples, the quantitative measure can include mutant allele fraction. In one or more further illustrative examples, the quantitative measure can indicate a tumor fraction for an individual sample. In some embodiments, the quantitative measure indicating the tumor fraction can be determined via epigenetic analysis like methylation analysis and/or fragmentation pattern analysis or via somatic variant analysis (e..g. maximum mutant allele fraction can be used to indicate the tumor fraction). A subset of the training samples can be determined that have values of the quantitative measure within a specified range of values. An additional group of training samples can be determined that includes samples from the subset of training samples having nucleic acid molecules with one or more somatic mutations present. Further, another group of training samples can be determined from a different group of subjects in which a tumor is not detected. A second computational model can be trained using training data derived from the three groups of training samples. After the training process, the second computational model can be implemented to determine an indication of cancer being present in test subjects.

[00164] In this way, the implementations described herein identify specific datasets from among a larger dataset that are used to train a machine learning classification model. At least a portion of the training datasets are determined based on values of a quantitative measure generated by a different machine learning model that are included in a particular band or range. In various examples, the band or range of quantitative measure values used to determine at least a portion of the training data for the second, machine learning classification model can be based on a biological condition, such as one or more types of cancer being detected. The use of the specific training datasets described in implementations herein to train the machine learning classification model produces a model that is more reliable and provides more accurate results than computational models that are not trained according to implementations described herein. Additionally, because the training of the machine learning classification model is performed using less training data than previously implemented processes, the amount of processing resources and memory resources used to produce the machine learning classification model is less than the previously implemented training processes.

[00165] Figure 1 is a diagrammatic representation of an example environment 100 that identifies nucleic acids that correspond to classification regions of a reference sequence, where the classification regions have at least a threshold number of CpGs, according to one or more implementations. In one or more examples, the disease under consideration is a type of cancer. Non-limiting examples of such cancers include biliary tract cancer, bladder cancer, transitional cell carcinoma, urothelial carcinoma, brain cancer, gliomas, astrocytomas, breast carcinoma, metaplastic carcinoma, cervical cancer, cervical squamous cell carcinoma, rectal cancer, colorectal carcinoma, colon cancer, hereditary nonpolyposis colorectal cancer, colorectal adenocarcinomas, gastrointestinal stromal tumors (GISTs), endometrial carcinoma, endometrial stromal sarcomas, esophageal cancer, esophageal squamous cell carcinoma, esophageal adenocarcinoma, ocular melanoma, uveal melanoma, gallbladder carcinomas, gallbladder adenocarcinoma, renal cell carcinoma, clear cell renal cell carcinoma, transitional cell carcinoma, urothelial carcinomas, Wilms tumor, leukemia, acute lymphocytic leukemia (ALL), acute myeloid leukemia (AML), chronic lymphocytic (CLL), chronic myeloid (CML), chronic myelomonocytic (CMML), liver cancer, liver carcinoma, hepatoma, hepatocellular carcinoma, cholangiocarcinoma, hepatoblastoma, Lung cancer, non-small cell lung cancer (NSCLC), mesothelioma, B-cell lymphomas, non- Hodgkin lymphoma, diffuse large B-cell lymphoma, Mantle cell lymphoma, T cell lymphomas, non-Hodgkin lymphoma, precursor T-lymphoblastic lymphoma/leukemia, peripheral T cell lymphomas, multiple myeloma, nasopharyngeal carcinoma (NPC), neuroblastoma, oropharyngeal cancer, oral cavity squamous cell carcinomas, osteosarcoma, ovarian carcinoma, pancreatic cancer, pancreatic ductal adenocarcinoma, pseudopapillary neoplasms, acinar cell carcinomas. Prostate cancer, prostate adenocarcinoma, skin cancer, melanoma, malignant melanoma, cutaneous melanoma, small intestine carcinomas, stomach cancer, gastric carcinoma, gastrointestinal stromal tumor (GIST), uterine cancer, or uterine sarcoma.

[00166] The environment 100 can include a sample 102. The sample 102 can be derived from a biological fluid obtained from a subject. For example, the sample 102 can be derived from blood obtained from a subject. In one or more additional examples, the sample 102 can be derived from tissue of a subject. In various examples, the sample 102 can be derived from multiple sources. To illustrate, the sample 102 can be derived from one or more fluids of a subject and/or from tissue of a subject. In one or more illustrative examples, the subject can be a mammal. In one or more additional illustrative examples, the subject can be a human. In one or more further illustrative examples, the subject can be a non-human mammal.

[00167] The sample 102 can include a number of nucleic acids 104. Individual nucleic acids 104 can include a number of regions that have at least a threshold number of cytosine molecules and guanine molecules. In one or more examples, individual nucleic acids 104 can include regions having at least a threshold number of cytosine- guanine dinucleotides. In various examples, at least a portion of the cytosine-guanine pairs included in the regions can be sequentially located in sequences of the nucleic acids 104. In one or more illustrative examples, a region of a nucleic acid having at least a threshold amount of cytosine-guanine pairs can be referred to herein as a “CG region” or a “CpG region.” In one or more examples, a CG region can include at least 200 CpG dinucleotides. In one or more illustrative examples, a CG region can include from 200 CpG dinucleotides to 5000 CpG dinucleotides, from 300 CpG dinucleotides to 3000 CpG dinucleotides, from 200 CpG dinucleotides to 2500 CpG dinucleotides, or from 500 CpG dinucleotides to 1500 CpG dinucleotides. Additionally, a CG region can have a GC percentage of at least 50% and an observed-to-expected CpG ratio of at least 60%. The observed-to-expected CpG ratio can be calculated where the observed CpG is the number of CpGs identified in a given genomic region and the expected CpGs is the number of cytosines multiplied by the number of guanines divided by the number of bases in the genomic region. The expected CpGs can also be calculated by:

((number of cytosines + number of guanines)/2)²/length of genomic region.

For example, a CG region can be determined using the techniques described by Gardiner-Garden M, Frommer M (1987). "CpG islands in vertebrate genomes". Journal of Molecular Biology. 196 (2): 261-282. and/or Saxonov S, Berg P, Brutlag DL (2006). "A genome-wide analysis of CpG dinucleotides in the human genome distinguishes two distinct classes of promoters". Proc Natl Acad Sci USA. 103 (5): 1412-1417.

[00168] In the illustrative example of Figure 1 , a portion of a sequence of an example nucleic acid 104 can include a first CG region 106, a second CG region 108, and a third CG region 110. Although the illustrative example of Figure 1 illustrates a portion of a sequence of a nucleic acid 104 having three CG regions, nucleic acids 104 included in the sample 102 can have a different number of CG regions. For example, individual nucleic acids 104 included in the sample 102 can include at least 1 CG region, at least 5 CG regions, at least 10 CG regions, at least 25 CG regions, at least 50 CG regions, at least 100 CG regions, at least 250 CG regions, at least 500 CG regions, or at least 1000 CG regions.

[00169] Individual CG regions can correspond to a number of molecules with one or more methylated cytosines. In the illustrative example of Figure 1 , the CG region 106 can include a molecule with a methylated cytosine 112. In the illustrative example of Figure 1 , the molecule with a methylated cytosine 112 is 5-methylcytosine. Individual CG regions can also correspond to a number of molecules with an unmethylated cytosine. For example, the CG region 106 can include a molecule with an unmethylated cytosine 116. In various examples, at least a portion of the CG regions of a nucleic acid 104 can correspond to classification regions of a reference genome. Classification regions can correspond to genomic regions of a reference genome that correspond to non-sequence differences that are consistent with one or more biological conditions, such as one or more types of cancer. In at least some examples, the non-sequence differences can include one or more mutations that are consistent with one or more biological conditions. In one or more examples, a classification region can correspond to a genomic region of the reference sequence for which molecules derived from subjects having at least one form of cancer. In at least some examples, nucleic acid molecules having at least a threshold amount of methylated cytosines in at least one CG region (e.g., hypermethylated molecules) can be derived from subjects in which cancer is present and correspond to a classification. In one or more additional examples, nucleic acid molecules having less than a threshold amount of methylated cytosines (e.g., hypomethylated molecules) in at least one CG region can be derived from subjects in which cancer is present and correspond to a classification region.

[00170] In addition to the classification regions, the CG regions can include one or more positive control regions, such as positive control region 118. The positive control region 108 can be mapped to nucleic acid molecules having at least a threshold number of methylated cytosine molecules in at least one CG region and that are derived from subjects that are free of cancer and are derived from subjects in which cancer is present. In various examples, the positive control region 106 can be hypermethylated in cells derived from subjects that are free of cancer and also in cells derived from subjects in which cancer is present. The CG regions can also include one or more negative control regions, such as negative control region 120. The negative control region 120 can be mapped to nucleic acid molecules having less than a threshold number of methylated cytosine molecules in at least one CG region and that are derived from subjects that are free of cancer and also subjects in which cancer is present. In one or more illustrative examples, the negative control region 120 can be hypomethylated in subjects that are free of cancer and also in subjects in which cancer is present. In various examples, the positive control regions and the negative control regions can be used to perform normalization calculations. The normalization calculations can be performed to generate input data for one or more models that are implemented to determine tumor metrics for a given sample 102.

[00171] A first molecule separation process 122 can be performed. The first molecule separation process 122 can separate nucleic acids 104 included in the sample 102 based on an amount of methylated cytosines of the individual nucleic acids 104. In one or more examples, the first molecule separation process can separate nucleic acids 104 included in the sample 102 based on amounts of methylated cytosines included in CG regions of individual nucleic acids 104. In various examples, the first molecule separation process 122 can separate the nucleic acids 104 into a plurality of groups with individual groups corresponding to respective amounts of methylated cytosines of the nucleic acids 104.

[00172] In the illustrative example of Figure 1 , the first molecule separation process 122 can be performed in relation to a first methylation threshold 124. Performing the first molecule separation process 122 with regard to the first methylation threshold 124 can produce a first partition of nucleic acids 126. In one or more examples, the first methylation threshold 124 can indicate a first threshold number of molecules with a methylated cytosine located in CG regions of the nucleic acids 104. The first molecule separation process 122 can identify a number of nucleic acids 104 having fewer molecules with a methylated cytosine in CG regions than the first methylation threshold 124. In various examples, the first methylation threshold 124 can correspond to a first methylation rate.

[00173] The first molecule separation process 122 can also be performed with respect to a second methylation threshold 128. The second methylation threshold 128 can indicate an amount of methylated cytosines in one or more genomic regions of the nucleic acids 104 that is greater than the amount of methylated cytosines in the one or more regions corresponding to the first methylation threshold 124. The second methylation threshold 124 can indicate a number of molecules with a methylated cytosine per a number of nucleic acids. In one or more additional examples, the second methylation threshold 124 can correspond to a rate of methylation of nucleic acids that is greater than the rate of methylation that corresponds to the first methylation threshold 124. Performing the first molecule separation process 122 with respect to the second methylation threshold 128 can produce a second partition of nucleic acids 130. In one or more examples, the first molecule separation process 122 can identify nucleic acids 104 having a greater amount of methylated cytosines than the first methylation threshold 124 and having a lower amount of methylated cytosines than the second methylation threshold 128 to produce the second partition of nucleic acids 130. [00174] Additionally, the first molecule separation process 122 can also be performed with respect to a third methylation threshold 132. The third methylation threshold 132 can indicate an amount of methylated cytosines in one or more genomic regions of the nucleic acids 104 that is greater than the amount of methylated cytosines in the one or more regions corresponding to the first methylation threshold 124 and greater than the amount of methylated cytosines in the one or more regions corresponding to the second methylation threshold 128. The third methylation threshold 132 can indicate a number of molecules with a methylated cytosine per a number of nucleic acids. In one or more additional examples, the third methylation threshold 132 can correspond to a rate of methylated cytosines that is greater than the rate of methylation that corresponds to the first methylation threshold 124 and greater than the rate of methylation that corresponds to the second methylation threshold 128. Performing the first molecule separation process 122 with respect to the third methylation threshold 132 can produce a third partition of nucleic acids 134. In one or more examples, the first molecule separation process 122 can identify nucleic acids 104 having a greater amount of methylated cytosines than nucleic acids 104 included in the second partition of nucleic acids 128. In this way, the amount of methylated cytosines of nucleic acids included in the first partition 122, the second partition 126, and the third partition 130 increases from the first partition 122 to the second partition 126 and increases from the second partition 126 to the third partition 130. In one or more illustrative examples, the first partition of nucleic acids 126 can be referred to as a hypomethylation partition, the second partition of nucleic acids 130 can be referred to as an intermediate partition, and the third partition of nucleic acids 134 can be referred to as a hypermethylation partition.

[00175] In one or more examples, the amount of methylated cytosines of nucleic acids can correspond to a strength of binding to methyl binding domain (MBD). In these scenarios, the first partition 126, the second partition 130, and the third partition 134 can be produced based on different strengths of binding to MBD for nucleotides having different amounts of methylated cytosines. In one or more examples, the first molecule separation process 122 can include a series of washes where the nucleic acids 104 are contacted with solutions having different concentrations of sodium chloride (NaCI). [00176] Partitioning of the nucleic acids can be performed by contacting the nucleic acids with a modified nucleotide specific binding reagent, such as a MBD of a MBP. A modified nucleotide specific binding reagent can bind to 5-methylcytosine (5mC). The modified nucleotide specific binding reagent, such as a MBD, can be coupled to paramagnetic beads, such as Dynabeads® M-280 Streptavidin via a biotin linker. Partitioning into fractions with different extents of methylation can be performed by increasing the NaCI concentration in a series of washes. The sequences eluted from the modified nucleotide specific binding reagent are partitioned into two or more fractions (e.g., hypo, hyper) depending on which wash (e.g., NaCI concentration) eluted the sequences. Resulting partitions can include one or more of the following nucleic acid forms: double-stranded DNA (dsDNA), shorter DNA fragments and longer DNA fragments.

[00177] The binding of the nucleic acids with the modified nucleotide specific binding reagent can be a function of number of methylated (or modified) sites per molecule, with molecules having more methylation eluting under increased salt concentrations. To elute the DNA into distinct populations based on the extent of methylation, one can use a series of elution buffers of increasing NaCI concentration. Salt concentrations can, in one or more implementations, range from about 100 nM to about 2500 mM NaCI. In various implementations, the process results in three (3) partitions. Molecules are contacted with a solution at a first salt concentration and comprising a molecule comprising a methyl binding domain, which molecule can be attached to a capture moiety, such as streptavidin. At the first salt concentration a population of molecules will bind to the MBD and a population will remain unbound. The unbound population can be separated as a “hypomethylated” population (hypo partition). For example, the first partition 126 can be representative of the hypomethylated form of DNA is that which remains unbound at a low salt concentration. In one or more illustrative examples, the concentration of NaCI of the solution used to produce the first partition 126 can be about 100 nM, about 120 nM, about 140 nM, about 160 nM, about 180 nM, about 200 nM. or about 250 nM. The second partition 130 can be referred to as a “residual partition” or an “intermediate partition” and can be representative of intermediate methylated DNA is eluted using an intermediate salt concentration, e.g., between 100 mM and 2000 mM concentration. In one or more additional illustrative examples, the concentration of NaCI of the solution used to produce the second partition 130 can be from about 100 mM to about 500mM, from about 100 mM to about 1000 mM, from about 100 mM to about 1500 mM, from about 250 mM to about 1000 mM, from about 250 mM to about 1500 mM, from about 500 mM to about 1500 mM, from about 250 mM to about 2000 mM, from about 500 mM to about 2000 mM, or from about 1000 mM to about 2000mM. This is also separated from the sample. The third partition 134 can be representative of hypermethylated form of DNA (hyper partition) and is eluted using a high salt concentration, e.g., at least about 2000 mM. In one or more further illustrative examples, the concentration of NaCI of the solution used to produce the third partition 134 can be from about 2000 mM to about 5000 mM, from about 2000 mM to about 4000 mM, from about 2000 mM to about 3500 mM, from about 2000 mM to about 3000 mM, or from about 2500 mM to about 4000 mM.

[00178] In various examples, the first partition 126 can correspond to a first range of binding strengths of nucleic acids to MBD and to a first range of methylated CG regions and the second partition 130 can correspond to a second range of binding strengths of nucleic acids to MBD and to a second range of methylated CG regions. The first range of binding strengths can be less than the second range of binding strengths. In one or more scenarios, a first solution having a first NaCI concentration can separate a first group of nucleic acids having the first range of binding strengths from MBD and a second solution having a second NaCI concentration can separate a second group of nucleic acids having the second range of binding strengths from MBD with the second NaCI concentration being greater than the first NaCI concentration. Additionally, the third partition 134 can correspond to a third range of binding strengths and a third range of methylated CG regions. The third range of binding strengths can be greater than the first range of binding strengths and the second range of binding strengths. In one or more instances, a third solution having a third NaCI concentration can separate a third group of nucleic acids having the third range of binding strengths from NaCI. The third NaCI concentration can be greater than the first NaCI concentration and the second NaCI concentration.

[00179] In one or more illustrative examples, a plurality of nucleic acids derived from at least one of blood or tissue of a subject can be combined with a solution including an amount of MBD to produce a nucleic acid-MBD solution. A first wash of the nucleic acid- MBD solution can be performed with a first solution including a first NaCI concentration to produce a first nucleic acid fraction and a first residual solution. The first nucleic acid fraction can include a first portion of the plurality of nucleic acids and the first residual solution can include a second portion of the plurality of nucleic acids. In one or more examples, the first portion of the plurality of nucleic acids can have a first range of binding strengths to MBD that are less than a second range of binding strengths to MBD of the second portion of the plurality of nucleic acids.

[00180] Additionally, a second wash of the first residual solution can be performed with a second solution including a second concentration of NaCI that is greater than the first concentration of NaCI to produce a second nucleic acid fraction and a second residual solution. The second nucleic acid fraction can include a first subset of the second portion of the plurality of nucleic acids and the second residual solution can include a second subset of the second portion of the plurality of nucleic acids. The first subset of the second portion of the plurality of nucleic acids can have a third range of binding strengths to MBD that are less than a fourth range of binding strengths to MBD of the second subset of the second portion of the plurality of nucleic acids. Further, a third wash of the second residual solution can be performed with a third solution including a third concentration of NaCI that is greater than the second concentration of NaCI to produce a third nucleic acid fraction that includes the second subset of the second portion of the plurality of nucleic acids.

[00181] Subsequent to the first wash, the second wash, and the third wash a determination can be made that the first portion of the plurality of nucleic acids are associated with the first partition 126. The first portion of the plurality of nucleic acids can be attached with molecular barcodes from a first set of molecular barcodes indicating the first partition 126. In this way, a sequencing read that corresponds to the first partition 126 can be identified based on determining that the sequencing read includes the first molecular barcode. In addition, a determination can be made that the first subset of the second portion of the plurality of nucleic acids is associated with an additional partition of the plurality of partitions. In these situations, a second set of molecular barcodes different from the first set of molecular barcodes can be attached to the second portion of the plurality of nucleic acids with the second molecular barcode indicating the additional partition. As a result, a sequencing read that corresponds to the additional partition can be identified based on determining that the sequencing read includes one or more molecular barcodes from among the second set of molecular barcodes. Further, a determination can be made that the second subset of the second portion of the plurality of nucleic acids is associated with the second partition 130. A third set of molecular barcodes different from the first set of molecular barcodes and the second set of molecular barcodes can then be attached to the second subset of the second portion of the plurality of nucleic acids where the third set of molecular barcodes indicate the second partition 130. In these instances, a sequencing read that corresponds to the second partition 130 can be identified based on determining that the sequencing read includes a third molecular barcode from among the third set of molecular barcodes.

[00182] In at least some examples, the first molecule separation process 122 can result in nucleic acids being present in at least one of the first partition 126, the second partition 130, or the third partition 134 having an amount of methylation that is different from the amount of methylation of the other nucleic acids in the respective partition. For example, the first partition 126 can include a number of nucleic acids having amounts of methylation that correspond to the amounts of methylation of nucleic acids included in at least one of the second partition 130 or the third partition 134. Additionally, at least one of the second partition 130 or the third partition 134 can include nucleic acids having amounts of methylation that correspond to the amounts of methylation of nucleic acids included in the first partition 126. The presence of nucleic acids in at least one of the first partition 126, the second partition 130, or the third partition 134 that do not correspond to the amounts of methylation of at least a majority of the other nucleic acids included in the respective partition can cause data noise when performing computational operations with respect to sequence reads produced from nucleic acids included in the first partition 126, the second partition 130, and the third partition 134. The data noise can result in inaccuracies with respect to calculations made based on sequence reads derived from nucleic acids included in the first partition 126, the second partition 130, and the third partition 134.

[00183] To reduce or eliminate data noise associated with nucleic acids being present in at least one of the first partition 126, the second partition 130, or the third partition 134 that have amounts of methylation that are not consistent with the amounts of methylation of at least a majority of other molecules included in the respective partitions, a second molecule separation process 136 can be performed after the first molecule separation process 122. The second molecule separation process 136 can be performed with respect to nucleic acids included in the first partition 126, nucleic acids included in the second partition 130, and nucleic acids included in the third partition 134. In one or more examples, the second molecule separation process 136 can include performing digestion of the nucleic acids included in the first partition 126 using methylation dependent restriction enzyme (MDRE) and nucleic acids included in the second partition 130 and the third partition 134 can be digested using methylation sensitive restriction enzyme (MSRE). Digestion of the nucleic acids included in the first partition 126 with MDRE can result in separation of nucleic acids included in the first partition having amounts of methylation corresponding to the second partition 130 and the third partition 134 from nucleic acids having amounts of methylation corresponding to the first partition. Additionally, digestion of nucleic acids included in the second partition 130, and the third partition 134 with MSRE can result in separation of the nucleic acids having amounts of methylation corresponding to the first partition 126 from the nucleic acids of the second partition 130 and the nucleic acids of the third partition 134. By removing nucleic acids from the first partition 126 having amounts of methylation that correspond to the second partition 130 and the third partition 134 and by removing nucleic acids from the second partition 130 and the third partition 134 that have amounts of methylation that correspond to the first partition 126, an additional group of nucleic acids 138 can be produced. The additional group of nucleic acids 138 can include nucleic acids corresponding to methylation amounts of the second partition 130 and the third partition 134 with a minimal amount or no nucleic acids having amounts of methylation corresponding to the first partition 126. For example, less than 50% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 50% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 60% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 70% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 90% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 95% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 97% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 99% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 99.5% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, or at least 99.9% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134.

[00184] The architecture 100 can include a sequencing machine 140. In one or more examples, the sequencing machine 140 can be any of a number of sequencing machines that can perform one or more sequencing operations that amplify nucleic acids present in a sample 104. In various examples, the sequencing machine 140 can perform next- generation sequencing operations. In one or more examples, the sample 104 can include an amount of at least one bodily fluid extracted from a subject. In one or more additional examples, the sample 104 can include a tissue sample that is obtained from a subject.

[00185] In one or more examples, prior to sequencing, the extracted polynucleotides can be partitioned into two or more partitions based on the binding strength of the of binding strengths of polynucleotides to MBD. A blunt-end ligation can be performed on the partitioned polynucleotides and adapters, as well as tags (e.g., molecular barcodes) can be added to the partitioned polynucleotides. The tagged polynucleotides in the one or more partitions (e.g., hyper and/or intermediate partitions) can be treated with one or more methylation sensitive restriction enzymes (MSREs). In some examples, the hypo partition can be treated with one or more methylated dependent restriction enzymes (MDREs). Post the MSRE and/or MDRE treatment, the molecules can also be enriched by causing hybridization between the extracted polynucleotides and probes that correspond to target regions of a reference sequence. The enrichment process can identify thousands, hundreds of thousands, up to millions of polynucleotides that correspond to on-target regions associated with the probes.

[00186] Subsequent and/or prior to the enrichment process, the molecules can be amplified according to one or more amplification processes. The one or more amplification processes can produce thousands, up to millions of copies of individual nucleic acid molecules. In one or more examples, a portion of the unenriched polynucleotides can be amplified, in some instances, but not to the extent that the enriched polynucleotides are amplified. The one or more amplification processes can generate an amplification product that undergoes one or more sequencing operations. After performing one or more sequencing operations with respect to the sample 104, the sequencing machine 140 can produce a sequencing data 142.

[00187] The sequencing data 142 can include alphanumeric representations of the nucleic acids included in an amplification product. For example, the sequencing data 142 can include, for individual nucleic acids of the amplification product, data that corresponds to a string of letters that represent the respective chains of nucleotides that correspond to the individual nucleic acids.

[00188] The sequencing data 142 can be stored in one or more data files. For example, the sequencing data 142 can be stored in a FASTQ file that comprises a text- based sequencing data file format storing raw sequence data and quality scores. In one or more additional examples, the sequencing data 142 can be stored in a data file according to a binary base call (BCL) sequence file format. In one or more further examples, the sequencing data 142 can be stored in a BAM file. In one or more examples, the sequencing data 142 can comprise at least about one gigabyte (GB), at least about 2 GB, at least about 3GB, at least about 4 GB, at least about 5 GB, at least about 8 GB, or at least about 10 GB. An individual sequence representation included in the sequencing data 106 can be referred to herein as a “read” or a “sequencing read.” In various examples, individual first nucleic acids included in the pool 138 can correspond to multiple sequence representations included in the sequencing data 142 as a result of the amplification of the individual first nucleic acids. In one or more additional examples, individual second nucleic acids included in the pool 138 can correspond to a single sequence representation included in the sequencing data 142 as a result of the absence of amplification of the individual second nucleic acids.

[00189] FIG. 2 is an example architecture 200 to analyze sequencing data to determine one or more metrics indicating the presence of a tumor in subjects, in accordance with one or more implementations. The architecture 200 can include one or more sequencing machines 202 that perform one or more sequencing operations with respect to a number of samples 204. The one or more samples 204 can be obtained from subjects 206. In one or more illustrative examples, a first portion of the subjects 206 can be free of cancer. That is, a tumor is not detected in the first portion of the subjects 206. Additionally, a tumor can be present in a second portion of the subjects 206.

[00190] One or more molecule separation processes 208 can be performed with respect to the samples 204. The one or more separation processes 208 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and/or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[00191] Prior to the one or more molecule separation processes 208, nucleic acid molecules can be extracted from a sample 204. In one or more implementations, the nucleic acid molecules comprise cell-free nucleic acids (e.g., cell-free DNA). In various implementations, the sample 204 can be a sample selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, combinations thereof, and/or the like. In one or more additional examples, the sample 204 can comprise a sample selected from one or more of whole blood, a blood fraction, a tissue biopsy, pleural fluid, pericardial fluid, cerebrospinal fluid, and peritoneal fluid. In one or more illustrative examples, the cell-free nucleic acid molecules can be extracted from the sample 204 where the sample 204 is obtained from a subject 206 known to have cancer (e.g., a cancer patient), or a subject 206 suspected of having cancer.

[00192] The extraction of nucleic acid molecules from the sample 204 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the sample 204 and applying one or more proteases to break down proteins included in the sample 204. The extraction of nucleic acid molecules from the sample 204 can also include a number of washing and/or elution techniques to separate the nucleic acid molecules from other components included in the sample 204. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from the sample 204 prior to being subjected to the one or more separation processes 208.

[00193] The nucleic acid molecules extracted from samples 204 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5- methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation processes 208 can separate nucleic acid molecules extracted from samples 204 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation processes 208 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the one or more molecule separation processes 208 can include the first molecule separation process 122 and the second molecule separation process 136 of Figure 1.

[00194] The one or more molecule separation processes 208 can produce a pool 210 that includes a portion of the nucleic acid molecules extracted from one or more samples 204 and subjected to the one or more molecule separation processes 208. For example, the pool 210 can include a number of nucleic acid molecules having the second levels of methylation and a number of nucleic acid molecules having the third levels of methylation. Thus, the nucleic acid molecules included in the pool 210 can have at least a threshold amount of methylation. In one or more illustrative examples, the nucleic acid molecules included in the pool 210 can have at least a threshold amount of methylation in CG regions of the nucleic acid molecules.

[00195] The one or more sequencing machines 202 can perform one or more sequencing operations to produce sequencing data 212 that corresponds to the pool 210. The architecture 200 can include a computing system 214 that obtains the sequencing data 212 from the one or more sequencing machines 202 and analyzes the sequencing data 212. For example, the computing system 214 can analyze the sequencing data 212 to determine one or more metrics indicating that a tumor may be present in a subject 206 that provided at least one sample 204. The computing system 214 can include one or more computing devices 216. The one or more computing devices 216 can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices 216 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 214 and the sequencing machine 202 can be owned, operated, maintained, and/or controlled by a single organization. In one or more additional examples, the computing system 214 and the sequencing machine 202 can be owned, operated, maintained, and/or controlled by multiple organizations.

[00196] At operation 218, the computing system 214 can analyze the sequencing data 212. Analyzing the sequencing data 212 can include determining one or more first sequence representations 220 included in the sequencing data 212 that correspond to one or more classification regions of a reference sequence. The one or more classification regions can correspond to genomic regions of a reference sequence that are mapped to nucleic acid molecules having an amount of methylation in cfDNA obtained from subjects in which cancer is present relative to an amount of methylation of the molecules that map to the same genomic regions of the reference sequence in cfDNA obtained from subjects in which a tumor is not present. In at least some examples, the amount of methylation present in nucleic acid molecules that map to a classification region and are derived from subjects in which cancer is present is less than the amount of methylation present in nucleic acid molecules that map to the classification region and are derived from subjects in which cancer is not present. In one or more additional examples, the amount of methylation present in nucleic acid molecules that map to a classification region and are derived from subjects in which cancer is present is greater than the amount of methylation present in nucleic acid molecules that map to the classification region and are derived from subjects in which cancer is not present. The one or more classification regions can also include at least a threshold amount of cytosine-guanine content. In various examples, the one or more classification regions can include a series of cytosine-guanine (CG) pairs in the 5’— >3’ direction (CpG sites), such as at least 3 CpG sites, at least 5 CpG sites, at least 8 CpG sites, at least 10 CpG sites, at least 12 CpG sites, at least 15 CpG sites, at least 18 CpG sites, or at least 20 CpG sites.

[00197] In addition, the computing system 214 can analyze the sequencing data 212 to determine one or more second sequence representations 222 that correspond to one or more control regions of a reference sequence. The one or more control regions can include one or more positive control regions and/or one or more negative control regions. In various examples, a positive control region can comprise a genomic region of a reference sequence having at least a threshold amount of molecules with a methylated cytosine and including at least a threshold number of CpG sites. A positive control region can correspond to nucleic acid molecules having at least a threshold amount of methylation in one or more CG regions and that are obtained from subjects in which cancer is present and in samples obtained from subjects in which a tumor is not present. In at least some examples, the threshold amount of methylation can correspond to at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 15 or more CpGs being methylated in nucleic acid molecules. In one or more illustrative examples, positive control regions can be mapped to nucleic acid molecules that are hypermethylated in one or more CG regions and are derived from samples obtained from both subjects in which cancer is present and subjects in which cancer is not present. In one or more examples, a negative control region can comprise a genomic region of a reference sequence having less than a threshold amount of molecules with a methylated cytosine and at least a threshold number of CpG sites. A negative control region can correspond to nucleic acid molecules having less than an additional threshold amount of methylation in one or more CG regions and that are obtained from subject in which cancer is present and in samples obtained from subjects in which a tumor is not present. In various examples, the additional threshold amount of methylation can correspond to no greater than 1, no greater than 2, no greater than 3, no greater than 4, no greater than 5, no greater than 6, or no greater than 7 CpGs being methylated in nucleic acid molecules. In one or more additional illustrative examples, negative control regions can be mapped to nucleic acid molecules that are hypomethylated in one or more CG regions and are derived from samples obtained from both subjects in which cancer is present and subjects in which cancer is not present.

[00198] In one or more illustrative examples, the first sequence representations 220 can be determined by aligning sequence representations included in the sequencing data 212 with one or more classification regions of a reference sequence. In addition, the second sequence representations 222 can be determined by aligning sequence representations included in the sequencing data 212 with one or more control regions of a reference sequence. The alignment process can identify the first sequence representations 220 by determining a number of sequence representations included in the sequencing data 212 that correspond to one or more classification regions of the reference sequence. Further, the alignment process can identify the second sequence representations 222 by determining a number of sequence representations that correspond to one or more control regions of the reference sequence.

[00199] In one or more illustrative examples, the alignment process can determine an amount of homology between individual sequence representations included in the sequence data 212 and portions of the reference sequence. The amount of homology between a given sequence representation and the reference sequence can indicate a number of positions of the reference sequence that have the same nucleotide as corresponding positions of the given sequence representation. The computing system 214 can determine that a sequence representation is aligned with a portion of a reference sequence based on determining that the sequence representation and the portion of the reference sequence have at least a threshold amount of homology. In scenarios where a sequence representation has at least the threshold amount of homology with respect to multiple portions of the reference sequence, the portion of the reference sequence having the greatest amount of homology with the sequence representation can be determined to be aligned with the sequence representation.

[00200] The amount of homology between a given sequence representation and a portion of a reference sequence can be determined using BLAST programs (basic local alignment search tools) and PowerBLAST programs (Altschul et al., J. Mol. Biol., 1990, 215, 403-410; Zhang and Madden, Genome Res., 1997, 7, 649-656) or by using the Gap program (Wisconsin Sequence Analysis Package, Genetics Computer Group, University Research Park, Madison Wis.), using default settings, which uses the algorithm of Needleman and Wunsch (J. Mol. Biol. 48; 443-453 (1970)).The amount of homology between a sequence representation and a portion of the reference sequence can also be determined using a Burrows-Wheeler aligner (Li, H., & Durbin, R. (2009). Fast and accurate short read alignment with Burrows-Wheeler transform. Bioinformatics, 25(14), 1754-1760).

[00201] In one or more examples, after the sequence representations included in the sequencing data 212 have been aligned with a reference sequence, the aligned sequence representations can be analyzed to identify one or more groups of sequence representations. For example, individual aligned sequence representations can correspond to individual sequencing reads that are included in the sequencing data 212. In these scenarios, the aligned sequence representations can include multiple reads that correspond to a single nucleic acid molecule included in the sample pool 210. In one or more additional examples, the aligned sequence representations can correspond to individual nucleic acid molecules included in the pool 210. In these situations, the computing system can determine a group of reads included in the sequence data 212 that correspond to an individual nucleic acid molecule included in the pool 210 based on molecular barcodes that are common to each group of sequencing reads. That is, individual nucleic acid molecules included in the pool 210 can be encoded with molecular barcodes that uniquely identify the individual nucleic acid molecules and, in at least some cases, the individual nucleic acid molecules can be represented by multiple sequencing reads included in the sequencing data 212. Accordingly, when multiple sequence representations are present in the sequencing data 212 that correspond to a single nucleic acid molecule included in the pool 210, the computing system 214 can group the multiple sequence representations together. In various examples, the groups of sequence representations that correspond to a single nucleic acid molecule included in the pool 210 can be referred to herein as “families.” Additionally, start and stop positions with respect to the reference sequence of the aligned sequence representations having a common molecular barcode can be used to group the sequence representations that correspond to individual nucleic acids included in the pool 210. In one or more illustrative examples, an individual sequence representation that represents a family of sequence representations that corresponds to a single nucleic acid molecule included in the pool 210 can be referred to herein as a “consensus sequence representation.”

[00202] At operation 224, the computing system 214 can analyze the first sequence representations and the second sequence representations 222 to generate metrics that correspond to individual classification regions. In the illustrative example of Figure 2, the computing system 214 can analyze the first sequence representations 220 and the second sequence representations 222 to generate classification region metrics 226. The classification region metrics 226 can include quantitative measures determined based on a number of first sequence representations 220 having at least a threshold amount of methylated cytosines. In one or more illustrative examples, the classification region metrics 226 can include quantitative measures determined based on a number of sequencing reads corresponding to a number of the first sequence representations 220 having at least a threshold amount of methylated cytosines located. In one or more additional illustrative examples, the classification region metrics 226 can include quantitative measures determined based on a number of nucleic acid molecules that correspond to a number of the first sequence representations 220. In various examples, the classification region metrics 226 can include quantitative measures determined based on a number of first sequence representations 220 having at least a threshold amount of methylated cytosines and a number of second sequence representations 222 that correspond to control regions of a reference sequence. In one or more further illustrative examples, the classification region metrics 226 can include quantitative measures related to a ratio of a number of first sequence representations 220 having at least a threshold amount of methylated cytosines in relation to a number of second sequence representations. In at least some examples, the sequence representations of the second sequence representations 222 used by the computing system 214 to generate quantitative measures included in the classification region metrics 226 can include sequence representations that correspond to positive control regions of a reference sequence.

[00203] The classification region metrics 226 can also be determined by performing one or more normalization operations with respect to quantitative measures generated by the computing system 214 using at least one of the first sequence representations 220 and the second sequence representations 222. For example, a logarithm calculation can be performed with respect to quantitative measures generated by the computing system 214 using at least one of the first sequence representations 220 or the second sequence representations 222. Additionally, the classification region metrics 226 can be determined by adding a pseudocount to quantitative measures determined by the computing system 214 using at least one of the first sequence representations 220 or the second sequence representations 222. In one or more illustrative examples, the one or more normalization operations can include determining quantitative measures that correspond to a ratio of first sequence representations 220 for an individual classification region with respect to a number of second sequence representations 222 that correspond to positive control regions of a reference sequence.

[00204] In one or more illustrative examples, the computing system 214 can determine a number of the first sequence representations 220 that correspond to individual classification regions of a reference sequence and that have at least a threshold amount of methylated cytosines located in the individual classification regions. In these scenarios, the computing system 214 can determine individual classification region metrics 226 for individual classification regions. In addition, the computing system 214 can determine a number of the second sequence representations 222 that correspond to positive control regions. In at least some examples, the computing system 214 can, for individual classification regions, determine a ratio including a number of first sequence representations 220 that correspond to the individual classification region and that have at least a threshold amount of molecules with a methylated cytosine in the classification region in relation to a total number of the second sequence representations 222 the correspond to positive control regions of a reference sequence. In one or more examples, the computing system 214 can add a value of a pseudocount to the ratio to determine a classification region metric 226 for the individual classification region. The value of the pseudocount can be at least 1 , at least 1.2, at least 1.4, at least 1.6, at least 1.8, or at least 2. Further, the computing system 214 can perform a log base 10 operation with respect to the combination of the ratio and the pseudocount to determine a classification region metric 226 for an individual classification region. In at least some illustrative examples, the computing system 214 can determine at least a portion of the classification region metrics according to the following equation:

where x, is a total number of first sequence representations 220 for an individual classification region, i, having at least a threshold amount of methylated cytosines included in the region, I, and x_Positive_contmi is a total number of the second sequence representations 222 that correspond to positive control regions of a reference sequence. [00205] At operation 228, the computing system 214 can execute a model to determine an indication of cancer based on the classification region metrics 226. In the illustrative example of Figure 2, the computing system 214 can execute a model using the classification region metrics 226 to generate model output 230. In one or more examples, the model output 230 can indicate a status of tumor detection 232 or a status of tumor not detected 234 in relation to a sample 204 provided by a subject 206. In one or more additional examples, the computing system 214 can execute a model to determine an estimate of tumor fraction 236 for a sample 204. In one or more further examples, the computing system 214 can execute a model to determine a probability of a tumor being present in a subject 206 that provided a sample 204.

[00206] In one or more examples, the model can include a classification model that implements one or more machine learning techniques. In one or more illustrative examples, the model can include a linear regression model. In various examples, the model can be executed to determine a probability of a tumor being present 238 in a subject 206 that provided a sample 204 based on the classification region metrics 226. In one or more illustrative examples, the computing system 214 can execute the model to determine weights for individual classification regions. The weights for individual classification regions can be different. For example, the computing system 214 can determine that a first weight of a first classification region metric 226 for a first classification region is different from a second weight of a second classification region metric 226 for a second classification region. In at least some illustrative examples, a probability of a tumor being present 238 in a subject 206 that provided a sample 204 can be determined by the computing system 214 by executing a model that corresponds to the following equation:

where w, is a weight of an individual classification region, the score of the region i is calculated using Equation (1 ), and b is a slope corresponding to a linear regression model. In at least some examples, the probability of a tumor being present 238 can be used to generate a status of tumor detected 232 or a status of tumor not detected 234. In one or more further illustrative examples, the computing system 214 can analyze the probability of a tumor being present 238 with respect to a threshold probability to determine a status of tumor detected 232 or a status of tumor not detected 234 for a sample 204. The computing system 214 can determine that a sample 204 corresponds to the status of tumor detected 232 in response to determining that a probability of a tumor being present 238 for the sample 204 is at least the threshold probability. Additionally, the computing system 214 can determine that a sample 204 corresponds to the status of tumor not detected 234 in response to determining that a probability of a tumor being present 238 for the sample 204 is less than the threshold probability.

[00207] In one or more additional examples, the computing system 214 can execute a model that determines a maximum mutant allele fraction (MAF). In various examples, the computing system 214 can execute a model using the maximum MAF value to determine tumor fraction 236 for a sample 204. In one or more illustrative examples, the computing system 214 can execute a model using the classification region metrics 226 to determine a logit transformed maximum MAF value that can then be used by the computing system 214 to estimate tumor fraction for a sample 204. In various examples, the computing system 214 can analyze maximum MAF values to determine a probability of cancer being present 238 in a subject 206 that provided a sample 204. In various examples, a Huber regression (Huber, P. J. 1964. “Robust Estimation of a Location Parameter.” Annals of Mathematical Statistics 35 (1): 73-101) can be performed to determine a maximum MAF value based on the classification region metrics 226.

[00208] In various examples, the model output 230 can also include a tumor tissue indication 240. The tumor tissue indication 240 can indicate one or more tissues from which cancer cells that produced genomic material detected in the sample 204 originate. In one or more examples, the tumor tissue indication 240 can correspond to one or more tissues of origin for cancer cells that produced genomic material detected in the sample 204. In these scenarios, the computing system 214 can generate multiple models with individual models corresponding to a given tissue type. The output from individual models can be analyzed to determine additional metrics that indicate a tissue from which cancer cells that produced genomic material detected in one or more samples originate. In at least some examples, the output for the individual models can indicate at least one of tumor fraction 236 or a probability of tumor being present 238. The computing system 214 can analyze the respective model outputs to determine the model having at least one of a greatest value for tumor fraction or a greatest probability of cancer being present. The computing system 214 can then generate a tumor tissue indication 240 that corresponds to the model having the greatest value for tumor fraction and/or a greatest probability of cancer being present.

[00209] For example, samples 204 can be obtained from subjects 206 in which different types of cancer are present. To illustrate, first samples can be obtained from a first group of subjects in which a first classification of cancer is present and second samples can be obtained from a second group of subjects in which a second classification of cancer is present. The sequencing data generated from the first samples can be analyzed by the computing system 214 to generate first metrics that correspond to classification regions for the first classification of cancer and the first metrics can be used to generate a first model that corresponds to the first classification of cancer. Additionally, the sequencing data generated from second samples can be analyzed by the computing system 214 to generate second metrics that correspond to classification regions for the first classification of cancer and the second metrics can be used to generate a second model that corresponds to the second classification of cancer. After the models have been trained, the computing system 214 can analyze sequencing data obtained from one or more additional subjects that were not included in the training subjects to determine classification region metrics for the one or more additional subjects. The classification region metrics can then be analyzed using the different tumor classification models to generate model outputs. The model outputs can be analyzed by the computing system to determine a model having greatest values for the respective model outputs and determine the tumor tissue classification that corresponds to the model.

[00210] In one or more additional illustrative implementations, the model output 230 can also indicate methylation status for one or more genomic regions of a reference sequence. For example, the computing system 214 can analyze the classification region metrics 226 to determine a methylation status of one or more promoter regions of a reference sequence. In various examples, the one or more promoter regions can include at least one promoter region that is related to the presence of a tumor in a subject. In one or more illustrative examples, the classification region metrics 226 can indicate a number of sequence representations having at least a threshold amount of methylation with respect to the one or more promoter regions. In these scenarios, the computing system 214 can determine that a promoter region is methylated in response to determining that the number of sequence representations having at least a threshold amount of molecules with a methylated cytosine in the promoter region is greater than a threshold number.

[00211] In still other illustrative implementations, the computing system 214 can analyze the sequencing data 212 to determine a quantitative measure that corresponds to a number of sequence representations that correspond to a promoter region and determine an additional quantitative measure that correspond to an additional number of sequence representations that correspond to a number of positive control regions. Normalized metrics can be determined based on the quantitative measure and the additional quantitative measure. The normalized metrics can be analyzed with respect to a threshold to determine a methylation status of the promoter region. In various examples, the threshold may be different for different promoter regions. The threshold can be determined using a cancer-free dataset and the threshold value is set such that false positive rates are no greater than 5%, no greater than 4%, no greater than 3%, no greater than 2%, or no greater than 1 % and at a specificity of at least 80%, at least 90%, at least 95%, at least 98%, or at least 99%. In at least some examples, the computing system 214 can analyze the promoter region with regard to the threshold in situations where at least 4 sequence representations correspond to the promoter region, where at least 5 sequence representations correspond to the promoter region, where at least 6 sequence representations correspond to the promoter region, where at least 7 sequence representations correspond to the promoter region, where at least 8 sequence representations correspond to the promoter region, where at least 9 sequence representations correspond to the promoter region, where at least 10 sequence representations correspond to the promoter region, where at least 11 sequence representations correspond to the promoter region, or where at least 12 sequence representations correspond to the promoter region.

[00212] In one or more further illustrative examples, the computing system 214 can combine results from multiple models to determine the model output 230. For example, the computing system 214 can execute models with respect to one or more epigenetic signals, such as methylation of classification regions, to determine one or more first tumor metrics. With regard to methylation, the computing system 214 can execute both a classification model, such as a logistic regression model, that produced an indication of cancer being present in a subject providing a sample and an additional model that predicts tumor fraction for a sample. In one or more examples, the epigenetic signals can also correspond to fragment lengths of sequence representations generated from samples. In addition, the computing system 214 can execute one or more additional models with respect to genomic signals to generate further tumor metrics with respect to samples. In various examples, the genomic signals can correspond to the presence of one or more single nucleotide variants (SNVs) and/or the presence of insertions or deletions at one or more genomic regions of a reference sequence. In at least some examples, the computing system can include an integration system that combines tumor metrics generated by executing a number of models with regard to data corresponding to the genomic signals and the epigenetic signals to produce an aggregated tumor metric for a given sample. In some embodiments, using the quantitative measure obtained from the model output 230 can be analyzed with respect to a threshold. In situations where the quantitative measure obtained from the model output is at least the threshold value, the computing system 214 can determine that the indication of cancer is being present in the subject. In situations where the quantitative measure obtained from the model output is less than the threshold value, the computing system 214 can determine that the indication of cancer is being absent or not detected in the subject. In some embodiments, the threshold used to determine whether the indication of cancer is being present is calculated using a set of normal samples and is set at a particular value that provides high specificity.

[00213] In various additional implementations, the computing system 214 can determine methylation status of individual genomic regions. In one or more illustrative examples, the computing system 214 can determine methylation status of one or more promoter regions. In one or more examples, the sequencing data 212 can be analyzed to determine sequence representations that correspond to one or more genomic regions. For example, the sequencing data 212 can be analyzed to determine a number of sequence representations that correspond to one or more promoter regions. In at least some examples, the computing system 214 can determine a number of sequence representations that correspond to individual promoter regions that have at least a threshold amount of methylated cytosines.

[00214] For each genomic region and for an individual sample, the computing system 214 can determine a number of sequence representations that correspond to polynucleotide molecules having at least the threshold number of methylated cytosines in the genomic region. The computing system 214 can perform one or more normalization operations using the counts of polynucleotide molecules or sequence reads that correspond to the genomic region and have at least the threshold number of methylated cytosines to generate normalized metrics. To illustrate, the computing system 214 can divide the counts of polynucleotide molecules or reads that correspond to the genomic region and have at least the threshold number of methylated cytosines by the number of molecules or sequencing reads that correspond to a control region, such as a positive control region. In another instance, the computing system 214 can perform the normalized metrics by dividing the counts of polynucleotide molecules or reads that correspond to the genomic region and have at least the threshold number of methylated cytosines by the number of molecules or sequencing reads in a control dataset (i.e., the control dataset comprises of tumor not-detected samples) corresponding to the same genomic region and have at least the same threshold number of methylated cytosines. [00215] The normalized metrics can be analyzed with respect to a threshold value. The threshold value can correspond to a given genomic region, such as a given promoter region. In various examples, the threshold value can be different for different promoter regions. In these scenarios, a first promoter region can have a first threshold value and a second promoter region can have a second threshold value. In situations where the normalization metric is at least the threshold value, the computing system 214 can determine that the genomic region has a first methylation status. In scenarios where the normalization metric is less than the threshold value, the computing system 214 can determine that the genomic region has a second methylation status. In one or more illustrative examples, the first methylation status can be labeled as “methylated” and the second methylation status can be labeled as “not methylated.”

[00216] The threshold value for a given genomic region can be determined based on training data obtained from samples of individuals in which cancer is not detected. In one or more examples, sequence representations obtained from the training samples can be analyzed to determine a z-score with respect to the number of polynucleotide molecules that correspond to the genomic region and that have at least the threshold amount of methylated cytosines. In one or more illustrative examples, the threshold value for a promoter region that is used to determine the normalization metrics for the promoter region can be derived from the z-score calculated based on the training samples with respect to the promoter region.

[00217] Although the illustrative example of Figure 2 describes that models can be generated to determine a number of indicators with respect to the presence or absence of cancer in a given subject, in at least some additional examples, the sequencing data 212 can be analyzed by the computing system 214 to determine indicators of the presence of cancer without training specific models. In one or more examples, the computing system 214 can determine a tumor fraction value based on sequencing data 212 generated from one or more samples obtained from a single subject in which it is unknown whether or not cancer is present in the subject. In one or more examples, the computing system 214 can determine a change in the tumor fraction value based on sequencing data 212 generated from one or more samples obtained at two or more time points from a single subject. The change in the tumor fraction value can be used to monitor the subject’s response to treatment. In one or more additional examples, a first sample can be obtained from a subject prior to or at onset of at least one administration of a treatment or a procedure related to cancer and one or more second samples can be obtained from the subject after at least one of administration of a treatment or a procedure related to cancer. In one or more illustrative examples, the one or more second samples can be obtained at least one week, at least two weeks, at least three weeks, at least four weeks, at least five weeks, at least six weeks, at least eight weeks, or at least ten weeks after administration of the treatment or procedure. In at least some examples, first sample and the second sample can be derived from at least one of a bodily fluid obtained from the subject or tissue obtained from the subject.

[00218] In one or more examples, one or more samples can be obtained from a given subject. The sequencing data 212 generated from the one or more samples can be analyzed by the computing system to determine quantitative measures for a number of classification regions. In one or more examples, the quantitative measures can correspond to an amount of sequence representations that have at least a threshold amount of overlap with one or more classification regions. In one or more additional examples, the quantitative measures can correspond to sequence representations having at least a threshold amount of methylated cytosines in CpG regions having at least a threshold amount of CG content. In various examples, the indication of cancer being present in the subject can include tumor fraction. In one or more additional examples, the indication of cancer being present in the subject can include mutant allele fraction. In at least some examples, the quantitative measures can correspond to a number of sequencing reads that correspond to a given classification region in relation to a total number of sequencing reads across a plurality of positive control regions. In one or more further examples, the indicators of cancer being present can be used to determine an output that corresponds to cancer being present or not being present in a given individual in response to analyzing the one or more indicators of cancer being present with respect to one or more thresholds. In one or more illustrative examples, tumor fraction determined from one or more samples obtained from a subject can be analyzed with respect to one or more thresholds. In instances where tumor fraction is greater than a threshold level, the computing system 214 can determine that the probability of cancer being present in the subject is at least 80%, at least 85%, at least 90%, at least 95%, or at least 99%. Further, in situations where multiple samples are obtained from a subject, first quantitative measures generated from a first sample obtained from the subject can be analyzed with respect to second quantitative measures generated from a second sample obtained from the subject. In at least some examples, differences between the first quantitative measures and the second quantitative measures can be analyzed to determine an indication of treatment response in the subject.

[00219] The quantitative measures used to determine an indication of cancer being present in a subject can be determined by analyzing quantitative measures of a subset of classification regions. In at least some examples, the subset of classification regions can be different for different subjects. In one or more illustrative examples, values of quantitative measures for a number of classification regions can be analyzed with respect to one another and ranked according to the magnitude of the value of the quantitative measures. In various examples, the classification regions for a given sample can be ranked in descending order from the one or more classification regions having the greatest value of a quantitative measure to the one or more classification region having the least value of the quantitative measure.

[00220] In various examples, after ranking the quantitative measures of the classification regions, quantitative measures that correspond to a group of the classification regions can be removed before determining the indication of cancer being present in the subject. For example, the group of classification regions that are not used to determine the indication of cancer being present in the subject can include the 1 % of classification regions having the greatest quantitative measure values, the 2% of classification regions having the greatest quantitative measure values, 3% of classification regions having the greatest quantitative measure values, 4% of classification regions having the greatest quantitative measure values, 5% of classification regions having the greatest quantitative measure values, or the 6% of classification regions having the greatest quantitative measure values. In at least some examples, a number of classification regions having relatively high quantitative measure values can be excluded from the group of classification regions used to determine the indication of cancer being present in the subject because, in at least some cases, classification regions corresponding to quantitative measure values at or near the top of the ranked list can have non-tumor origins and/or be related to sequencing artifacts. Thus, by removing the quantitative measures that correspond to these classification regions from the analysis used to determine the indication of cancer being present in the subject, the accuracy with which the indication of cancer being present in the subject can increase. [00221] In one or more examples, after determining the group of classification regions to be used to determine an indication of cancer being present in the subject, a subset of classification regions of the group can then be determined by identifying at least 10 classification regions of the group, at least 25 classification regions of the group, at least 50 classification regions of the group, at least 75 classification regions of the group, at least 100 classification regions of the group, at least 150 classification regions of the group, at least 200 classification regions of the group, at least 250 classification regions of the group, at least 300 classification regions of the group, at least 350 classification regions of the group, at least 400 classification regions of the group, at least 450 classification regions of the group, or at least 500 classification regions of the group having the greatest values for the respective quantitative measure.

[00222] In at least some examples, one or more statistical measures, such as at least one of mean, median, or mode, can be applied to the quantitative measures of the subset of the classification regions of the group to generate an initial indication of cancer being present in the subject. In various examples, the initial indication of cancer can be modified according to a scaling factor. The scaling factor can be applied to the initial indication of cancer being present in the subject because, in at least some scenarios, the positive control regions can have different amounts of methylated CpGs. For example, at least a portion of the positive control regions can have fully methylated CpGs while other positive control regions may not be fully methylated. Additionally, in various situations, some classification regions can correspond to a high value of an indication of cancer being present in subjects, such as 90% tumor fraction, 95% tumor fraction, 99% tumor fraction, or 100% tumor fraction, but nucleic acid molecules that correspond to these classification regions may not be fully methylated. To account for these cases, the scaling factor can be applied to the initial indication of cancer being present in the subject to provide a more accurate determination of the indication. In one or more illustrative examples, the scaling factor can be determined by analyzing indications of cancer being present in subjects determined using one or more techniques described herein in relation to additional data that corresponds to additional indications of cancer being present in subjects, such as validation data or other techniques that generate data orthogonal to the indications of tumors being present in subjects described herein.

[00223] In various examples, the classification regions used to determine the quantitative measures can correspond to classification regions that correspond to one or more portions of differentially methylated regions. In one or more examples, the differentially methylated regions can include promoter regions that correspond to one or more classifications of cancer. For example, the classification regions can be determined by analyzing a number of sequencing representations across a differentially methylated region. In these scenarios, one or more portions of the differentially methylated regions that overlap with at least at threshold number of sequencing representations can be included in the classification regions. In one or more examples, the quantitative measures of the one or more portions of the differentially methylated regions can be determined based on the molecule count distribution of the differentially methylated region. For example, the quantitative measures can be determined based on the molecule count within one or more peaks of the molecule distribution of the differentially methylated region. To illustrate, in various examples, the distribution of molecules across a differentially methylated region can indicate one or more peaks where greater amounts of molecules overlap with one or more subregions within the differentially methylated region. In various examples, the one or more genomic regions that correspond to the one or more subregions of the differentially methylated regions that correspond to the highest amounts of sequence representations for a sample can be defined as classification regions. In at least some examples, the distribution of sequence representations can have a peak that corresponds to a subregion of the differentially methylated region having a higher number of sequence representations than other subregions of the differentially methylated region. In these scenarios, the subregion can be identified as a classification region. By determining subregions of at least a portion of the differentially methylated regions used to determine the indication of cancer being present in the subject, the amount of computing resources and memory resources used to determine the indication of cancer being present in the subject can be decreased.

[00224] To illustrate, a classification region can include one or more portions of a differentially methylated region in which at least 50% of the sequencing representations obtained from a sample overlap, at least 55% of the sequencing representations obtained from a sample overlap, at least 60% of the sequencing representations obtained from a sample overlap, at least 65% of the sequencing representations obtained from a sample overlap, at least 70% of the sequencing representations obtained from a sample overlap, at least 75% of the sequencing representations obtained from a sample overlap, at least 80% of the sequencing representations obtained from a sample overlap, at least 85% of the sequencing representations obtained from a sample overlap, at least 90% of the sequencing representations obtained from a sample overlap, at least 95% of the sequencing representations obtained from a sample overlap, or at least 99% of the sequencing representations obtained from a sample overlap. In one or more illustrative examples, the one or more portions of the differentially methylated region that comprise a classification region can be contiguous with respect to a reference sequence.

[00225] In various examples, the computing system 214 can use a biological age of a subject in conjunction with the classification region metrics 226 to determine the model output 230. The biological age of a subject can be different from a chronological age of a subject. The chronological age of a subject can be measured from a date of birth of the subject. The biological age can correspond to a measure of health of the subject taking into account various biological conditions present in a subject, levels of various analytes present in a subject, physical characteristics of a subject, one or more combinations thereof, and the like.

[00226] The biological age of subjects can be determined using an additional computational model. The additional computational model can be trained using classification region metrics 226 derived from additional samples obtained from additional training subjects and the chronological age of the additional training subjects. In one or more examples, the additional computational model can be trained using sequencing reads derived from the samples obtained from the additional training subjects. In various examples, the sequencing reads used to train the additional computational model can correspond to nucleic acid molecules derived from the additional samples that include CpG regions with at least a threshold amount of methylation. In one or more illustrative examples, the sequencing reads used to train the additional computational model can correspond to nucleic acid molecules derived from the additional samples that are included in a hypermethylation partition that corresponds to the one or more molecule separation processes 208. The determination of biological age by the computing system 214 using the additional computational model can be different from existing systems, methods, and techniques because methylation data derived from plasma samples can be used rather than the whole blood samples used to generate methylation data in existing systems, methods, and techniques. The implementations described herein can also be different from existing systems, methods, and techniques because quantitative measures determined by the additional computational model can be based on an analysis of genomic regions that correspond to a diagnostic assay for identifying subjects in which cancer is present. In existing systems, methods, and techniques the quantitative measures used to determine biological age can be based simply on an analysis of genomic regions that correspond to age-related conditions.

[00227] In at least some examples, a number of sequencing reads that correspond to a number of genomic regions can be analyzed by the additional computational model to determine a biological age of a subject. In various examples, quantitative measures of multiple genomic regions can be combined and then analyzed by one or more machine learning models to determine a biological of a subject. For example, k-nearest neighbors techniques can be applied to quantitative measures corresponding to number of sequencing reads corresponding to a number of genomic regions to generate modified quantitative measures. In one or more examples, the modified quantitative measures can correspond to additional genomic regions that include one or more portions of a plurality of genomic regions of a reference sequence. The modified quantitative measures can be provided as input to a regression machine learning model to determine the biological age of a subject. In one or more illustrative examples, the regression machine learning model can include an Elastic Net machine learning model.

[00228] In one or more examples, the biological age of a subject can be a feature used in a computational model used to determine the model output 230. For example, subjects having a biological age that is greater than the chronological age of the subjects can have a higher likelihood of a tumor being present than subjects having a biological age that is similar to or less than the chronological age of the subjects. In one or more additional examples, the biological age of a subject can be used to determine responsiveness to one or more treatments for one or more types of cancer. In one or more illustrative examples, the biological age of subjects can correspond to one or more components of a machine learning model used to generate the model output 230. The one or more components of the machine learning model that correspond to biological age of subjects can have various weights.

[00229] Figure 3 is a diagrammatic representation of an example framework 300 to train a computational model 302 to determine one or more tumor metrics with respect to a sample, in accordance with one or more implementations. The framework 300 can include the computing system 214. The computing system 214 can execute the computational model 302 to generate one or more model outputs 304. In one or more examples, the computational model 302 can be a machine learning model. The model output 304 can include an indication corresponding to the presence or absence of a tumor in a subject that provided a sample. In one or more illustrative examples, the model output 304 can include a tumor fraction. In one or more additional illustrative examples, the model output 304 can include a probability of cancer being present in a subject. In one or more further illustrative examples, the model output can include an indication of cancer being present in a subject or an indication of cancer not being present in a subject. In still other illustrative examples, the model output 304 can indicate methylation status of one or more regions of nucleic acid molecules. To illustrate, the computing system 214 can execute the computational model 302 with respect to quantitative measures corresponding to a promoter region to determine an amount of methylation of the promoter region. In other illustrative examples, the model output 304 can include a tumor tissue indication of the sample. [00230] The framework 300 can also include a sequence representation 306. In one or more examples, the sequence representation 306 can be generated based on analyzing nucleic acid molecules that are derived from a sample provided by a subject. The sequence representation 306 can include genomic regions having a number of nucleotides that correspond to a number of regions of interest. For example, the sequence representation 306 can include a sequence of nucleotides that corresponds to a first classification region 308. In addition, the sequence representation 306 can include a sequence of nucleotides that corresponds to a second classification region 310. Further, the sequence representation 306 can include a sequence of nucleotides that corresponds to a third classification region 312. In various examples, the first classification region 308, the second classification region 310, and the third classification region 312 of the sequence representation 306 can have differing amounts of methylated cytosines included in the respective classification regions 308, 310, 312. In one or more additional examples, the sequence representation 306 can include a sequence of nucleotides that corresponds to a positive control region 314 and a sequence of nucleotides that corresponds to a negative control region 316.

[00231] The computational model 302 can include a number of components that correspond to individual classification regions. In one or more examples, the components of the computational model 302 can have respective values that correspond to quantitative metrics of the respective classification regions. The quantitative metrics can indicate a number of sequence representations that correspond to the respective classification regions. In one or more examples, the computational model 302 can include a number of weights that are related to the respective components of the computational model 302. For example, the computational model 302 can include a first model component 318 that has a first weight 320. The first model component 318 can correspond to the first classification region 308. In addition, the computational model 302 can include a second model component 322 that has a second weight 324. The second model component 322 can correspond to the second classification region 310. In various examples, at least one of the first weight 320, the second weight 324, or the third weight 328 can be different from at least another one of the first weight 320, the second weight 324, or the third weight 328. [00232] In one or more illustrative examples, a value for the first model component 318, the second model component 322, and the third model component 326 can be determined on a per sample basis. To illustrate, for different samples, the computational model 302 can determine different values for at least one of the first model component 318, the second model component 322, or the third model component 326. In various examples, the computing system 214 can determine first quantitative measures for the first classification region 308 based on sequencing data for a sample. The computing system 214 can execute the computational model 302 to determine a value for the first model component 318 based on the first quantitative measures. Additionally, the computing system 214 can determine second quantitative measures for the second classification region 310 based on sequencing data for the sample. The computing system 214 can execute the computational model 302 to determine a value for the second model component 322 based on the second quantitative measures. Further, the computing system 214 can determine third quantitative measures for the third classification region 312 based on sequencing data for the sample. The computing system 214 can execute the computational model 302 to determine a value for the third model component 326 based on the third quantitative measures. The first quantitative measures, the second quantitative measures, and the third quantitative measures can be determined based on numbers of sequence representations that have at least a threshold amount of methylation in CG regions that correspond to the first classification region 308, the second classification region 310, and the third classification region 312, respectively. In one or more additional illustrative examples, a value for the first weight 320, a value for the second weight 324, and a value for the third weight 328 can be determined on a per sample basis. For example, for different samples, the computational model 302 can determine different values for at least one of the first weight 320, the second weight 324, or the third weight 328.

[00233] In one or more examples, the computing system 214 can perform a training process to generate the computational model 302. In various examples, the training process can determine one or more features related to classification region metrics that can be used to determine the model output 304. Additionally, the training process can determine one or more parameters related to classification region metrics that can be used to determine the model output 304. For example, the training process can be used to determine the model components to include in the computational model 302 and the corresponding weights of the model components.

[00234] In the illustrative example of Figure 3, the training process can be performed using training data 330. The training data 330 can include information obtained with respect to at least a first group of subjects 332 and information obtained with respect to at least a second group of subjects 334. In one or more examples, the first group of subjects 332 can include subjects in which a tumor is not detected and the second group of subjects 334 can include subjects in which a tumor is detected. In various examples, the training data 330 can include characteristics related to amounts of methylation of classification regions of the reference sequence 306 for the first group of subjects 332 and the second group of subjects 334. For example, the training data 330 can indicate quantitative measures corresponding to numbers of sequence representations that have at least a threshold level of methylation for the classification regions 308, 310, 312 for the first group of subjects 332 and the second group of subjects 334. The training data 330 can also include weights for model components based on an analysis of sequencing data of the first group of subjects 332 and the second group of subjects 334. In one or more illustrative examples, the training data 330 can include values for the first weight 320, values for the second weight 324, and values for the third weight 328 based on classification region metrics determined from sequencing data obtained from samples provided by the first group of subjects 332 and the second group of subjects 334.

[00235] The training data 330 can also include information corresponding to additional characteristics of the first group of subjects 332 and the second group of subjects 334. To illustrate, the training data 330 can include medical records information, medical history information, cancer treatment history information, demographic information, genomics information, one or more combinations thereof, and the like.

[00236] In one or more examples, the computing system 214 can train the computational model 302 to determine an indication related to one or more types of cancer being present in an individual. Additionally, in various examples, the computational model 302 can comprise multiple different models, such that the computational model 302 is an ensemble model. In these situations, the computing system 214 can perform one or more training processes with respect to individual models of the ensemble model. In one or more illustrative examples, the computational model 302 can include a number of individual models that each correspond to determining model outputs for individual genomic regions, such as genes or for a specified group of genes. For example, the computational model 302 can include a number of individual models to generate maximum MAF values for individual genes or for a specified group of genes. In these scenarios, the training of the computational model 302 can have more constraints than other models used to determine indications of cancer being present in individuals because of the use of genomic information in the training process. As a result, in situations where the computational model 302 is training using genomic information, the accuracy of the output of the computational model 302 can be increased. Further, although the training of the computational model 302 can incorporate genomic information to determine maximum MAF values, the use of the computational model 302 to determine indications of cancer for test subjects after training can be performed without the use of genomic information and can be based on input vectors that correspond to quantitative measures determined from sequencing data obtained from the test subjects.

[00237] The computing system 214 can obtain a first training dataset 336 up to an Nth training dataset 338 to perform a training process to generate the computational model 302. In one or more examples, the first training dataset 336 can include a first portion of the training data 330 corresponding to the first group of subjects 332 and the second group of subjects 334 that is used to train the computational model 302 and the Nth training dataset 338 can include a second portion of the training data 330 corresponding to the first group of subjects 332 and the second group of subjects 334 as part of a validation process for the computational model 302. In various examples, the computational model 302 can be updated over time and undergo multiple training processes. In these scenarios, the first training dataset 336 can include a portion of the training data 330 for the first group of subjects 332 and the second group of subjects 334 that corresponds to a first period of time and the Nth training dataset 338 can include a portion of the training data 330 for the first group of subjects 332 and the second group of subjects 334 that corresponds to a second period of time. [00238] In one or more examples, during the training process for the computational model 302, the computing system 214 can perform one or more optimization operations. In one or more illustrative examples, the computing system 214 can identify, during the training process for the computational model 302, one or more samples obtained from at least one of the first group of subjects 332 or the second group of subjects 334 that are outliers with respect to samples obtained from other subjects included in at least one of the first group of subjects 332 or the second group of subjects 334. To illustrate, the computing system 214 can determine that model output 304 generated for one or more subjects included in at least one of the first group of subjects 332 or the second group of subjects 334 has at least a threshold amount of difference with the model output 304 generated for one or more additional subjects included in at least one of the first group of subjects 332 or the second group of subjects 334. In one or more examples, the computing system 214 can identify at least one of one or more first subjects 332 or one or more second subjects 334 have model output 304 that is at least one standard deviation, at least 1.5 standard deviations, at least 2 standard deviations, at least 2.5 standard deviations, or at least 3 standard deviations different from a mean model output 304 determined for an additional group of at least one of the first group of subjects 332 or the second group of subjects 334. In various examples, the computing system 214 can apply a penalty to information generated from samples that correspond to subjects that are outliers with respect to information generated from samples that correspond to additional subjects.

[00239] In one or more additional examples, one or more optimization processes implemented by the computing system 214 in the training of the computational model 302 can correspond to a number of training cycles and/or a number of iterations for individual training cycles that are performed during the training process.

[00240] In one or more illustrative examples, the computing system 214 can perform at least 1000 iterations of a training process to generate the computational model 302, at least 3000 iterations of a training process to generate the computational model 302, at least 5000 iterations of a training process to generate the computational model 302, at least 8000 iterations of a training process to generate the computational model 302, at least 10,000 iterations of a training process to generate the computational model 302, at least 12,000 iterations of a training process to generate the computational model 302, or at least 15,000 iterations of a training process to generate the computational model 302. In various examples, the computing system 214 can end the training process before convergence of a loss function related to the computational model 302. In one or more examples, the number of iterations of the training process to produce the computation model 302 can correspond to a number of iterations of the training process performed before the training process is stopped and before the convergence of the loss function.

[00241] In one or more examples, a first stage of the training process implemented by the computing system 214 to generate the computational model 302 can include determining samples included in the training data 330 that include somatic mutations indicative one or more types of cancer in relation to samples included in the training data 330 that do not include somatic mutations indicative of the one or more types of cancer. The computing system 214 can then performing a training process for the computational model 302 using the samples of the training data 330 that include one or more somatic mutations indicative of the one or more types of cancer and using a number of samples obtained from subjects in which a tumor is not detected. In various examples, at least 100 iterations of the first stage of the training process can be performed.

[00242] Further, the training process performed by the computing system 214 can include a second stage that includes predicting values of tumor metrics of samples that do not include somatic mutations with respect to the one or more types of cancer. The computing system 214 can the perform at least 100 additional iterations of the second stage of the training process to generate the computational model 302. The second stage of the training process performed by the computing system 214 to generate the computational model 302 can also include training the computational model 302 using portions of the training data 330 corresponding to samples having somatic mutations indicative of the one or more types of cancer, using the predicted values of sample that do not include somatic mutations indicative of the one or more types of cancer, and portions of the training data 330 that correspond to samples obtained from subjects in which a tumor is not detected. In various examples, the second stage of the training process performed by the computing system 214 to generate the computational model 302 can be performed at least 2 additional times, at least 3 additional times, at least 4 additional times, at least 5 additional times, or at least 6 additional times. After the first stage of the training process and the second stage of the training process have been completed, the computing system 214 can perform a validation process for the computational model 302 using information obtained from different samples included in the training data 330.

[00243] In one or more illustrative examples, the computing system 214 can perform a training process for multiple computational models 302. In these scenarios, individual computational models 302 trained by the computing system 214 can correspond to different tissue types that are sources of genomic material obtained from subjects included in the training data 330. In one or more examples, the individual computational models 302 trained by the computing system 214 can correspond to different classification of cancer, such as colorectal cancer, lung cancer, pancreatic cancer, bladder cancer, breast cancer, liver cancer, skin cancer, or one or more additional classifications of cancer. In situations where the computing system 214 trains multiple computational models 302 that correspond to different classifications of cancer, the output from individual computational models 302 can be aggregated and analyzed by the computational system 214 to determine a tissue of origin for a subject.

[00244] In various examples, the individual computational models 302 that correspond to a given tissue from which genomic material included in samples is derived can have different model components. For example, a first computational model generated by the computing system 214 that corresponds to a first tissue type can have first model components that correspond to a first set of classification regions. In addition, a second computational model generated by the computing system 214 that corresponds to a second tissue type can have second model components that correspond to a second set of classification regions that has at least one classification region different from the first set of classification regions. Additionally, the weights for the individual components of the computational models that correspond to different tissue types can be different. That is, in situations where the first set of classification regions of the first computational model and the second set of classification regions of the second computational model have at least one classification region in common, the weights for the model component that corresponds to the at least one common classification region can be different in relation to the first computational model and the second computational model.

[00245] Additionally, one or more additional normalization processes can be performed by the computing system when generating the computational model 302. For example, in at least some scenarios, molecules treated with MBD can be partitioned differently across different samples. In one or more examples, molecules can be partitioned differently across different samples due to differences in the composition of reagents used to treat the molecules with MBD. In one or more additional examples, molecules can be partitioned differently across different samples due to at least one of equipment differences or process conditions used to treat the molecules with MBD.

[00246] To illustrate, for one or more first samples, treatment with MBD can cause first molecules having regions with first CG content to be separated into a first partition and second molecules having regions with second CG content to be separate into a second partition. In addition, for one or more second samples, treatment with MBD can cause third molecules having third CG content that is different from the first CG content to be separated into the first partition and fourth molecules having regions with fourth CG content that is different from the second CG content to be separated into the second partition. In various examples, the first molecules can be treated with MBD and separated into the first partition and the second molecules can be treated with MBD and separated into the second partition across a first cutoff range of CG content. Further, the third molecules can be treated with MBD and separated into the first partition and the fourth molecules can be treated with MBD and separated into the second partition across a second cutoff range of CG content that is different from the first cutoff range.

[00247] In one or more illustrative examples, the first cutoff range of CG content can include from 3-10 CpGs having methylated cytosines and the second cutoff range can include from 6-14 CpGs having methylated cytosines. In one or more additional illustrative examples, the first cutoff range of CG content can include from 4-9 CpGs having methylated cytosines and the second cutoff range can include from 7-13 CpGs having methylated cytosines. In one or more further illustrative examples, the first cutoff range of CG content can include from 5-8 CpGs having methylated cytosines and the second cutoff range can include from 8-12 CpGs. In still other illustrative examples, the first cutoff range of CG content can include 4-7 CpGs and the second cutoff range can include from 6-10 CpGs. In various examples, the first cutoff range of CG content and the second cutoff range of CG content can be used to determine the threshold amount of methylated cytosines used to determine at least one of training sequencing reads or testing sequencing reads. In at least some examples, the threshold amount of methylated cytosines can include a cutoff number that corresponds to a probability, such as at least about 80%, at least about 85%, at least about 90%, at least about 95%, or at least about 99% of individual molecules treated with MBD being separated into a given partition. In one or more examples, the threshold amount of methylated cytosines can correspond to 5 methylated cytosines, 6 methylated cytosines, 7 methylated cytosines, 8 methylated cytosines, 9 methylated cytosines, 10 methylated cytosines, 11 methylated cytosines, 12 methylated cytosines, 13 methylated cytosines, or 14 methylated cytosines.

[00248] In one or more examples, the computing system 214 can generate metrics for individual classification regions based on quantitative measures that are determined by analyzing a first number of sequencing reads to identify a first number of nucleic acid molecules having a first amount of CG content and by analyzing a second number of sequencing reads to identify a second number of nucleic acid molecules having a second amount of CG content. In at least some examples, the second number of nucleic acid molecules can be used to modify a metric determined using the first number of nucleic acid molecules to account for variations in the separation of molecules treated using MBD for different samples. In various examples, for individual classification regions, a first metric can be determined for a given sample by determining a first quantitative measure that corresponds to a number of molecules having a threshold amount of methylated cytosines and having a first amount of cytosine-guanine content in one or more partitions (for example, second partition 130 and/or third partition 134) that correspond to the individual classification region. In some embodiments, the first amount of CG content can be at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 15, at least 20, at least 25, or at least 30 CpGs in the nucleic acid molecules. In some embodiment, the first amount of CG content can be between 5-10, 5-15, 5-20, 5-30, 10-15, 10-20, IQ- 30, 15-20, 15-30 or 20-40 CpGs in the nucleic acid molecules. [00249] The first metric can also be determined for a given sample by determining a second quantitative measure that corresponds to a number of molecules having a threshold amount of methylated cytosines and having the first amount of cytosine-guanine content in one or more partitions (for example, second partition 130 and/or third partition 134) that correspond to a plurality of control regions (e.g., positive control regions). To illustrate, for an individual classification region, the first metric can be determined using the first quantitative measure for the individual classification region and the second quantitative measure that corresponds to the plurality of control regions.

[00250] The normalization process can also include determining, for a given sample, a second metric for the given sample by determining one or more additional quantitative measures based on a number of molecules in one or more partitions (e.g., second partition 130 and/or third partition 134) having at least the threshold amount of methylated cytosines and a second amount of cytosine-guanine content that correspond to the plurality of control regions, where the second amount of cytosine-guanine content is less than the first amount of cytosine-guanine content. In some embodiments, the second amount of CG content can be between 5-10, 5-15, 10-15, 10-20 or 15-20 CpGs in the nucleic acid molecules. In one or more examples, the plurality of control regions can be positive control regions and/or negative control regions. In one or more examples, the second metric can be determined using the additional quantitative measure and the second quantitative measure. In at least some examples, the second metric can be determined for a given sample by determining a ratio of the one or more additional quantitative measures with respect to the second quantitative measure. In one or more additional examples, the second metric can be determined for a given sample by determining the logarithm, such as the logarithm according to base 10, of a ratio of the one or more additional quantitative measures with respect to the second quantitative measure.

[00251] In one or more illustrative examples, the second metric for a given sample can include a combination of values, where individual values correspond to an additional quantitative measure based on a number of molecules having at least a threshold amount of methylated cytosines and a given number of CpGs for the plurality of control regions and the second quantitative measure. For example, a first additional quantitative measure can be determined based on a first number of molecules having at least the threshold amount of methylated cytosines in control regions having a first number of CpGs, such as 6, and a second additional quantitative measure can be determined based on a second number of molecules having at least the threshold amount of methylated cytosines in control regions having a second number of CpGs, such as 7. In at least some examples, more additional quantitative measures can be determined based on additional numbers of molecules having the threshold amount of methylated cytosines in control regions having additional numbers of CpGs, such as 8 CpGs, 9, CpGs, 10 CpGs, and the like up to an upper threshold of CpGs, such as 12 CpGs, 13 CpGs, or 14 CpGs. Ratios determined using the additional quantitative measures with respect to the second quantitative measures can be determined and summed to determine the second metric. [00252] In various examples, a correlation factor can also be determined for individual classification regions in relation to different amounts of CpGs that can be used to determine the second metric. In one or more examples, the correlation factor can modify the individual additional quantitative measures and then the modified individual additional quantitative measures can be aggregated to determine the second metric. In one or more additional examples, the first metric and the second metric can be combined to determine a normalized metric that corresponds to a given classification region. In one or more illustrative examples, the second metric can be subtracted from the first metric to determine the normalized metric.

[00253] In one or more additional illustrative examples, the correlation factor for a given classification region can be determined for each of a plurality of different amounts of cytosine-guanine content, such as a first correlation factor for 6 CpGs, a second correlation factor for 7 CpGs, a third correlation factor for 8 CpGs, and so forth up to a threshold amount of CG content. In at least some examples, the correlation factor can be determined by analyzing training data using one or more linear regression techniques. For example, the training data 330 can be fit to a linear regression model for individual classification regions to determine the correlation factor. In various examples, the fitting of at least a portion of the training data 330 to the linear regression model can be performed by aggregating the additional quantitative measures for a given classification region across a range of CG content, such a 6 CpGs, 7 CpGs, up to a threshold number of CpGs, and determining a mean quantitative measure.

[00254] In one or more examples, the normalized metrics can reduce variation of quantitative measures determined for individual samples. In at least some examples, the reduction in variation can result in increased accuracy of model outputs 304 in relation to at least some model outputs 304 determined without implementing the additional normalization process to determine the normalized metric.

[00255] Figure 4 is a diagrammatic representation of a framework 400 for generating training data for use in training a computational model that determines indications of cancer being present in subjects, in accordance with one or more example implementations. In the framework 400, a plurality of subjects 402 can provide a plurality of samples 404. In one or more examples, at least a portion of the plurality of samples 404 can include biological fluid samples. In one or more illustrative examples, the plurality of samples 404 can be selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, whole blood, a blood fraction, pleural fluid, pericardial fluid, cerebrospinal fluid, peritoneal fluid, one or more combinations thereof, and the like. In addition, the plurality of samples 404 can include tissue samples. For example, at least a portion of the plurality of samples 404 can be obtained from a tissue biopsy. In various examples, the plurality of subjects 402 can include subjects in which a tumor has been detected.

[00256] Additionally, nucleic acid molecules can be extracted from the plurality of samples 404. In at least some examples individual samples of the plurality of samples 404 can comprise an amount of cell-free nucleic acid molecules. The extraction of nucleic acid molecules from the plurality of samples 404 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the plurality of samples 404 and applying one or more proteases to break down proteins included in the plurality of samples 404. The extraction of nucleic acid molecules from the plurality of samples 404 can also include a number of washing and/or elution techniques to separate the nucleic acid molecules from other components included in the plurality of samples 404. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from individual samples of the plurality of samples 404. [00257] The framework 400 can also include one or more molecule separation and sequencing processes 406 that are performed with respect to the plurality of samples 404. The one or more molecule separation and sequencing processes 406 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and/or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[00258] The nucleic acid molecules extracted from plurality of samples 404 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5-methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation and sequencing processes 406 can separate nucleic acid molecules extracted from plurality of samples 404 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation and processes 406 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the molecule separation proceeds of the one or more molecule separation and sequencing processes 406 can include the first molecule separation process 122 and the second molecule separation process 136 described with respect to Figure 1. [00259] The sequencing processes included in the molecule separation and sequencing processes 406 can be performed by one or more sequencing machines that produce positive sample sequencing data 408. In one or more examples, the positive sample sequencing data 408 can include sequencing reads that correspond to nucleic acid molecules derived from the plurality of samples 404 having at least threshold levels of methylation. In one or more illustrative examples, positive sample sequencing data 408 can include sequencing reads corresponding to nucleic acid molecules having at least a threshold amount of methylation in CG regions of the nucleic acid molecules. In one or more additional illustrative examples. The positive sample sequencing data 408 can include sequencing reads corresponding to nucleic acid molecules that are hypermethylated.

[00260] The framework 400 can also include a computing system 410. The computing system 410 can obtain the positive sample sequencing data 408 and then analyze the positive sample sequencing data 408 to determine subsets of nucleic acid molecules that are to be used in training a classification model that can determine metrics indicating the presence of cancer or not in a subject. The computing system 410 can include one or more computing devices that can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices implementing the computing system 410 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 410 and the equipment used to perform the molecule separation and sequencing processes 406 can be implemented owned, operated, maintained, and/or controlled by a single organization. In one or more additional examples, the computing system 410 and the molecule separation and the equipment used to perform the sequencing processes 406 can be implemented, owned, operated, maintained, and/or controlled by multiple organizations. In one or more illustrative examples, the sequencing operations included in the molecule separation and sequencing processes 406 can include the operations performed by the sequencing machine 140 described with respect to Figure 1 and the sequencing machine 202 described with respect to Figure 2. [00261] The computing system 410 can include a first computational model 412. In one or more examples, the first computational model 412 can include a classification model that implements one or more machine learning techniques. In one or more additional examples, the first computational model 412 can include a linear regression model. In one or more illustrative examples, the first computational model 412 can include one or more implementations of the computational model 302 described with respect to Figure 3. In one or more scenarios, the first computational model 412 can be trained using sequencing data derived from samples obtained from individuals in which cancer is present and individuals in which cancer is not present. In various examples, the first computational model 412 can analyze the positive sample sequencing data 408 to determine a model output indicating an indication of cancer for individual samples of the plurality of samples 404. In at least some examples, the first computational model 412 can analyze, for individual samples of the plurality of samples 404, a number of sequencing reads included in the positive sample sequencing data 408 corresponding to individual classification regions. In one or more implementations, the first computational model 412 can, for individual samples of the plurality of samples 404, determine quantitative measures for individual classification regions based on the number of sequencing reads included in the positive sample sequencing data 408 that correspond to the individual classification regions. The first computational model 412 can determine a sample quantitative measure 414 for individual samples of the plurality of samples 404 according to the individual quantitative measures for the individual classification regions. The sample quantitative measures 414 can correspond to an indication of cancer being present in individual subjects of the plurality of subjects 402. In one or more additional illustrative examples, the first computational model 412 can analyze the positive sample sequencing reads 408 to determine sample quantitative measures 414 that include mutant allele fractions for individual samples of the plurality of samples 404. In one or more further examples, the first computational model 412 can analyze the positive sample sequencing reads 408 to determine sample quantitative measures 414 that include tumor fractions for individual samples of the plurality of samples 404.

[00262] The computing system 410 can include a training data analysis system 416 that analyzes the sample quantitative measures 414 in relation to a number of analysis criteria. The computing system 410 can apply a number of analysis criteria to the sample quantitative measures 414 to determine a number of sets of training samples to train a computational model that is different from the first computational model 412. In one or more examples, the training data analysis system 416 can apply first analysis criteria 418 to the sample quantitative measures 414. The first analysis criteria 418 can indicate one or more ranges of values for the sample quantitative measures 414. The one or more ranges of values for the sample quantitative measures 414 can be determined through a number of experiments to determine an optimal range of values for the sample quantitative measures 414 for training of the additional computational model. In various examples, the training data analysis system 416 can apply the first analysis criteria 418 to the sample quantitative measures 414 to produce first training samples 418.

[00263] In one or more examples, the computing system 410 can determine the first training samples 418 by analyzing the individual values for the sample quantitative measures 414 to determine whether or not the values are within the range indicated by the first analysis criteria 418. In situations where the value for an individual sample quantitative measure 414 is within a range of values indicated by the first analysis criteria 418, training data analysis system 416 can add the individual sample quantitative measure 414 to the first training samples 418. In scenarios where the value for an individual sample quantitative measure 414 is outside of the range of values indicated by the first analysis criteria 418, the training data analysis system 416 can add the individual sample quantitative measure 414 to a set of residual training samples (not shown in Figure 4). In at least some examples, the residual training samples can be used to generate in silico samples that can be used to train one or more additional computational models.

[00264] In one or more illustrative examples, the first analysis criteria 418 can correspond to a range of mutant allele fraction values for the sample quantitative measures 414. In one or more implementations, the mutant allele fraction values can be expressed as percentage values. In one or more additional examples, individual sample quantitative measures 414 can include values for tumor fraction of individual samples of the plurality of samples 404. In one or more further examples, individual sample quantitative measures 414 can include values for fragment length distributions for individual samples of the plurality of samples 404. In still other examples, individual sample quantitative measures 414 can include values of one or more protein biomarker concentrations in individual samples of the plurality of samples 404. The individual sample quantitative measures 414 can also include values indicating B-cell concentrations in individual samples of the plurality of samples 404. Additionally, the individual sample quantitative measures 414 can include values indicating T-cell concentrations in individual samples of the plurality of samples 414. Further, the individual sample quantitative measures 414 can include values indicating ratios of B-cell concentrations to T-cell concentrations for individual samples of the plurality of samples 414.

[00265] In at least some examples, the first analysis criteria 418 can correspond to a range of mutant allele fraction values based on one or more types of cancer to be detected. For example, the first analysis criteria 418 can correspond to a first range of mutant allele fraction values in situations where a first type of cancer is being detected and the first analysis criteria 418 can correspond to a second range of mutant allele fraction values in situations where a second type of cancer is being detected. In still other example, the first analysis criteria 418 can correspond to a first range of mutant allele fraction values in situations where one or more first stages of cancer are being detected and a second range of mutant allele fraction values in situations where one or more second stages of cancer are being detected. The second range of mutant allele fraction values can be different from the first range of mutant allele fraction values. In at least some examples, the second range of mutant allele fraction values can partially overlap with the first range of mutant allele fraction values. In various examples, the second range of mutant allele fraction values may not overlap with the first range of mutant allele fraction values.

[00266] In one or more additional illustrative examples, the first analysis criteria 418 can indicate a range of mutant allele fraction values that correspond to no greater than 50% of the sample quantitative measures 414, no greater than 40% of the sample quantitative measures 414, no greater than 30% of the sample quantitative measures 414, no greater than 20% of the sample quantitative measures 414, no greater than 15% of the sample quantitative measures, no greater than 10% of the sample quantitative measures 414, or no greater than 5% of the sample quantitative measures 414. In various illustrative examples, the first analysis criteria 414 can indicate a range of mutant allele fraction values from 1% of the sample quantitative measures 414 to 50% of the sample quantitative measures 414, from 5% of the sample quantitative measures 414 to 40% of the sample quantitative measures 414, from 10% of the sample quantitative measures 414 to 30% of the sample quantitative measures 414, from 1% of the sample quantitative measures 414 to 10% of the sample quantitative measures 414, or from 5% of the sample quantitative measures 414 to 15% of the sample quantitative measures 414.

[00267] In one or more further illustrative examples, the first analysis criteria 418 can indicate mutant allele fraction values for the sample quantitative measures 414 of no greater than 0.001%, no greater than 0.005%, no greater than 0.008%, no greater than 0.01 %, no greater than 0.03%, no greater than 0.05%, no greater than 0.08%, no greater than 0.1 %, no greater than 0.3%, no greater than 0.5%, no greater than 0.8%, no greater than 1.0%, no greater than 1.5%, no greater than 2%, no greater than 3%, no greater than 5%, no greater than 8%, or no greater than 10%. In various examples, the first analysis criteria 418 can indicate mutant allele fraction values for the sample quantitative measures 414 from 0.001 % to 10%, from 0.005% to 1 %, from 0.01 % to 1%, from 0.01% to 0.1%, from 0.05% to 5%, or from 0.1 % to 1 %.

[00268] The training data analysis system 416 can also apply second analysis criteria 420 to the first training samples 418 to produce second training samples 422 and third training samples 424. In one or more examples, the second analysis criteria 420 can correspond to the presence of somatic mutations present in nucleic acid molecules derived from the plurality of samples 404. For example, the second training samples 422 can include a first subset of the first training samples 418 in which at least a threshold number of somatic variants are present. Additionally, the third training samples 424 can include a second subset of the first training samples 418 in which less than the threshold number of somatic mutations are present. In one or more illustrative examples, the second subset of the first training samples 418 can correspond to nucleic acid sequences in which no somatic mutations are present.

[00269] In various examples, the training data analysis system 416 can analyze the first training samples 418 with respect to the second analysis criteria 420 by analyzing nucleic acid sequences included in the positive sample sequencing data 408 that correspond to the first training samples 418 with respect to one or more reference sequences. In at least some examples, the training data analysis system 416 can analyze nucleotides of individual positions of nucleic acid molecules included in the positive sample sequencing data 408 that correspond to the first training samples 418 with nucleotides present at individual positions of the one or more reference sequences. The training data analysis system 416 can determine that one or more somatic mutations are present in a first training sample 418 in response to determining that a nucleic acid sequence corresponding to the first training sample 418 has a first nucleotide present at a given position that is different from a second nucleotide present at the given position of at least one reference sequence. In one or more additional examples, the second analysis criteria 420 can include a list of somatic mutations. In these scenarios, the training data analysis system 416 can analyze nucleic acid molecule sequences included in the positive sample sequencing data 408 that correspond to the first training samples 418 with respect to the list of somatic mutations. For a first subset of the first training samples 418 in which a corresponding nucleic acid molecule sequence includes one or more somatic mutations included in the list of somatic mutations, the training data analysis system 416 can add the first subset of first training samples 418 to the second training samples 422. For a second subset of the first training samples 418 in which a corresponding nucleic acid molecule sequence does not include one or more somatic mutations included in the list of somatic mutations, the training data analysis system 416 can add the second subject of first training samples 418 to the third training samples 422. [00270] The computing system 410 can perform a training process 426 for a second computational model 428 using the second training samples 422 and the third training samples 424. In one or more examples, additional datasets can be used in the training process 426. For example, the computing system 410 can perform the training process 426 for the second computational model 428 using at least one of methylation data or sequencing data derived from samples obtained from subjects in which a tumor is not detected. In one or more additional examples, the computing system 410 can perform the training process 426 for the second computational model 428 using at least one of methylation data or sequencing data that correspond to in silico samples derived from the at least one of methylation data or sequencing data combine from a plurality of additional samples. In one or more illustrative examples, the second computational model 428 can include a classification model. In one or more additional illustrative examples, the second computational model 428 can include a regression model. The regression model can comprise a linear regression model. Additionally, the regression model can comprise a logistic regression model. Further, the regression model can comprise a ridge regression model. In still other examples, the regression model can comprise a lasso regression model. The regression model can also include a polynomial regression model.

[00271] In one or more examples, the training process 426 can be performed with respect to a loss function of the second computational model 428. In one or more illustrative examples, the loss function can comprise a Huber loss function. In one or more additional illustrative examples, the loss function of the second computational model 428 can comprise a support vector regression loss function. In one or more further illustrative examples, the loss function of the second computational model 428 can comprise a ridge loss function. In various illustrative examples, the loss function of the second computational model 428 can comprise a lasso loss function. In still other illustrative examples, the loss function of the second computational model 428 can comprise an elastic net loss function. The loss function of the second computational model 428 can also include a square error loss function.

[00272] The second computational model 428 can generate a model output that corresponds to an indication of cancer being present in one or more subjects. In one or more examples, an output of the second computational model 428 can indicate if a tumor is detected in one or more subjects or if a tumor is not detected in one or more subjects. In one or more additional examples, an output of the second computational model 428 can correspond to values for tumor fraction for one or more subjects. In one or more further examples, an output of the second computational model 428 can include values indicating a probability of a tumor being present in one or more subjects. In still other examples, an output of the second computational model 428 can indicate a stage of cancer present in one or more subjects. In at least some examples, an output of the second computational model 428 can indicate a type of tissue in which a tumor is present in one or more subjects. In various examples, an output of the second computational model 428 can include an indication of a type of tissue in which a tumor is present in the one or more subjects as well as at least one of one or more values for tumor fraction, a stage of cancer, or a probability of a tumor being present in one or more subjects.

[00273] Using a portion of the sample quantitative measures 414 for training of the second computational model 428 as described herein can result in fewer processing resources and fewer memory resources being used to determine a trained version of the second computational model 428 than in scenarios where all or almost all of the sample quantitative measures 414 are used to train the second computational model 428. Additionally, by training the second computational model 428 using data derived from a specifically selected subset the plurality of training samples 404, the second computational model 428 can produce output that is more accurate and reliable than if data derived from all or almost all of the plurality of samples 404 was used.

[00274] Figure 5 is a diagrammatic representation of a framework 500 of a training process for a computational model that produces indications of cancer being present in one or more subjects, in accordance with one or more example implementations. In the framework 500, a plurality of subjects 502 can provide a plurality of samples 504. In one or more examples, at least a portion of the plurality of samples 504 can include biological fluid samples. In one or more illustrative examples, the plurality of samples 504 can be selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, whole blood, a blood fraction, pleural fluid, pericardial fluid, cerebrospinal fluid, peritoneal fluid, one or more combinations thereof, and the like. In addition, the plurality of samples 504 can include tissue samples. For example, at least a portion of the plurality of samples 504 can be obtained from a tissue biopsy. In various examples, the plurality of subjects 502 can include subjects in which a tumor has not been detected.

[00275] Additionally, nucleic acid molecules can be extracted from the plurality of samples 504. In at least some examples individual samples of the plurality of samples 504 can comprise an amount of cell-free nucleic acid molecules. The extraction of nucleic acid molecules from the plurality of samples 504 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the plurality of samples 504 and applying one or more proteases to break down proteins included in the plurality of samples 504. The extraction of nucleic acid molecules from the plurality of samples 504 can also include a number of washing and/or elution techniques to separate the nucleic acid molecules from other components included in the plurality of samples 504. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from individual samples of the plurality of samples 504.

[00276] The framework 500 can also include one or more molecule separation and sequencing processes 506 that are performed with respect to the plurality of samples 504. The one or more molecule separation and sequencing processes 506 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and/or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[00277] The nucleic acid molecules extracted from plurality of samples 504 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5-methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation and sequencing processes 506 can separate nucleic acid molecules extracted from plurality of samples 504 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation and processes 506 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the molecule separation proceeds of the one or more molecule separation and sequencing processes 506 can include the first molecule separation process 122 and the second molecule separation process 136 described with respect to Figure 1.

[00278] The sequencing processes included in the molecule separation and sequencing processes 506 can be performed by one or more sequencing machines that produce negative sample sequencing data 508. In one or more examples, the negative sample sequencing data 508 can include sequencing reads that correspond to nucleic acid molecules derived from the plurality of samples 504 having at least threshold levels of methylation. In one or more illustrative examples, negative sample sequencing data 508 can include sequencing reads corresponding to nucleic acid molecules having at least a threshold amount of methylation in CG regions of the nucleic acid molecules. In one or more additional illustrative examples, the negative sample sequencing data 508 can include sequencing reads corresponding to nucleic acid molecules that are hypermethylated.

[00279] The framework 500 can also include a computing system 510. The computing system 510 can obtain the negative sample sequencing data 508 and then analyze the negative sample sequencing data 508 in conjunction with data corresponding to the second training samples 422 and the third training samples 424 described with respect to Figure 4 to be used in training a classification model that can determine metrics indicating the presence of cancer or not in a subject The computing system 510 can include one or more computing devices that can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices implementing the computing system 510 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 510 and the equipment used to perform the molecule separation and sequencing processes 506 can be implemented owned, operated, maintained, and/or controlled by a single organization. In one or more additional examples, the computing system 510 and the molecule separation and the equipment used to perform the sequencing processes 506 can be implemented, owned, operated, maintained, and/or controlled by multiple organizations. In one or more illustrative examples, the sequencing operations included in the molecule separation and sequencing processes 506 can include the operations performed by the sequencing machine 140 described with respect to Figure 1 and the sequencing machine 202 described with respect to Figure 2.

[00280] The computing system 510 can include a training data analysis system 512. In one or more examples, the training data analysis system 512 can perform at least a portion of the operations described with respect to the training data analysis system 412 of Figure 4. The training data analysis system 512 can determine values of quantitative measures of samples that are used in the training of the second computational model. For example, the training data analysis system 512 can determine pseudovalues for negative training samples 514. In one or more examples, the training data analysis system 512 can determine one or more predetermined values for individual samples of the plurality of samples 506 that correspond to the plurality of subjects 502 in which a tumor is not detected. In various examples, the pseudovalues for negative training samples 514 can correspond to values for mutant allele fractions of the plurality of samples 502. In one or more illustrative examples, at least a portion of the pseudovalues for the negative training samples 504 can have negative values. In one or more additional illustrative examples, at least a portion of the pseudovalues for the negative training samples 504 can have a same value. In one or more further examples, at least a portion of the pseudovalues for the negative training samples 504 can have a different value. In one or more scenarios, the pseudovalues for negative training samples 514 can be determined through one or more experimental processes to determine optimal values for the pseudovalues for negative training samples 514 to produce the second computational model, such that the second computational provides accurate and reliable output indicating the presence or absence of cancer in subjects.

[00281] The training data analysis system 512 can also determine quantitative measures for second training samples 516. The quantitative measures for second training samples 516 can correspond to the sample quantitative measures 414 generated by the first computational model 412 and that correspond to the second training samples 422 as described with respect to Figure 4. To illustrate, the quantitative measures for second training samples 516 can include a portion of the sample quantitative measures 414 that correspond to nucleic acid molecules of a subset of the samples of the plurality of samples 404 for which one or more somatic mutations are present.

[00282] The training data analysis system 512 can also determine first sample weights 518 for the pseudovalues for negative training samples 514 and second sample weights 520 for the quantitative measures for second training samples 516. The first sample weights 518 and the second sample weights 520 can indicate weightings of the pseudovalues for negative training samples 514 and the quantitative measures for second training samples 516 during a training process for the second computational model. In one or more examples, at least a portion of the first sample weights 518 can be different from the second sample weights 520. In one or more additional examples, at least a portion of the first sample weights 518 can be the same as the second sample weights 520.

[00283] The computing system 510 can perform a second computational model training process 522. The second computational model training process 522 can include a number of iterations. In one or more examples, the training data used during different iterations of the second computational model training process 522 can be different. For example, first training data used during one or more first iterations of the second computational model training process 522 can be different from second training data used during one or more second iterations of the second computational model training process 522. In one or more additional examples, at least a portion of the training data used during the second computational model training process 522 can be common for each iteration of the second computational model training process 522. In still other examples, values for at least a portion of the training data used during the second computational model training process 522 can be the same during each iteration of the second computational model training process 522. In one or more illustrative examples, each iteration of the second computational model training process 522 can use the pseudovalues for negative training samples 514 and the quantitative measures for second training samples 516.

[00284] In the illustrative example of Figure 5, the second computational model training process can include a first training process iteration 524. The first training process iteration 524 can produce an initial version of the second computational model 528. The first training process iteration 524 can use the pseudovalues for negative training samples 514, the first sample weights 518, the quantitative measures for second training samples 516, and the second sample weights 520. Additionally, the first training process iteration 524 can use third training sample sequencing data 528. The third training sample sequencing data 528 can include sequence representations of nucleic acid molecules derived from one or more samples of the plurality of samples 404 described with respect to Figure 4 that correspond to subjects in which a tumor is detected, that have sample quantitative measures 414 within a specified range corresponding to the first analysis criteria 418, and that have nucleic acid sequences for which somatic variants are not present in accordance with the second analysis criteria 420.

[00285] In one or more illustrative examples, the first training process iteration 524 can use the pseudovalues for negative training samples 514, the first sample weights 518, the quantitative measures for second training samples 516, and the second sample weights 520 to generate the initial version of the second computational model 526. The first training process iteration 524 can then apply the initial version of the second computational model 526 to the third training sample sequencing data 528 to produce quantitative measures for third training samples 532. In at least some examples, the quantitative measures for third training samples 530 can correspond to values related to mutant allele fractions for the third training samples 424. The quantitative measures for third training samples 530 can then be used in conjunction with the pseudovalues for negative trainings samples 514, the quantitative measures for second training samples 516, the first sample weights 518, and the second sample weights 520 in subsequent iterations of the second computational model training process 524. Although not shown in the illustrative example of Figure 5, the quantitative measures for third training samples 530 can be associated with additional sample weights that can be applied to values of the quantitative measures for third training samples 530.

[00286] In at least some examples, at least a portion of the quantitative measures for the third training samples 530 can be determined using a specified value that is based on a statistical analysis of the quantitative measures for the third training samples 530. For example, the computing system 510 can determine a plurality of groups of values for the quantitative measures for the third training samples 530. To illustrate, the computing system 510 can determine a number of quantiles for the quantitative measures for the third training samples 530. The individual quantiles can be associated with a given range of values of the quantitative measures for the third training samples 530. In at least some examples, the computing system 510 can determine a default quantitative measure value for one or more third samples in one or more of the quantiles. In various examples, the default value can correspond to a cutoff value for another quantile determined by the computing system 510. In various examples, for a portion of the third samples having quantitative measures below a 50% quantile, below a 60% quantile, below a 70% quantile, below a 75% quantile, below an 80% quantile, below an 85% quantile, below a 90% quantile, below a 95% quantile, or below a 99% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the given quantile. In one or more illustrative examples, for a portion of the third samples having quantitative measure values below a 95% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 95% quantile. In one or more additional illustrative examples, for a portion of the third samples having quantitative measure values below a 90% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 90% quantile. In one or more further illustrative examples, for a portion of the third samples having quantitative measure values below an 85% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 85% quantile. In still other illustrative examples, for a portion of the third samples having quantitative measure values below a 80% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 80% quantile.

[00287] The second computational model training process 522 can include additional training process iterations 532. Individual iterations of the additional training process iterations 532 can generate Nth versions of the second computational model 534. For example, a second iteration included in the additional training process iterations 532 can produce a second version of the second computational model included in the Nth version of the second computational model 534 and a third iteration included in the additional training process iterations 532 can produce a third version of the second computational model included in the additional training process iterations 532. The pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, and the quantitative measures for third training samples 530 can be used in individual additional training process iterations 532. In various examples, for individual additional training process iterations 532, the Nth versions of the second computational model 534 can produce values for the quantitative measures for the third training samples 530. In this way, at least a portion of the values for the quantitative measures for third training samples 530 used in individual additional training process iterations 532 can be different than the values of the quantitative measures for third training samples 530 due to changes in the second computational model between different subsequent versions of the second computational model.

[00288] Although not shown in the illustrative example of Figure 5, the additional training process iterations 532 can be performed using in silico training data. The in silico training data can be produced using information derived from at least a portion of the plurality of samples 504 obtained from the plurality of subjects 502 in which a tumor is not detected and using information derived from one or more samples obtained from one or more subjects in which a tumor is detected. For example, in silico training data can be produced by the computing system 510 using at least a portion of the negative sample sequencing data 508 and at least a portion of the positive sample sequencing data 408 that corresponds to at least a portion of the plurality of samples 404 having sample quantitative measures 414 described with respect to Figure 4 that do not correspond to the first analysis criteria 418. To illustrate, the in silico training data can be produced by combining information related to a portion of the plurality of samples 404 obtained from one or more subjects of the plurality of subjects 402 for which a tumor is detected and that have respective sample quantitative measures 414 outside of a specified range of values and information related to one or more of the plurality of samples 504 obtained from one or more subjects of the plurality of subjects 504 for which a tumor is not detected. In at least some examples, the in silico training data can include at least one of sequencing data or quantitative measures for one or more individual in silico training samples. [00289] In one or more examples, the second computational model training process 522 can include evaluating values of a loss function of the second computational model after one or more iterations of the second computational model training process 522. In various examples, the second computational model training process 522 can be stopped in response to values of the loss function corresponding to convergence of the second computational model. In one or more additional examples, the second computational model training process 522 can be stopped after a specified number of iterations. In at least some examples, the second computational model training process 522 can be stopped before convergence of the loss function to minimize overfitting of the second computational model. In one or more illustrative examples, the second computational training process 522 can be stopped after at least 2 iterations, at least 3 iterations, at least 4 iterations, at least 5 iterations, at least 6 iterations, at least 7 iterations, at least 8 iterations, at least 9 iterations, at least 10 iterations, at least 15 iterations, at least 20 iterations, at least 25 iterations, at least 50 iterations, or at least 100 iterations.

[00290] The second computational model training process 522 can produce a trained version of the second computational model 536. The trained version of the second computational model 536 can include a classification model having a number of variables and weights that correspond to features of the training samples that can be indicative of a tumor being present in subjects. In one or more examples, the trained version of the second computational model 534 can include a classification model having a number of variables and weights that correspond to at least one of methylation information with respect to classification regions, sequencing information, or somatic variant information that can be indicative of a tumor being present in subjects. The trained version of the second computational model 536 can produce a model output 538. The model output 538 can include an indication that a tumor is present in a subject or an indication that a tumor is not present in a subject. Additionally, the model output 538 can include a probability of cancer being present in a subject. Further, the model output 538 can indicate tumor fraction for one or more samples obtained from a subject. The model output 538 can also correspond to a measure related to mutant allele fraction of a sample obtained from a subject. In still other examples, the model output 538 can indicate a stage of cancer for a subject. In various examples, the model output 538 can indicate the presence of one or more types of cancer in a subject.

[00291] In one or more illustrative examples, the trained version of the second computational model 536 can determine the model output 538 by analyzing methylation data and sequencing data derived from one or more samples obtained from a subject in relation to classification regions of a reference sequence to generate the model output 538. In at least some examples, the trained version of the second computational model 536 can produce the model output for a same subject at different points in time. For example, the trained version of the second computational model 536 can determine the model output 538 using data derived from one or more samples obtained from a subject prior to one or more medical interventions being performed. Additionally, the trained version of the second computational model 536 can determine the model output 538 using data derived from one or more additional samples obtained from the subject after the one or more medical interventions are performed. In one or more examples, the one or more medical interventions can include at least one of surgery, chemotherapy, radiation therapy, or another cancer treatment. In at least some illustrative examples, the trained version of the second computational model 536 can implement at least a portion of the processes, techniques, frameworks, and architectures described with respect to Figure 1 , Figure 2, and/or Figure 3 to generate the model output 538.

[00292] In various examples, the second computational model training process 522 can be performed for multiple instances of the second computational model. After the second computational model training process 522 is performed for each instance of the second computational model, the trained version of the second computational model 536 can be produced using a combination of features of the multiple instances of the second computational model. In one or more illustrative examples, the computing system 510 can implement the second computational model training process 522 using at least the pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, the third training sample sequence data 528, the quantitative measures for third training samples 530, in silico training data, or one or more combinations thereof with respect to a first instance of the second computational model to generate a first trained version of the second computational model. The computing system 510 can also implement the second computational model training process using at least the pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, the third training sample sequence data 528, the quantitative measures for third training samples 530, in silico training data, or one or more combinations thereof with respect to one or more second instances of the second computational model to generate one or more second trained versions of the second computational model. Features of the first trained version of the second computational model and the one or more second trained versions of the second computational model can then be combined to produce the trained version of the second computational model 536. In at least some examples, average values of variable weights of the first trained version of the second computational model and the one or more second trained versions of the second computational model, average values of parameters of the first trained version of the second computational model and the one or more second trained versions of the second computational model, and average values of other features of the first trained version of the second computational model and the one or more second trained versions of the second computational model can be generated to produce the trained version of the second computational model 536. In various examples, one or more combinations of variables included in the first trained version of the second computational model and the one or more second trained versions of the second computational model can be included in the trained version of the second computational model 536.

[00293] In one or more examples, multiple instances of the trained version of the second computational model 536 can be produced by the computing system 510 with individual instances of the trained version of the second computational model 536 corresponding to one or more specified cancer types. For example, the computing system 510 can produce at least two of a first trained version of the second computational model that corresponds to one or more first cancer types, a second trained version of the second computational model that corresponds to one or more second cancer types, a third trained version of the second computational model that corresponds to one or more third cancer types, a fourth trained version of the second computational model that corresponds to one or more fourth cancer types, a fifth trained version of the second computational model that corresponds to one or more fifth cancer types, a sixth trained version of the second computational model that corresponds to one or more sixth cancer types, a seventh trained version of the second computational model that corresponds to one or more seventh cancer types, an eighth trained version of the second computational model that corresponds to one or more eighth cancer types, a ninth trained version of the second computational model that corresponds to one or more ninth cancer types, or a tenth trained version of the second computational model that corresponds to one or more tenth cancer types, In various examples, the computing system 510 can generate trained versions of the second computational model 536 to detect up to 12 cancer types, up to 13 cancer types, up to 14 cancer types, up to 15 cancer types, up to 16 cancer types, up to 17 cancer types, up to 18 cancer types, up to 19 cancer types, up to 20 cancer types, or more.

[00294] To produce the different instances of the trained version of the second computational model 536 that correspond to an individual cancer type or a specified set of cancer types, the second computational model can be trained by the computing system 510 using training data that corresponds to the individual cancer type or the specified set of cancer types. For example, the computing system 510 can implement the training data analysis system 512 to generate quantitative measures for second training samples 516, where the second training samples are derived from individuals in which one or more somatic mutations corresponding to an individual cancer type or a specified set of cancer types are present. To illustrate, in scenarios where the computing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more colorectal cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more colorectal cancers are present. In one or more additional examples, in scenarios where the computing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more lung cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more lung cancers are present, in one or more further examples, in scenarios where the computing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more breast cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more breast cancers are present.

[00295] After the trained version of the second computational model 536 has been produced, the trained version of the second computational model 536 can be implemented with respect to one or more samples obtained from test subjects to generate the model output 538 for the individual test subjects. In implementations where the computing system 510 produces multiple trained versions of the second computational model to detect multiple cancer types, individual instances of the trained second computational model can provide model output. In one or more examples, the model output can indicate a probability of one or more cancer types being present in the test subject. For example, a first trained version of the second computational model can determine a first model output indicating one or more first probabilities of one or more first cancer types being present in test subjects, a second trained version of the second computational model can determine a second model output indicating one or more second probabilities of one or more second cancer types being present in test subjects, and a third trained version of the second computational model can determine a third model output indicating one or more third probabilities of one or more third cancer types being present in test subjects. In one or more illustrative examples, the computing system 510 can produce a first trained version of the second computational model that determines a first indication of colorectal cancer being present in a test subject, a second trained version of the second computational model that determines a second indication of lung cancer being present in a test subject, and a third trained version of the second computational model that determines a third indication of breast cancer being present in a test subject.

[00296] In various examples, the model outputs generated by multiple instances of the trained version of the second computational model can be analyzed to determine an overall output indicating at least one type of cancer present in a test subject. In one or more examples, individual instances of the trained version of the second computational model can produce a probability of a given type of cancer being present in a test subject. The computing system 510 can determine a model output having a highest probability and generate an indication that the cancer corresponding to the highest probability is present in the test subject. In some instances, the computing system 510 can determine a model output having a highest score and generate an indication that the cancer corresponding to the highest score is present in the test subject. In at least some examples, the computing system 510 can analyze output from multiple instances of the trained version of the computational model with respect to a threshold value. The threshold value can correspond to a minimum probability for determining that a given type of cancer is present in a test subject. In one or more additional examples, the threshold value can correspond to a minimum tumor fraction for determining that a given type of cancer is present in a test subject. In at least some examples, the computing system 510 can determine that the output from more than one trained version of the second computational model is at least a threshold value. In these scenarios, the computing system 510 can determine that more than one cancer type is present in a test subject. Further, in the scenarios where the computing system 510 determines that the output from more than one trained version of the second computational model is at least a threshold value, the computing system 510 can determine that cancer has metastasized in a test subject.

[00297] In one or more examples, the computing system 510 can implement one or more additional computational models to analyze the output from a number of instances of the trained second computational model. The one or more additional computational models implemented by the computing system 510 to analyze output from multiple instances of the trained version of the second computational model can include one or more machine learning models or one or more statistical models. In one or more illustrative examples, output from individual instances of the trained version of the second computational model can be assigned weights by the computing system 510 to determine a type of cancer present in a test subject.

[00298] Figure 6 is a diagrammatic framework 600 of a process to train a computational model using biological sample data and in silico training data, in accordance with one or more example implementations. The framework 600 can include a computing system 602. In one or more examples, the computing system 602 can perform at least a portion of the operations described with respect to at least one of the computing system 214 of Figure 2 and Figure 3, the computing system 410 of Figure 4, or the computing system 510 of Figure 5. Additionally, the computing system 602 can include a training data analysis system 604. In various examples, the training data analysis system 604 can perform at least a portion of the operations described with respect to the training data analysis system 416 of Figure 4 and the training data analysis system 512 of Figure 5.

[00299] Training sample methylation and sequencing data 606 can be accessed by the computing system 602. The training sample methylation and sequencing data 606 can include sequence representations of nucleic acid molecules derived from samples obtained from a plurality of subjects. The training sample methylation and sequencing data 606 can also include methylation data indicating methylation states of nucleotides of the nucleic acid molecules. In one or more illustrative examples, the training sample methylation and sequencing data 606 can indicate methylation states of cytosines of the nucleic acid molecules. In one or more additional illustrative examples, the training sample methylation and sequencing data 606 can indicate methylated cytosines of the nucleic acid molecules. In one or more further illustrative examples, the training sample methylation and sequencing data 606 can include sequencing representations and methylation state data of nucleic acid molecules having one or more CG regions with at least a threshold amount of methylation. For example, the training sample methylation and sequencing data 606 can include sequence representations that correspond to nucleic acid molecules that are identified as being included in a hypermethylated partition. A first portion of the training sample methylation and sequencing data 606 can include sequence representations and methylation states of nucleic acid molecules derived from first samples obtained from first subjects in which a tumor is detected. A second portion of the training sample methylation and sequencing data 606 can include sequence representations and methylation states of nucleic acid molecules derived from second samples obtained from second subjects in which a tumor is not detected.

[00300] In one or more examples, the training data analysis system 604 can analyze the training sample methylation and sequencing data 606 to determine residual positive training samples data 608 and negative training samples data 610. The training data analysis system 604 can also generate in-band positive training samples data 612. The residual positive training samples data 608 can include sequence representations and methylation data that correspond to nucleic acid molecules having a quantitative measure that is outside of a specified quantitative measure range and derived from samples obtained from subjects in which a tumor is detected. The negative training samples data 610 can include sequence representations and methylation data that correspond to nucleic acid molecules derived from samples obtained from subjects in which a tumor is not detected. In addition, the in-band positive training samples data 612 can include sequence representations and methylation data that correspond to nucleic acid molecules having a quantitative measure that is within the specified quantitative measure range and that are derived from samples obtained from subjects in which a tumor is detected. In one or more illustrative examples, the specified quantitative measure range can correspond to a range of mutant allele fraction values.

[00301] The computing system 602 can also include an in silico sample system 614 that generates in silico training samples 616. The in silico sample system 614 can analyze the residual positive training samples data 608 and the negative training samples data 610 to generate the in silico training samples 616. In one or more examples, the in silico sample system 614 can combine at least one of first quantitative measures or first sequence representations corresponding to first nucleic acid molecules represented in the residual positive training samples data 608 with at least one of second quantitative measures or second sequence representations corresponding to second nucleic acid molecules represented in the negative training samples data 610. In one or more illustrative examples, the in silico sample system 614 can combine a first portion of data from one or more first samples corresponding to the residual positive training samples date 608 with a second portion of data from one or more second samples corresponding to the negative training samples data 610 to produce one or more in silico training samples 616 having quantitative measures within the specified quantitative measure range. In various examples, the in silico sample system 614 can combine a first portion of data from one or more first samples corresponding to the residual positive training samples date 608 with a second portion of data from one or more second samples corresponding to the negative training samples data 610 to reduce one or more values of the quantitative measure for one or more samples corresponding to the residual positive training samples data 608 to produce in silico training samples 616 having modified quantitative measures values within the specified quantitative measure range.

[00302] In one or more additional illustrative examples, for a given in silico training sample 616, a proportion of one or more residual positive training samples that is combined with a proportion of one or more negative training samples can be 5/95, 10/90, 15/85, 20/80, 25/75, 30/70, 35/65, 40/60, 45/55, or 50/50. In various illustrative examples, an amount of one or more residual positive training samples that is combined with one or more negative training samples can be a numerical value that can be represented by a percentage value, a fraction, or a decimal value less than 1. In one or more further illustrative examples, the in silico training samples 616 can have sequence representations that correspond to the proportion of the one or more residual positive training samples that is combined with a proportion of one or more negative training samples. To illustrate, an individual in silico training sample 616 can be generated by combining a first residual positive sample and a first negative training sample. In situations where the proportion of amount of data of the first residual positive sample and the first negative training sample is 20/80, the in silico training sample 616 can have 20% of the sequence representation of the first positive training sample and 80% of the sequence representation of the first negative training sample. In still other examples, the in silico training sample 616 can have 5.275% of the sequence representation of the first positive training sample and 94.725% of the sequence representation of the first negative training sample. In one or more additional illustrative implementations, the in silico training sample 616 can have 4.725% of the sequence representation of a first positive training sample, 5.370% of the sequence representation of a second positive training sample, and 89.905% of a negative training sample In this way, the in silico training samples 616 can represent a hybrid of one or more residual positive training samples and one or more negative training samples.

[00303] The computing system 602 can include a quantitative measures model 618 that analyzes the in silico training samples 616 to generate in silico training samples data 620. In one or more examples, the quantitative measures model 618 can generate quantitative measures included in the in silico training samples data 620 that correspond to the in silico training samples 616. In this way, the in silico training samples data 620 can include at least one of a sequence representation or a quantitative measure that corresponds to individual in silico training samples 616. In one or more illustrative examples, the quantitative measures model 618 can generate mutant allele fraction values for the individual in silico training samples 616.

[00304] In various examples, the in silico training samples data 620 can be used in conjunction with the negative samples training data 610 and the in-band positive samples training data 612 to generate a classification computational model 622. For example, the in silico training samples data 620, the negative samples training data 610, and the in- band positive samples training data 612 can be used in a training process for the classification computational model 622. In at least some examples, the training process for the classification computational model 622 can the same as or similar to the training process of the second computational model described with respect to Figures 4 and 5. In one or more illustrative examples, the classification computational model 622 can produce an output that includes an indication of cancer for a given subject. In at least some examples, the indication of cancer for a given subject can include in indication that cancer is present in a subject or an indication that cancer is absent in a subject. The indication of cancer for the given subject can also include at least one of a probability of cancer being present in the given subject or a tumor fraction for the given subject. In one or more additional examples, the indication of cancer for a given subject can correspond to a stage of cancer present in a subject and/or one or more types of cancer.

[00305] In this way, the framework 600 can implement at least three models to generate the classification computational model 622. For example, a first model can be implemented to determine quantitative measures for at least a portion of the samples obtained from subjects in which cancer is present. The training data analysis system 604 can use the quantitative measures generated by the first model to determine the residual positive trainings samples data 608 and the in-band positive training samples data 612. In one or more illustrative examples, the first model can correspond to the first computational model 412 described with respect to Figure 4. The second model can correspond to the quantitative measures model 618. The quantitative measures model 618 can include a quantitative measures generator that determines quantitative measures for individual samples. The quantitative measures model 618 can be trained on data that is at least partially different from the data used to train the first model. In various examples, the quantitative measures model 618 is not a classification model and does not generate an indication of cancer for a given subject. Further, the third model can comprise the classification computational model 622. In these scenarios, the classification computational model 622 determine an indication of cancer for one or more subjects based on the information generated by the first model and the second model.

[00306] Figure 7 is a flowchart of an example method 700 to determine tumor metrics in a subject based on levels of methylation of classification regions, according to one or more implementations. At operation 702, the method 700 can include obtaining training sequence data including training sequencing reads derived from a plurality of samples of a plurality of subjects. Individual training sequencing reads can include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples. Individual training sequencing reads can have a threshold amount of molecules with a methylated cytosine included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content. In one or more illustrative examples, the plurality of samples can include cell-free nucleic acids. In one or more examples, methylated cytosines can be determined using at least one of (i) sodium bisulfite conversion and sequencing, (ii) Tet-assisted bisulfite sequencing (TAB-Seq), differential enzymatic cleavage, (iii)MBD partitioning, and/or treatment with MSRE and/or MDRE, or (iv) other conversion procedures using enzymes - e.g., Enzymatic Methyl Sequencing (EM-Seq), Direct Methylation Sequencing (DM-Seq) or single-enzyme 5- methylcytosine sequencing (SEM-seq)-. In one or more additional examples, methylated cytosines can be determined using one or more single molecule sequencing methods, such as nanopore DNA sequencing or those described in Eid, J., et al. (2009) Real-time DNA sequencing from single polymerase molecules. Science, 323(5910), 133-138.

[00307] In one or more examples, the training process can include obtaining, by the computing system, testing sequence data from an additional subject that is not included in the plurality of subjects. The testing sequence data can include testing sequencing reads derived from a sample of the additional subject. Individual testing sequencing reads can include a nucleotide sequence corresponding to a fragment of a nucleic acid included in the additional sample. Additionally, individual testing sequencing reads can have at least the threshold amount of molecules with a methylated cytosine included in regions of the nucleotide sequence having at least the threshold cytosine-guanine content. Based on the additional sequence data, a model can be executed to determine the indication of cancer being present in the additional subject. The testing sequencing reads can then be analyzed to determine a first quantitative measure derived from the testing sequencing reads that correspond to the individual classification regions of the plurality of classification regions. Further, the testing sequencing reads can be analyzed to determine a second quantitative measure derived from the testing sequencing reads that correspond to the individual control regions the plurality of control regions. The metric can then be determined for the individual classification regions based on the first quantitative measure for the individual classification regions and the second quantitative measure for the plurality of control regions. Subsequently, an input vector can be generated that includes the metrics for the individual classification regions. The model can use the input vector to determine the indication of cancer being present in the additional subject.

[00308] In situations where the model is trained to determine an estimate of tumor fraction, the training sequencing reads can comprise a first portion of the training sequence data and a second portion of the training sequence data includes additional training sequencing reads that are different from the training sequencing reads. In these scenarios, at least one of the first portion of the training sequence data or the second portion of the training sequence data can be analyzed to determine an individual frequency of a plurality of variants present in individual samples of the plurality of samples. With respect to individual samples, a variant of the plurality of variants having a maximum frequency can then be determined that corresponds to the individual frequency having a greatest value among individual frequencies derived from an individual sample. In one or more illustrative examples, the maximum mutant allele frequency can be determined for individual samples. In various examples, individual measures of tumor fraction for the individual samples can then be determined based on the greatest value of the individual frequencies derived from the individual sample.

[00309] In at least some examples, the training process for the model can include one or more optimization operations. For example, the training process can include determining one or more additional weights of individual samples included in the training data based on the indication of cancer for the individual samples being within a threshold confidence level. In response to determining that the indication of cancer for an individual sample is outside of the threshold confidence level a penalty to can be applied to the individual sample during the training process.

[00310] The one or more training optimization operations can also include performing, using the one or more machine learning algorithms, one or more first iterations of the training process for the model using a portion of the training data. In addition, first output data for the model can be generated based on the one or more first iterations of the training process. The first output data can correspond to one or more first additional indications of cancer being present in first individual subjects of the plurality of subjects and the first individual subjects can correspond to the portion of the training data. Further, the training process can include combining the first output data and the training data to produce additional training data and performing one or more second iterations of the training process for the model using a portion of the additional training data. Second output data can then be generated for the model based on the one or more second iterations of the training process. The second output data can indicate one or more second additional indications of cancer being present in second individual subjects of the plurality of subjects where the second individual subjects corresponding to the portion of the additional training data. In one or more illustrative examples, the weights for the individual classification regions of the plurality of classification regions can be determined based on the first output data and the second output data.

[00311] Further, the training process can include determining that a number of indications of cancer are present that were determined during one or more iterations of the training process and have at least a threshold value for one or more samples included in the training data. In these scenarios, modifications to one or more weights of the model are not modified or are modified by a minimal amount. Additionally, an additional number of indications of cancer being present can be determined that were determined during the one or more iterations of the training process and are less than the threshold value for one or more additional samples included in the training data. In these scenarios, modifications to one or more additional weights of the model can be determined and the one or more additional weights are modified by more than the minimal amount.

[00312] In addition, at operation 704, the process 700 can include analyzing the training sequencing reads to determine a first quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions. In one or more examples, the first quantitative measure can be determined based on the number of training sequencing reads. In one or more additional examples, the first quantitative measure can be determined based on a number of polynucleotide molecules that correspond to the training sequencing reads. At least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of molecules with a methylated cytosine in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content. In various examples, the plurality of classification regions can correspond to genomic regions in which at least one mutation occurs in patients in which cancer is detected. Additionally, the plurality of classification regions can correspond to a first plurality of classification regions for a first cancer type and the model can be generated for a second cancer type based on a second plurality of classification regions that are different from the first plurality of classification regions.

[00313] At operation 706, the process 700 can include analyzing the training sequencing reads to determine a second quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions. In one or more examples, the second quantitative measure can be determined based on the number of training sequencing reads. In one or more additional examples, the second quantitative measure can be determined based on a number of polynucleotide molecules that correspond to the training sequencing reads. Individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content. Additionally, the individual control regions can have at least the threshold amount of molecules with a methylated cytosine in subjects in which cancer is detected and in additional subjects in which cancer is not detected. [00314] Further, at operation 708, the process 700 can include determining a metric for the individual classification regions of the plurality of classification regions based on the first quantitative measure for the individual classification regions and the second quantitative measure for the plurality of control regions. In one or more examples, the metric for the individual classification regions is determined based on a scaling factor and an error correction factor. In one or more illustrative examples, the scaling factor can include a logarithmic function and the error correction factor can include a pseudocount. [00315] At operation 710, the process 700 can include generating, by the computing device, training data that includes the metric for the individual classification regions of the plurality of classification regions for the training sequence reads. In implementations where the indication of cancer is tumor fraction, the training data can include the individual measures of tumor fraction for the individual samples of the plurality of samples and the model can be executed with respect to individual measures of tumor fraction for the individual samples of the plurality of samples.

[00316] The process 700 can also include, at operation 712, implementing, using the training data, one or more machine learning algorithms to generate a model to determine an indication of cancer being present in subjects based on amounts of molecules with methylated cytosines in at least a portion of the plurality of classification regions. The model can determine weights for individual classification regions of the plurality of classification regions and at least a portion of the weights of the individual classification regions can be different from one another. In various examples, the one or more machine learning algorithms can include one or more classification algorithms and the indication of cancer being present corresponds to a probability of cancer being present in the additional subject. In one or more additional examples, the one or more machine learning algorithms include one or more regression algorithms and the indicator corresponds to an estimate of tumor fraction of the additional sample. In one or more illustrative examples, a limit of detection for the model to determine tumor fraction of samples can be no greater than 0.01 % given 95% sensitivity, no greater than 0.05% given 95% sensitivity, no greater than 0.1% given 95% sensitivity, no greater than 0.15% given 95% sensitivity, no greater than 0.2% given 95% sensitivity, no greater than 0.25% given 95% sensitivity, or no greater than 0.3% given 95% sensitivity. [00317] In various examples, the sequence reads provided to the model during the training process or after the training process have at least a threshold amount of methylated cytosines in classification regions. The sequence reads that satisfy the methylation levels can be produced, at least in party, using one or more molecule separation processes. The molecule separation processes can include combining a plurality of nucleic acids derived from at least one of blood or tissue of a subject with a solution including an amount of methyl binding domain (MBD) proteins to produce a nucleic acid-MBD protein solution. A plurality of washes can then be performed of the nucleic acid-MBD protein solution with a salt solution to produce a number of nucleic acid fractions. Individual nucleic acid fractions can have a threshold number of molecules with a methylated cytosine in regions of the plurality of nucleic acids having at least the threshold cytosine-guanine content. In one or more illustrative examples, a wash of the plurality of washes can be performed with a solution having a concentration of sodium chloride (NaCI) and can produce a nucleic acid fraction of the number of nucleic acid fractions having a range of binding strengths to MBD proteins.

[00318] In one or more examples, a first nucleic acid fraction can be determined is associated with a first partition of a plurality of partitions of nucleic acids. The first partition corresponding to a first range of binding strengths to MBD proteins. Further, a first molecular barcode can be attached to nucleic acids of the first nucleic acid fraction. The first molecular barcode can be associated with the first partition. In addition, a second nucleic acid fraction can be determined that is associated with a second partition of the plurality of partitions of nucleic acids. The second partition can correspond to a second range of binding strengths to MBD proteins different from the first range of binding strengths to MBD proteins. A second molecular barcode can be attached to nucleic acids of the second nucleic acid fraction. The second molecular barcode being associated with the second partition.

[00319] In one or more additional examples, at least a portion of the number of nucleic acid fractions can be combined with an amount of restriction enzyme that cleaves molecules with one or more unmethylated cytosines to produce at least a portion of the plurality of samples used to produce the sequencing reads. In these scenarios, the threshold amount of molecules with a methylated cytosine corresponds to a minimum frequency of molecules with a methylated cytosine within a region having at least the threshold cytosine-guanine content. In one or more further examples, at least a portion of the number of nucleic acid fractions are combined with an amount of a restriction enzyme that cleaves molecules with a methylated cytosine to produce at least a portion of the plurality of samples used to produce the sequencing reads. In these situations, the threshold amount of molecules with a methylated cytosine corresponds to a maximum frequency of molecules with a methylated cytosine within a region having at least the threshold cytosine-guanine content.

[00320] Figure 8 is a flowchart of an example method 800 to train a computational model that generates one or more indications of tumors being present in one or more subjects, according to one or more implementations. At operation 802, the method 800 can include obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects. In one or more examples, a tumor is detected in the first plurality of subjects. Additionally, individual training sequencing reads correspond to molecules can have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine- guanine content.

[00321] In addition, the method 800 can include, at operation 804, determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples. In one or more examples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples.

[00322] The method 800 can also include, at operation 806, analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values. Further, at operation 808, the method 800 can include determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present.

[00323] In still other examples, the method 800 can include, at operation 810, obtaining a second group of training samples derived from a second plurality of subjects, wherein a tumor is not detected with respect to the second plurality of subjects. At operation 812, the method can include performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model. In one or more illustrative examples, the second computational model can implement a regression model. For example, the second computational model can include a linear regression model, a logistic regression model, a polynomial regression model, a lasso regression model, or a ridge regression model. The training process for the second computational model can include a first iteration. The first iteration can include determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values. The first iteration can also include determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples. Further, the first iteration can include determining an initial version of the second computational model based on the first training data and the second training data.

[00324] The training process of the second computational model can also include analyzing the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent. The initial version of the second computation model can then determine, based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples. Third training data can also be obtained that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples.

[00325] The training process of the second computational model can further include at least a second iteration that comprises determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data. Based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure can be determined. A threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples can then be determined and one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value can then be identified. In one or more examples, the respective additional individual values of the quantitative measure can be modified to correspond to the threshold value in the third training data.

[00326] In various examples, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects can be determined. The first weights can be based on a first number of the plurality of samples. Additionally, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects can be determined. The second weights can be determined based on a second number of the second group of training samples and an additional weighting factor.

[00327] In one or more illustrative examples, the second computational model can be trained using a loss function. The loss function can include a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function In at least some examples, the training process of the second computational model can include a plurality of iterations and individual iterations of the plurality of iterations can be stopped before convergence of the Huber loss function.

[00328] Additionally, at operation 814, the method 800 can include analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[00329] In various examples, the indication of cancer being present in a test subject can be analyzed with respect to a threshold value. For example, the indication of cancer being present generated by a trained version of the second computational model can include a probability of a type of cancer being present in the test subject. In these scenarios, the probability generated by the second computational model can be analyzed with respect to a threshold probability of the cancer type being present in a test subject. In addition, the indicated of cancer being present generated by a trained version of the second computational model can include a tumor fraction. In these instances, the tumor fraction produced by the second computational model can be analyzed with respect to a threshold tumor fraction. In at least some examples, the threshold value for the indication can be determined by analyzing at least one of sequencing data or methylation data derived from samples obtained from subjects in which cancer is not present. In one or more examples, the threshold value can be determined such that the trained version of the second computational model has a specificity of at least about 80%, at least about 82%, at least about 85%, at least about 88%, at least about 90%, at least about 92%, at least about 95%, at least about 98%, or at least about 99%.

[00330] In at least some examples, the second computational model can be included in a plurality of computational models that determine indications of cancer being present in individuals. In these scenarios, a plurality of groupings of the training data can be determined. Individual groupings of the plurality of groupings of the training data can include a training portion and a validation portion. Training processes for the plurality of computational models can be performed using the plurality of groupings of the training data. In these situations, determining indications of cancer being present in one or more subjects can include performing one or more statistical operations based on output from each computational model of the plurality of computational models. In one or more illustrative examples, the one or more statistical operations can include computing an average of variable weights or other parameters for the plurality of computational models. [00331] In one or more examples, a plurality of types of cancer can be detected in the first plurality of subjects. In these instances, the second computational model can determine a plurality of indications of cancer being present in the one or more test subjects. The individual indications of cancer being present in the one or more test subjects can correspond, to an individual type of cancer of the plurality of types of cancer. In one or more additional examples, a single type of cancer can be detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects can correspond to the single type of cancer. In one or more further examples, the indication of cancer being present in the one or more test subjects can includes a first result indicating a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects. In still other examples, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[00332] In one or more additional examples, a number of quantitative measures can be determined during the training process for the second computational model and for determining the indication of cancer being present in the test subject. In various examples, sequencing data can be analyzed to determine the number of quantitative measures. The sequencing data can include individual sequencing reads that include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of one or more samples. To determine the quantitative measures, the sequencing reads can be analyzed to determine a first region quantitative measure derived from the sequencing reads that corresponds to individual classification regions of a plurality of classification regions. At least a portion of the individual classification regions of the plurality of classification regions can correspond to genomic regions of a reference genome that have a threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least a threshold cytosine-guanine content. The sequencing reads can also be analyzed to determine a second region quantitative measure derived from the sequencing reads that correspond to a plurality of control regions. Individual control regions of the plurality of control regions can correspond to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected. Further, a metric for the individual classification regions of the plurality of classification regions can be determined based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions. The individual values of the quantitative measure for individual samples of the plurality of samples can be determined based on the metric for the individual classification regions.

EXEMPLARY METHODS A. Determining an indication of cancer in a sample

[00333] A method includes obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects. A tumor may be detected in the first plurality of subjects. The method may also include determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples. The individual values of the quantitative measure may indicate an amount of mutant alleles present in first nucleic acids of the individual samples. The method may also include analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values. The method may also include determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present. The method may also include obtaining a second group of training samples derived from a second plurality of subjects. A tumor may not be detected with respect to the second plurality of subjects. The method may also include performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model. The method may also include analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[00334] A computing apparatus may include a processor and memory storing instructions that, when executed by the processor, configure the apparatus to obtain training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects. A tumor may be detected in the first plurality of subjects. The computing apparatus may also determine, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples. The individual values of the quantitative measure may indicate an amount of mutant alleles present in first nucleic acids of the individual samples. The computing apparatus may also analyze the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values. The computing apparatus may also determine a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present. The computing apparatus may also obtain a second group of training samples derived from a second plurality of subjects. A tumor may not be detected with respect to the second plurality of subjects. The computing apparatus may also perform a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model. The computing apparatus may also analyze, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[00335] In one or more aspects, a non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to perform operations comprising obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects. A tumor may not be detected in the first plurality of subjects. The operations may also include determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples. The individual values of the quantitative measure may indicate an amount of mutant alleles present in first nucleic acids of the individual samples. The operations may also include analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values. The operations may also include determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present. The operations may also include obtaining a second group of training samples derived from a second plurality of subjects. A tumor may not be detected with respect to the second plurality of subjects. The operations may also include performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model. The operations may also include analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

B. Partitioning the sample into a plurality of subsamples

[00336] In some embodiments described herein, different forms of DNA (e.g., hypermethylated and hypomethylated DNA) are physically partitioned based on one or more characteristics of the DNA. This approach can be used to determine, for example, whether certain sites or regions are hypermethylated or hypomethylated. Partitioning can be performed before attaching adapters to DNA molecules in the sample, e.g., so as to facilitate including partition tags in the adapters. Partition tags can be used to identify which partition a molecule was found in. Following partitioning (and attachment of adapters if applicable), further steps such as amplification, target capture, and sequencing may be performed.

[00337] Methylation profiling can involve determining methylation patterns across different regions of the genome. For example, after partitioning molecules based on extent of methylation (e.g., relative number of methylated nucleobases per molecule) and further steps as discussed above including sequencing, the sequences of molecules in the different partitions can be mapped to a reference genome. This can show regions of the genome that, compared with other regions, are more highly methylated or are less highly methylated. In this way, genomic regions, in contrast to individual molecules, may differ in their extent of methylation.

[00338] Partitioning nucleic acid molecules in a sample can increase a rare signal, e.g., by enriching rare nucleic acid molecules that are more prevalent in one partition of the sample. For example, a genetic variation present in hypermethylated DNA but less (or not) present in hypomethylated DNA can be more easily detected by partitioning a sample into hypermethylated and hypomethylated nucleic acid molecules. By analyzing multiple partitions of a sample, a multi-dimensional analysis of a single molecule can be performed and hence, greater sensitivity can be achieved. Partitioning may include physically partitioning nucleic acid molecules into partitions or subsamples based on the presence or absence of one or more methylated nucleobases. A sample may be partitioned into partitions or subsamples based on a characteristic that is indicative of differential gene expression or a disease state. A sample may be partitioned based on a characteristic, or combination thereof that provides a difference in signal between a normal and diseased state during analysis of nucleic acids, e.g., cell free DNA (cfDNA), non-cfDNA, tumor DNA, circulating tumor DNA (ctDNA) and cell free nucleic acids (cfNA). [00339] In some embodiments, hypermethylation and/or hypomethylation variable epigenetic target regions are analyzed to determine whether they show differential methylation characteristic of particular immune cell types, such as rare immune cell types, tumor cells or cells of a type that does not normally contribute to the DNA sample being analyzed (such as cfDNA).

[00340] In some instances, heterogeneous DNA in a sample is partitioned into two or more partitions (e.g., at least 3, 4, 5, 6 or 7 partitions). In some embodiments, each partition is differentially tagged. Tagged partitions can then be pooled together for collective sample prep and/or sequencing. The partitioning-tagging-pooling steps can occur more than once, with each round of partitioning occurring based on a different characteristic (examples provided herein), and tagged using differential tags that are distinguished from other partitions and partitioning means. In other instances, the differentially tagged partitions are separately sequenced.

[00341] In some embodiments, sequence reads from differentially tagged and pooled DNA are obtained and analyzed in silico. Tags are used to sort reads from different partitions. Analysis to detect genetic variants can be performed on a partition-by-partition level, as well as whole nucleic acid population level. For example, analysis can include in silico analysis to determine genetic variants, such as CNV, SNV, indel, fusion in nucleic acids in each partition. In some instances, in silico analysis can include determining chromatin structure. For example, coverage of sequence reads can be used to determine nucleosome positioning in chromatin. Higher coverage can correlate with higher nucleosome occupancy in genomic region while lower coverage can correlate with lower nucleosome occupancy or nucleosome depleted region (NDR).

[00342] In some embodiments, partitioning is on the basis of one or more characteristics such as methylation. Molecules can be sorted according to other characteristics, such as sequence length, nucleosome binding, sequence mismatch, immunoprecipitation, and/or proteins that bind to DNA, using appropriate techniques as part of data analysis or partitioning as applicable. Resulting partitions can include one or more of the following nucleic acid forms: single-stranded DNA (ssDNA), double-stranded DNA (dsDNA), shorter DNA fragments and longer DNA fragments. In some embodiments, partitioning based on a cytosine modification (e.g., cytosine methylation) or methylation generally is performed and is optionally combined with at least one additional partitioning step, which may be based on any of the foregoing characteristics or forms of DNA. In some embodiments, a heterogeneous population of nucleic acids is partitioned into nucleic acids with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include presence or absence of methylation; level of methylation; type of methylation (e.g., 5- methylcytosine versus other types of methylation, such as adenine methylation and/or cytosine hydroxymethylation); and association and level of association with one or more proteins, such as histones. Alternatively, or additionally, a heterogeneous population of nucleic acids can be partitioned into nucleic acid molecules associated with nucleosomes and nucleic acid molecules devoid of nucleosomes. Alternatively, or additionally, a heterogeneous population of nucleic acids may be partitioned into single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA). Alternatively, or additionally, a heterogeneous population of nucleic acids may be partitioned based on nucleic acid length (e.g., molecules of up to 160 bp and molecules having a length of greater than 160 bp).

[00343] The agents used to partition populations of nucleic acids within a sample can be affinity agents, such as antibodies with the desired specificity, natural binding partners or variants thereof (Bock et al., Nat Biotech 28: 1106-1114 (2010); Song et al., Nat Biotech 29: 68-72 (2011 )), or artificial peptides selected e.g., by phage display to have specificity to a given target. In some embodiments, the agent used in the partitioning is an agent that recognizes a modified nucleobase. In some embodiments, the modified nucleobase recognized by the agent is a modified cytosine, such as a methylcytosine (e.g., 5-methylcytosine). In some embodiments, the modified nucleobase recognized by the agent is a product of a procedure that affects the first nucleobase in the DNA differently from the second nucleobase in the DNA of the sample. In some embodiments, the modified nucleobase may be a “converted nucleobase,” meaning that its base pairing specificity was changed by the procedure. For example, certain procedures convert unmethylated or unmodified cytosine to dihydrouracil, or more generally, at least one modified or unmodified form of cytosine undergoes deamination, resulting in uracil (considered a modified nucleobase in the context of DNA) or a further modified form of uracil. Examples of partitioning agents include antibodies, such as antibodies that recognize a modified nucleobase, which may be a modified cytosine, such as a methylcytosine (e.g., 5-methylcytosine). In some embodiments, the partitioning agent is an antibody that recognizes a modified cytosine other than 5-methylcytosine, such as 5- carboxylcytosine (5caC). Alternative partitioning agents include methyl binding domain (MBDs) and methyl binding proteins (MBPs) as described herein, including proteins such as MeCP2.

[00344] Additional, non-limiting examples of partitioning agents are histone binding proteins which can separate nucleic acids bound to histones from free or unbound nucleic acids. Examples of histone binding proteins that can be used in the methods disclosed herein include RBBP4, RbAp48 and SANT domain peptides.

[00345] The binding of partitioning agents to particular nucleic acids and the partitioning of the nucleic acids into subsamples may occur to a certain extent or may occur in an essentially binary manner. In some instances, nucleic acids comprising a greater proportion of a certain modification bind to the agent at a greater extent than nucleic acids comprising a lesser proportion of the modification. Similarly, the partitioning may produce subsamples comprising greater and lesser proportions of nucleic acids comprising a certain modification. Alternatively, the partitioning may produce subsamples comprising essentially all or none of the nucleic acids comprising the modification. In all instances, various levels of modifications may be sequentially eluted from the partitioning agent.

[00346] In some embodiments, partitioning can comprise both binary partitioning and partitioning based on degree/level of modifications. For example, methylated fragments can be partitioned by methylated DNA immunoprecipitation (MeDIP), or all methylated fragments can be partitioned from unmethylated fragments using methyl binding domain proteins (e.g., MethylMinder Methylated DNA Enrichment Kit (ThermoFisher Scientific). Subsequently, additional partitioning may involve eluting fragments having different levels of methylation by adjusting the salt concentration in a solution with the methyl binding domain and bound fragments. As salt concentration increases, fragments having greater methylation levels are eluted.

[00347] In some instances, the final partitions are enriched in nucleic acids having different extents of modifications (overrepresentative or underrepresentative of modifications). Overrepresentation and underrepresentation can be defined by the number of modifications born by a nucleic acid relative to the median number of modifications per strand in a population. For example, if the median number of 5- methylcytosine residues in nucleic acid in a sample is 2, a nucleic acid including more than two 5-methylcytosine residues is overrepresented in this modification and a nucleic acid with 1 or zero 5-methylcytosine residues is underrepresented. The effect of the affinity separation is to enrich for nucleic acids overrepresented in a modification in a bound phase and for nucleic acids underrepresented in a modification in an unbound phase (i.e., in solution). The nucleic acids in the bound phase can be eluted before subsequent processing.

[00348] When using MeDIP or MethylMiner®Methylated DNA Enrichment Kit (ThermoFisher Scientific) various levels of methylation can be partitioned using sequential elutions. For example, a hypomethylated partition (no methylation) can be separated from a methylated partition by contacting the nucleic acid population with the MBD from the kit, which is attached to magnetic beads. The beads are used to separate out the methylated nucleic acids from the non- methylated nucleic acids. Subsequently, one or more elution steps are performed sequentially to elute nucleic acids having different levels of methylation. For example, a first set of methylated nucleic acids can be eluted at a salt concentration of 160 mM or higher, e.g., at least 150 mM, at least 200 mM, 300 mM, 400 mM, 500 mM, 600 mM, 700 mM, 800 mM, 900 mM, 1000 mM, or 2000 mM. After such methylated nucleic acids are eluted, magnetic separation is once again used to separate higher level of methylated nucleic acids from those with lower level of methylation. The elution and magnetic separation steps can be repeated to create various partitions such as a hypomethylated partition (enriched in nucleic acids comprising no methylation), a methylated partition (enriched in nucleic acids comprising low levels of methylation), and a hyper methylated partition (enriched in nucleic acids comprising high levels of methylation).

[00349] In some methods, nucleic acids bound to an agent used for affinity separation-based partitioning are subjected to a wash step. The wash step washes off nucleic acids weakly bound to the affinity agent. Such nucleic acids can be enriched in nucleic acids having the modification to an extent close to the mean or median (i.e., intermediate between nucleic acids remaining bound to the solid phase and nucleic acids not binding to the solid phase on initial contacting of the sample with the agent).

[00350] The affinity separation results in at least two, and sometimes three or more partitions of nucleic acids with different extents of a modification. While the partitions are still separate, the nucleic acids of at least one partition, and usually two or three (or more) partitions are linked to nucleic acid tags, usually provided as components of adapters, with the nucleic acids in different partitions receiving different tags that distinguish members of one partition from another. The tags linked to nucleic acid molecules of the same partition can be the same or different from one another. But if different from one another, the tags may have part of their code in common so as to identify the molecules to which they are attached as being of a particular partition.

[00351] For further details regarding portioning nucleic acid samples based on characteristics such as methylation, see WO2018/119452, which is incorporated herein by reference.

[00352] In some embodiments, the nucleic acid molecules can be fractionated into different partitions based on the nucleic acid molecules that are bound to a specific protein or a fragment thereof and those that are not bound to that specific protein or fragment thereof.

[00353] Nucleic acid molecules can be fractionated based on DNA-protein binding. Protein-DNA complexes can be fractionated based on a specific property of a protein. Examples of such properties include various epitopes, modifications (e.g., histone methylation or acetylation) or enzymatic activity. Examples of proteins which may bind to DNA and serve as a basis for fractionation may include, but are not limited to, protein A and protein G. Any suitable method can be used to fractionate the nucleic acid molecules based on protein bound regions. Examples of methods used to fractionate nucleic acid molecules based on protein bound regions include, but are not limited to, SDS-PAGE, chromatin-immuno-precipitation (ChIP), heparin chromatography, and asymmetrical field flow fractionation (AF4).

[00354] In some embodiments, the partitioning of the sample into a plurality of subsamples is performed by contacting the nucleic acids with an antibody that recognizes a modified nucleobase in the DNA, which may be is a modified cytosine or a product of the procedure that affects the first nucleobase in the DNA differently from the second nucleobase in the DNA of the sample. In some embodiments, the modified nucleobase is 5mC. In some embodiments, the modified nucleobase is 5caC. In some embodiments, the modified nucleobase is dihydrouracil (DHU). In some embodiments, the antibody that recognizes a modified nucleobase in the DNA is used to partition single-stranded DNA.

[00355] In some embodiments, the partitioning is performed by contacting the nucleic acids with a methyl binding domain (“MBD”) of a methyl binding protein (“MBP”). In some such embodiments, the nucleic acids are contacted with an entire MBP. In some embodiments, an MBD binds to 5-methylcytosine (5mC), and an MBP comprises an MBD and is referred to interchangeably herein as a methyl binding protein or a methyl binding domain protein. In some embodiments, an MBD binds to 5mC and 5hmC. In some embodiments, MBD is coupled to paramagnetic beads, such as Dynabeads® M-280 Streptavidin via a biotin linker. Partitioning into fractions with different extents of methylation can be performed by eluting fractions by increasing the NaCI concentration.

[00356] In some embodiments, bound DNA is eluted by contacting the antibody or MBD with a protease, such as proteinase K. This may be performed instead of or in addition to elution steps using NaCI as discussed above.

[00357] Examples of agents that recognize a modified nucleobase contemplated herein include, but are not limited to:

(a) MeCP2 is a protein that preferentially binds to 5-methyl-cytosine over unmodified cytosine.

(b) RPL26, PRP8 and the DNA mismatch repair protein MHS6 preferentially bind to 5- hydroxymethyl-cytosine over unmodified cytosine.

(c) FOXK1 , FOXK2, FOXP1 , FOXP4 and FOXI3 preferably bind to 5-formyl cytosine over unmodified cytosine (lurlaro et al., Genome Biol. 14: R119 (2013)). (d) Antibodies specific to one or more methylated or modified nucleobases or conversion products thereof, such as 5mC, 5caC, or DHU.

[00358] In general, elution is a function of the number of modifications, such as the number of methylated sites per molecule, with molecules having more methylation eluting under increased salt concentrations. To elute the DNA into distinct populations based on the extent of methylation, one can use a series of elution buffers of increasing NaCI concentration. Salt concentration can range from about 100 nm to about 2500 mM NaCI. In one embodiment, the process results in three (3) partitions. Molecules are contacted with a solution at a first salt concentration and comprising a molecule comprising an agent that recognizes a modified nucleobase, which molecule can be attached to a capture moiety, such as streptavidin. At the first salt concentration a population of molecules will bind to the agent and a population will remain unbound. The unbound population can be separated as a “hypomethylated” population. For example, a first partition enriched in hypomethylated form of DNA is that which remains unbound at a low salt concentration, e.g., 100 mM or 160 mM. A second partition enriched in intermediate methylated DNA is eluted using an intermediate salt concentration, e.g., between 100 mM and 2000 mM concentration. This is also separated from the sample. A third partition enriched in hypermethylated form of DNA is eluted using a high salt concentration, e.g., at least about 2000 mM.

[00359] In some embodiments, a monoclonal antibody raised against 5- methylcytidine (5mC) is used to purify methylated DNA. DNA is denatured, e.g., at 95°C in order to yield single-stranded DNA fragments. Protein G coupled to standard or magnetic beads as well as washes following incubation with the anti-5mC antibody are used to immunoprecipitate DNA bound to the antibody. Such DNA may then be eluted. Partitions may comprise unprecipitated DNA and one or more partitions eluted from the beads.

[00360] In some embodiments, sample DNA (e.g., between 5 and 200 ng) is mixed with methyl binding domain (MBD) buffer and magnetic beads conjugated with MBD proteins and incubated overnight. Methylated DNA (hypermethylated DNA) binds the MBD protein on the magnetic beads during this incubation. Non-methylated (hypomethylated DNA) or less methylated DNA (intermediately methylated) is washed away from the beads with buffers containing increasing concentrations of salt. For example, one, two, or more fractions containing non-methylated, hypomethylated, and/or intermediately methylated DNA may be obtained from such washes. Finally, a high salt buffer is used to elute the heavily methylated DNA (hypermethylated DNA) from the MBD protein. In some embodiments, these washes result in three partitions (hypomethylated partition, intermediately methylated fraction and hypermethylated partition) of DNA having increasing levels of methylation.

[00361] In some embodiments, partitioning procedures may result in imperfect sorting of DNA molecules among the subsamples. For example, a minority of the molecules in an unmethylated or hypomethylated subsample may be highly modified (e.g., hypermethylated), and/or a minority of the molecules in a hypermethylated subsample may be unmodified or mostly unmodified (e.g., unmethylated or mostly unmethylated). Such molecules are considered nonspecifically partitioned.

[00362] In some embodiments, nonspecifically partitioned molecules are removed using a methylation-dependent nuclease, e.g., a methylation dependent restriction enzyme (MDRE), digesting/cleaving the DNA where the restriction enzyme (RE) recognition site contains a methylated nucleotide but not cleaving the DNA where the restriction enzyme (RE) recognition site contains an unmethylated nucleotide. In some embodiments, nonspecifically partitioned molecules are removed using a methylation sensitive nuclease, e.g., a methylation sensitive restriction enzyme (MSRE), digesting/cleaving the DNA where the restriction enzyme (RE) recognition site contains an unmethylated nucleotide but not cleaving the DNA where the restriction enzyme (RE) recognition site contains a methylated nucleotide. For example, in some embodiments, a hypomethylated subsample is contacted with a methylation-dependent nuclease, such as a methylation-dependent restriction enzyme, thereby degrading nonspecifically partitioned DNA, e.g., methylated DNA, in the subsample. Alternatively, or in addition, a hypermethylated subsample is contacted with a methylation-sensitive endonuclease, such as a methylation-sensitive restriction enzyme, thereby degrading nonspecifically partitioned DNA in the subsample.

[00363] Degradation of nonspecifically partitioned DNA in one or more partitioned subsamples may improve the performance of methods that rely on accurate partitioning of DNA on the basis of a cytosine modification. For example, such degradation may provide improved sensitivity and/or simplify downstream analyses. In some embodiments, partitioning DNA on the basis of a modification, such as methylation, then removing nonspecifically partitioned DNA using MDREs and/or MSREs as described herein provides improved efficiency and/or cost over DNA analysis methods comprising procedures that affect a first nucleobase differently from a second nucleobase, such as bisulfite sequencing or bisulfite conversion.

[00364] In some embodiments, one or more nucleases are used to degrade nonspecifically partitioned DNA molecules. In some embodiments, a subsample is contacted with a plurality of nucleases. The subsample may be contacted with the nucleases sequentially or simultaneously. Simultaneous use of nucleases may be advantageous when the nucleases are active under similar conditions (e.g., buffer composition) to avoid unnecessary sample manipulation. Contacting a subsample with more than one methylation-dependent restriction enzyme can more completely degrade nonspecifically partitioned hypermethylated DNA. Contacting a subsample with more than one methylation-sensitive restriction enzyme can more completely degrade nonspecifically partitioned hypomethylated and/or unmethylated DNA.

[00365] In some embodiments, a methylation-dependent nuclease comprises one or more of MspJI, LpnPI, FspEI, or McrBC. In some embodiments, at least two methylation-dependent nucleases are used. In some embodiments, at least three methylation-dependent nucleases are used.

[00366] In some embodiments, a methylation-sensitive nuclease comprises one or more of Aatll, Accll, Acil, Aor13HI, Aor15HI, BspT104l, BssHII, BstUI, CfrIOl, Clal, Cpol, Eco52l, Haell, Hapll, Hhal, Hin6l, Hpall, HpyCH4IV, Mlul, Mspl, Nael, Notl, Nrul, Nsbl, PmaCI, Psp1406l, Pvul, Sacll, Sall, Smal, and SnaBI. In some embodiments, at least two methylation-sensitive nucleases are used. In some embodiments, at least three methylation-sensitive nucleases are used. In some embodiments, the methylation- sensitive nucleases comprise BstUI and Hpall. In some embodiments, the two methylation-sensitive nucleases comprise Hhal and Accll. In some embodiments, the methylation-sensitive nucleases comprise BstUI, Hpall and Hin6l. [00367] In some embodiments, the partitions of DNA are desalted and concentrated in preparation for enzymatic steps of library preparation.

C. Adapter Ligation

[00368] In some embodiments, adapters are added to the DNA. This may be done concurrently with an amplification procedure, e.g., by providing the adapters in a 5’ portion of a primer (where PCR is used, this can be referred to as library prep-PCR or LP-PCR). In some embodiments, adapters are added by other approaches, such as ligation. In some such methods, prior to partitioning or prior to capturing, first adapters are added to the nucleic acids by ligation to the 3’ ends thereof, which may include ligation to single- stranded DNA. The adapter can be used as a priming site for second-strand synthesis, e.g., using a universal primer and a DNA polymerase. A second adapter can then be ligated to at least the 3’ end of the second strand of the now double-stranded molecule. In some embodiments, the first adapter comprises an affinity tag, such as biotin, and nucleic acid ligated to the first adapter is bound to a solid support (e.g., bead), which may comprise a binding partner for the affinity tag such as streptavidin. For further discussion of a related procedure, see Gansauge et al., Nature Protocols 8:737-748 (2013). Commercial kits for sequencing library preparation compatible with single-stranded nucleic acids are available, e.g., the Accel-NGS® Methyl-Seq DNA Library Kit from Swift Biosciences. In some embodiments, after adapter ligation, nucleic acids are amplified.

[00369] Preferably, the adapters include different tags of sufficient numbers that the number of combinations of tags results in a low probability e.g., 95, 99 or 99.9% of two nucleic acids with the same start and stop points receiving the same combination of tags. Adapters, whether bearing the same or different tags, can include the same or different primer binding sites, but preferably adapters include the same primer binding site.

[00370] In some embodiments, following attachment of adapters, the nucleic acids are subject to amplification. The amplification can use, e.g., universal primers that recognize primer binding sites in the adapters.

[00371] In some embodiments, following attachment of adapters, the DNA is partitioned, comprising contacting the DNA with an agent that preferentially binds to nucleic acids bearing an epigenetic modification. The nucleic acids are partitioned into at least two subsamples differing in the extent to which the nucleic acids bear the modification from binding to the agents. For example, if the agent has affinity for nucleic acids bearing the modification, nucleic acids overrepresented in the modification (compared with median representation in the population) preferentially bind to the agent, whereas nucleic acids underrepresented for the modification do not bind or are more easily eluted from the agent. The nucleic acids can then be amplified from primers binding to the primer binding sites within the adapters. Partitioning may be performed instead before adapter attachment, in which case the adapters may comprise differential tags that include a component that identifies which partition a molecule occurred in. [0214] In some embodiments, the nucleic acids are linked at both ends to Y-shaped adapters including primer binding sites and tags. The molecules are amplified.

D. Tagging

[00372] “Tagging” DNA molecules is a procedure in which a tag is attached to or associated with the DNA molecules. Tags can be molecules, such as nucleic acids, containing information that indicates a feature of the molecule with which the tag is associated. For example, molecules can bear a sample tag (which distinguishes molecules in one sample from those in a different sample) or a molecular tag/molecular barcode/barcode (which distinguishes different molecules from one another (in both unique and non-unique tagging scenarios). For methods that involve a partitioning step, a partition tag (which distinguishes molecules in one partition from those in a different partition) may be included. In some embodiments, adapters added to DNA molecules comprise tags. In certain embodiments, a tag can comprise one or a combination of barcodes. As used herein, the term “barcode” refers to a nucleic acid molecule having a particular nucleotide sequence, or to the nucleotide sequence, itself, depending on context. A barcode can have, for example, between 10 and 100 nucleotides. A collection of barcodes can have degenerate sequences or can have sequences having a certain hamming distance, as desired for the specific purpose. So, for example, a molecular barcode can be comprised of one barcode or a combination of two barcodes, each attached to different ends of a molecule. Additionally, or alternatively, for different partitions and/or samples, different sets of molecular barcodes, or molecular tags can be used such that the barcodes serve as a molecular tag through their individual sequences and also serve to identify the partition and/or sample to which they correspond based the set of which they are a member.

[00373] In some embodiments, two or more partitions, e.g., each partition, is/are differentially tagged. Tags can be used to label the individual polynucleotide population partitions so as to correlate the tag (or tags) with a specific partition. Alternatively, tags can be used in embodiments that do not employ a partitioning step. In some embodiments, a single tag can be used to label a specific partition. In some embodiments, multiple different tags can be used to label a specific partition. In embodiments employing multiple different tags to label a specific partition, the set of tags used to label one partition can be readily differentiated for the set of tags used to label other partitions. In some embodiments, the tags may have additional functions, for example the tags can be used to index sample sources or used as unique molecular identifiers (which can be used to improve the quality of sequencing data by differentiating sequencing errors from mutations, for example as in Kinde et al., Proc Nat’l Acad Sci USA 108: 9530-9535 (2011 ), Kou et al., PLoS ONE, 11 : e0146638 (2016)) or used as non-unique molecule identifiers, for example as described in US Pat. No. 9,598,731 . Similarly, in some embodiments, the tags may have additional functions, for example the tags can be used to index sample sources or used as non-unique molecular identifiers (which can be used to improve the quality of sequencing data by differentiating sequencing errors from mutations).

[00374] In some embodiments, partition tagging comprises tagging molecules in each partition with a partition tag. After re-combining partitions (e.g., to reduce the number of sequencing runs needed and avoid unnecessary cost) and sequencing molecules, the partition tags identify the source partition. In some embodiments, the partition tags can serve as identifiers of the source partition and the molecule, i.e., different partitions are tagged with different sets of molecular tags, e.g., comprised of a pair of barcodes. In this way, the one or more molecular barcodes attached to the molecule indicates the source partition as well as being useful to distinguish molecules within a partition. For example, a first set of 35 barcodes can be used to tag molecules in a first partition, while a second set of 35 barcodes can be used tag molecules in a second partition.

[00375] In some embodiments, after partitioning and tagging with partition tags, the molecules may be pooled for sequencing in a single run. In some embodiments, a sample tag is added to the molecules, e.g., in a step subsequent to addition of partition tags and pooling. Sample tags can facilitate pooling material generated from multiple samples for sequencing in a single sequencing run.

[00376] Alternatively, in some embodiments, partition tags may be correlated to the sample as well as the partition. As a simple example, a first tag can indicate a first partition of a first sample; a second tag can indicate a second partition of the first sample; a third tag can indicate a first partition of a second sample; and a fourth tag can indicate a second partition of the second sample.

[00377] While tags may be attached to molecules already partitioned based on one or more characteristics, the final tagged molecules in the library may no longer possess that characteristic. For example, while single stranded DNA molecules may be partitioned and tagged, the final tagged molecules in the library are likely to be double stranded. Similarly, while DNA may be subject to partition based on different levels of methylation, in the final library, tagged molecules derived from these molecules are likely to be unmethylated. Accordingly, the tag attached to molecule in the library typically indicates the characteristic of the “parent molecule” from which the ultimate tagged molecule is derived, not necessarily to characteristic of the tagged molecule, itself.

[00378] As an example, barcodes 1 , 2, 3, 4, etc. are used to tag and label molecules in the first partition; barcodes A, B, C, D, etc. are used to tag and label molecules in the second partition; and barcodes a, b, c, d, etc. are used to tag and label molecules in the third partition. Differentially tagged partitions can be pooled prior to sequencing. Differentially tagged partitions can be separately sequenced or sequenced together concurrently, e.g., in the same flow cell of an Illumina sequencer.

[00379] After sequencing, analysis of reads can be performed on a partition-by- partition level, as well as a whole DNA population level. Tags are used to sort reads from different partitions. Analysis can include in silico analysis to determine genetic and epigenetic variation (one or more of methylation, chromatin structure, etc.) using sequence information, genomic coordinates length, coverage, and/or copy number. In some embodiments, higher coverage can correlate with higher nucleosome occupancy in genomic region while lower coverage can correlate with lower nucleosome occupancy or a nucleosome depleted region (NDR). E. Enriching/Capturing step; Amplification

[00380] Methods disclosed herein can comprise capturing DNA, such as cfDNA target regions. In some embodiments, the capturing comprises contacting the DNA with probes (e.g., oligonucleotides) specific for the target regions. Enrichment or capture may be performed on any sample or subsample described herein using any suitable approach known in the art.

[00381] In some embodiments, enrichment or capture is performed after attachment of adapters to sample molecules. In some embodiments, enrichment or capture is performed after a partitioning step. In some embodiments, enrichment or capture is performed after an amplification step. In some embodiments, sample molecules are partitioned, then adapters are attached, then sample molecules are amplified, and then the amplified molecules are subjected to enrichment or capture. The enriched or captured molecules may then be subjected to another amplification and then sequenced.

[00382] In some embodiments, the probes specific for the target regions comprise a capture moiety that facilitates the enrichment or capture of the DNA hybridized to the probes. In some embodiments, the capture moiety is biotin. In some such embodiments, streptavidin attached to a solid support, such as magnetic beads, is used to bind to the biotin. Nonspecifically bound DNA that does not comprise a target region is washed away from the captured DNA. In some embodiments, DNA is then dissociated from the probes and eluted from the solid support using salt washes or buffers comprising another DNA denaturing agent. In some embodiments, the probes are also eluted from the solid support by, e.g., disrupting the biotin-streptavidin interaction. In some embodiments, captured DNA is amplified following elution from the solid support. In some such embodiments, DNA comprising adapters is amplified using PCR primers that anneal to the adapters. In some embodiments, captured DNA is amplified while attached to the solid support. In some such embodiments, the amplification comprises use of a PCR primer that anneals to a sequence within an adapter and a PCR primer that anneals to a sequence within a probe annealed to the target region of the DNA.

[00383] In some embodiments, the methods herein comprise enriching for or capturing DNA comprising epigenetic and/or sequence-variable target regions. Such regions may be captured from an aliquot of a sample (e.g., a sample that has undergone attachment of adapters and amplification), while the step of partitioning the DNA with an agent that recognizes a modified cytosine, such as methyl cytosine, is performed on a separate aliquot of the sample. Enriching for or capturing DNA comprising epigenetic and/or sequence-variable target regions may comprise contacting the DNA with a first or second set of target-specific probes. Such target-specific probes may have any of the features described herein for sets of target-specific probes, including but not limited to in the embodiments set forth above and the sections relating to probes below. Capturing may be performed on one or more subsamples prepared during methods disclosed herein. In some embodiments, DNA is captured from the first subsample or the second subsample, e.g., the first subsample and the second subsample. In some embodiments, the subsamples are differentially tagged (e.g., as described herein) and then pooled before undergoing capture. Exemplary methods for capturing DNA comprising epigenetic and/or sequence-variable target regions can be found in, e.g., WO 2020/160414, which is hereby incorporated by reference.

[00384] The capturing step may be performed using conditions suitable for specific nucleic acid hybridization, which generally depend to some extent on features of the probes such as length, base composition, etc. Those skilled in the art will be familiar with appropriate conditions given general knowledge in the art regarding nucleic acid hybridization. In some embodiments, complexes of target-specific probes and DNA are formed.

[00385] In some embodiments, methods described herein comprise capturing a plurality of sets of target regions of cfDNA obtained from a subject. The target regions may comprise differences depending on whether they originated from a tumor or from healthy cells or from a certain cell type. The capturing step produces a captured set of cfDNA molecules. In some embodiments, cfDNA molecules corresponding to a sequence-variable target region set are captured at a greater capture yield in the captured set of cfDNA molecules than cfDNA molecules corresponding to an epigenetic target region set. In some embodiments, a method described herein comprises contacting cfDNA obtained from a subject with a set of target-specific probes, wherein the set of target-specific probes is configured to capture cfDNA corresponding to the sequence- variable target region set at a greater capture yield than cfDNA corresponding to the epigenetic target region set. For additional discussion of capturing steps, capture yields, and related aspects, see W02020/160414, which is incorporated herein by reference for all purposes.

[00386] It can be beneficial to capture cfDNA corresponding to the sequence- variable target region set at a greater capture yield than cfDNA corresponding to the epigenetic target region set because a greater depth of sequencing may be necessary to analyze the sequence-variable target regions with sufficient confidence or accuracy than may be necessary to analyze the epigenetic target regions. The volume of data needed to determine fragmentation patterns (e.g., to test for perturbation of transcription start sites or CTCF binding sites) or fragment abundance (e.g., in hypermethylated and hypomethylated partitions) is generally less than the volume of data needed to determine the presence or absence of cancer-related sequence mutations. Capturing the target region sets at different yields can facilitate sequencing the target regions to different depths of sequencing in the same sequencing run (e.g., using a pooled mixture and/or in the same sequencing cell).

[00387] In some embodiments, the DNA is amplified. In some embodiments, amplification is performed before the capturing step. In some embodiments, amplification is performed after the capturing step. In some embodiments, amplification is performed before and after the capturing step. In various embodiments, the methods further comprise sequencing the captured DNA, e.g., to different degrees of sequencing depth for the epigenetic and sequence-variable target region sets, consistent with the discussion herein.

[00388] In some embodiments, a capturing step is performed with probes for a sequence-variable target region set and probes for an epigenetic target region set in the same vessel at the same time, e.g., the probes for the sequence-variable and epigenetic target region sets are in the same composition. This approach provides a relatively streamlined workflow. In some embodiments, the concentration of the probes for the sequence-variable target region set is greater that the concentration of the probes for the epigenetic target region set. [00389] Alternatively, a capturing step is performed with a sequence-variable target region probe set in a first vessel and with an epigenetic target region probe set in a second vessel, or a contacting step is performed with a sequence-variable target region probe set at a first time and a first vessel and an epigenetic target region probe set at a second time before or after the first time. This approach allows for preparation of separate first and second compositions comprising captured DNA corresponding to a sequence- variable target region set and captured DNA corresponding to an epigenetic target region set. The compositions can be processed separately as desired (e.g., to partition based on methylation as described herein) and pooled in appropriate proportions to provide material for further processing and analysis such as sequencing.

[00390] In some embodiments, adapters are included in the DNA as described herein. In some embodiments, tags, which may be or include barcodes, are included in the DNA. In some embodiments, such tags are included in adapters. Tags can facilitate identification of the origin of a nucleic acid. For example, barcodes can be used to allow the origin (e.g., subject) whence the DNA came to be identified following pooling of a plurality of samples for parallel sequencing. This may be done concurrently with an amplification procedure, e.g., by providing the barcodes in a 5’ portion of a primer, e.g., as described herein. In some embodiments, adapters and tags/barcodes are provided by the same primer or primer set. For example, the barcode may be located 3’ of the adapter and 5’ of the target-hybridizing portion of the primer. Alternatively, barcodes can be added by other approaches, such as ligation, optionally together with adapters in the same ligation substrate.

[00391] Additional details regarding amplification, tags, and barcodes are discussed herein, which can be combined to the extent practicable with any of these embodiments.

F. Procedures that affect a first nucleobase in the DNA differently from a second nucleobase in the DNA or methylation-sensitive conversion methods

[00392] In some embodiments, methods disclosed herein comprise a step of subjecting DNA, or a subsample thereof, to a procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA, wherein the first nucleobase is a modified or unmodified nucleobase, the second nucleobase is a modified or unmodified nucleobase different from the first nucleobase, and the first nucleobase and the second nucleobase have the same base pairing specificity. In some embodiments, the procedure chemically converts the first or second nucleobase such that the base pairing specificity of the converted nucleobase is altered. In some embodiments, DNA is subjected to a procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA before library preparation using the DNA, before a first amplification of the DNA, before dividing the DNA into a plurality of subsamples, or any combination thereof. In certain embodiments, the DNA is subjected to the procedure before or after contacting the DNA with a methylation-sensitive nuclease.

[00393] In some embodiments, the procedure that affects a first nucleobase of the DNA differently from a second nucleobase of the DNA is performed prior to the sequencing and/or (a) prior to or after the selectively depleting the target nucleic acid comprising the wild-type sequence, the target nucleic acid comprising the converted nucleotide, or the target nucleic acid that does not comprise the converted nucleotide; (b) prior to the amplifying the selectively digested population of target nucleic acids; (c) prior to or after the partitioning the population of target nucleic acids into a plurality of subsamples; and/or (d) prior to or after a step of enriching for one or more sets of target regions of DNA.

[00394] In some embodiments, if the first nucleobase is a modified or unmodified adenine, then the second nucleobase is a modified or unmodified adenine; if the first nucleobase is a modified or unmodified cytosine, then the second nucleobase is a modified or unmodified cytosine; if the first nucleobase is a modified or unmodified guanine, then the second nucleobase is a modified or unmodified guanine; and if the first nucleobase is a modified or unmodified thymine, then the second nucleobase is a modified or unmodified thymine (where modified and unmodified uracil are encompassed within modified thymine for the purpose of this step).

[00395] In some embodiments, the first nucleobase is a modified or unmodified cytosine, then the second nucleobase is a modified or unmodified cytosine. For example, first nucleobase may comprise unmodified cytosine (C) and the second nucleobase may comprise one or more of 5-methylcytosine (mC) and 5-hydroxymethylcytosine (hmC). Alternatively, the second nucleobase may comprise C and the first nucleobase may comprise one or more of mC and hmC. Other combinations are also possible, such as where one of the first and second nucleobases comprises mC and the other comprises hmC.

[00396] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises bisulfite conversion. Treatment with bisulfite converts unmodified cytosine and certain modified cytosine nucleotides (e.g. 5-formyl cytosine (fC) or 5-carboxylcytosine (caC)) to uracil whereas other modified cytosines (e.g., 5-methylcytosine, 5-hydroxylmethylcystosine) are not converted. Thus, where bisulfite conversion is used, the first nucleobase comprises one or more of unmodified cytosine, 5-formyl cytosine, 5-carboxylcytosine, or other cytosine forms affected by bisulfite, and the second nucleobase may comprise one or more of mC and hmC, such as mC and optionally hmC. Sequencing of bisulfite-treated DNA identifies positions that are read as cytosine as being mC or hmC positions. Meanwhile, positions that are read as T are identified as being T or a bisulfite-susceptible form of C, such as unmodified cytosine, 5-formyl cytosine, or 5-carboxylcytosine. Performing bisulfite conversion, such as on a DNA sample as described herein, facilitates identifying positions containing mC or hmC using the sequence reads obtained from the exemplary sample. For an exemplary description of bisulfite conversion, see, e.g., Moss et al., Nat Commun. 2018; 9: 5068.

[00397] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises oxidative bisulfite (Ox- BS) conversion. This procedure first converts hmC to fC, which is bisulfite susceptible, followed by bisulfite conversion. Thus, when oxidative bisulfite conversion is used, the first nucleobase comprises one or more of unmodified cytosine, fC, caC, hmC, or other cytosine forms affected by bisulfite, and the second nucleobase comprises mC. Sequencing of Ox-BS converted DNA identifies positions that are read as cytosine as being mC positions. Meanwhile, positions that are read as T are identified as being T, hmC, or a bisulfite-susceptible form of C, such as unmodified cytosine, fC, or hmC. Performing Ox-BS conversion, such as on a DNA sample as described herein, thus facilitates identifying positions containing mC using the sequence reads obtained from the sample. For an exemplary description of oxidative bisulfite conversion, see, e.g., Booth et al., Science 2012; 336: 934-937.

[00398] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises Tet-assisted bisulfite (TAB) conversion. In TAB conversion, hmC is protected from conversion and mC is oxidized in advance of bisulfite treatment, so that positions originally occupied by mC are converted to U while positions originally occupied by hmC remain as a protected form of cytosine. For example, as described in Yu et aL, Cell 2012; 149: 1368-80, 0-glucosyl transferase can be used to protect hmC (forming 5-glucosylhydroxymethylcytosine (ghmC)), then a TET protein such as mTetl can be used to convert mC to caC, and then bisulfite treatment can be used to convert C and caC to U while ghmC remains unaffected. [00399] Alternatively, a carbamoyltransferase enzyme, such as 5- hydroxymethylcytosine carbamoyltransferase as described in Yang et al., Bio-protocol, 2023; 12(17): e4496, can be used to protect hmC (by converting hmC to 5- carbamoyloxymethylcytosine (5cmC)), then a TET protein such as mTetl or a TET2 comprising a T1372S mutation, can be used to convert mC to caC, and then bisulfite treatment can be used to convert C and caC to U while 5cmC remains unaffected. Thus, when TAB conversion is used, the first nucleobase comprises one or more of unmodified cytosine, fC, caC, mC, or other cytosine forms affected by bisulfite, and the second nucleobase comprises hmC. Sequencing of TAB-converted DNA identifies positions that are read as cytosine as being hmC positions. Meanwhile, positions that are read as T are identified as being T, mC, or a bisulfite-susceptible form of C, such as unmodified cytosine, fC, or caC. Performing TAB conversion, such as on a DNA sample as described herein, thus facilitates identifying positions containing hmC using the sequence reads obtained from the sample.

[00400] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises Tet-assisted conversion with a substituted borane reducing agent, optionally wherein the substituted borane reducing agent is 2-picoline borane, borane pyridine, tert-butylamine borane, or ammonia borane. In Tet-assisted pic-borane conversion with a substituted borane reducing agent conversion, a TET protein is used to convert mC and hmC to caC, without affecting unmodified C. caC, and fC if present, are then converted to dihydrouracil (DHU) by treatment with 2-picoline borane (pic-borane) or another substituted borane reducing agent such as borane pyridine, tert-butylamine borane, or ammonia borane, also without affecting unmodified C. See, e.g., Liu et al., Nature Biotechnology 2019; 37:424-429 (e.g., at Supplementary Fig. 1 and Supplementary Note 7). Thus, when this type of conversion is used, the first nucleobase comprises one or more of 5mC, 5fC, 5caC, or 5hmC, and the second nucleobase comprises unmodified cytosine. DHU is read as a T in sequencing. Thus, when this type of conversion is used, the first nucleobase comprises one or more of mC, fC, caC, or hmC, and the second nucleobase comprises unmodified cytosine. Sequencing of the converted DNA identifies positions that are read as cytosine as being unmodified C positions. Meanwhile, positions that are read as T are identified as being T, mC, fC, caC, or hmC. Performing TAP conversion, such as on a DNA sample as described herein, thus facilitates identifying positions containing unmodified C using the sequence reads obtained from the sample. This procedure encompasses Tet- assisted pyridine borane sequencing (TAPS), described in further detail in Liu et al. 2019, supra.

[00401] Alternatively, protection of hmC (e.g., using 0GT or 5- hydroxymethylcytosine carbamoyltransferase) can be combined with Tet-assisted conversion with a substituted borane reducing agent, e.g. as described above. In this method (TAPS-0), 5hmC can be protected from conversion, for example through glucosylation using 0-glucosyl transferase (PGT), forming 5- glucosylhydroxymethylcytosine (5ghmC), or through carbamoylation using 5- hydroxymethylcytosine carbamoyltransferase, forming 5cmC. This is described in Yu et aL, Cell 2012; 149: 1368-80. Treatment with a TET protein, such as mTetl or a TET2 comprising a T1372S mutation, then converts mC to caC but does not convert C, 5ghmC, or 5cmC. 5caC is then converted to DHU by treatment with pic-borane or another substituted borane reducing agent such as borane pyridine, tert-butylamine borane, or ammonia borane, also without affecting ghmC, 5cmC, or unmodified C. Thus, when Tet- assisted conversion with a substituted borane reducing agent is used, the first nucleobase comprises mC, and the second nucleobase comprises one or more of unmodified cytosine or hmC, such as unmodified cytosine and optionally hmC, fC, and/or caC. Sequencing of the converted DNA identifies positions that are read as cytosine as being either hmC or unmodified C positions. Meanwhile, positions that are read as T are identified as being T, fC, caC, or mC. Performing TAPSp conversion, such as on a DNA sample as described herein, thus facilitates distinguishing positions containing unmodified C or hmC on the one hand from positions containing mC using the sequence reads obtained from the sample. For an exemplary description of this type of conversion, see, e.g., Liu et al., Nature Biotechnology 2019; 37:424-429. 5-hydroxymethylcytosine carbamoyltransferase is described in Yang et aL, Bio-protocol, 2023; 12(17): e4496.

[00402] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises chemical-assisted conversion with a substituted borane reducing agent, optionally wherein the substituted borane reducing agent is 2-picoline borane, borane pyridine, tert-butylamine borane, or ammonia borane. In chemical-assisted conversion with a substituted borane reducing agent, an oxidizing agent such as potassium perruthenate (KRuO4) (also suitable for use in ox-BS conversion) is used to specifically oxidize hmC to fC. Treatment with pic-borane or another substituted borane reducing agent such as borane pyridine, tert-butylamine borane, or ammonia borane converts fC and caC to DHU but does not affect mC or unmodified C. Thus, when this type of conversion is used, the first nucleobase comprises one or more of hmC, fC, and caC, and the second nucleobase comprises one or more of unmodified cytosine or mC, such as unmodified cytosine and optionally mC. Sequencing of the converted DNA identifies positions that are read as cytosine as being either mC or unmodified C positions. Meanwhile, positions that are read as T are identified as being T, fC, caC, or hmC. Performing this type of conversion, such as on a DNA sample as described herein, thus facilitates distinguishing positions containing unmodified C or mC on the one hand from positions containing hmC using the sequence reads obtained from the sample. For an exemplary description of this type of conversion, see, e.g., Liu et al., Nature Biotechnology 2019; 37:424-429.

[00403] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises APOBEC-coupled epigenetic (ACE) conversion. In ACE conversion, an AID/APOBEC family DNA deaminase enzyme such as AP0BEC3A (A3A) is used to deaminate unmodified cytosine and mC without deaminating hmC, fC, or caC. Thus, when ACE conversion is used, the first nucleobase comprises unmodified C and/or mC (e.g., unmodified C and optionally mC), and the second nucleobase comprises hmC. Sequencing of ACE-converted DNA identifies positions that are read as cytosine as being hmC, fC, or caC positions. Meanwhile, positions that are read as T are identified as being T, unmodified C, or mC. Performing ACE conversion on a DNA sample as described herein thus facilitates distinguishing positions containing hmC from positions containing mC or unmodified C using the sequence reads obtained from the sample. For an exemplary description of ACE conversion, see, e.g., Schutsky et al., Nature Biotechnology 2018; 36: 1083-1090. [00404] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises enzymatic conversion of the first nucleobase, e.g., as in EM-Seq. See, e.g., Vaisvila R, et al. (2019) EM-seq: Detection of DNA methylation at single base resolution from picograms of DNA. bioRxiv; DOI: 10.1101/2019.12.20.884692, available at www.biorxiv.org/content/10.1101/2019.12.20.884692v1. For example, TET2 and T4-0GT or 5-hydroxymethylcytosine carbamoyltransferase (described in Yang et al., Bio-protocol, 2023; 12(17): e4496) can be used to convert 5mC and 5hmC into substrates that cannot be deaminated by a deaminase (e.g., APOBEC3A), and then a deaminase (e.g., APOBEC3A) can be used to deaminate unmodified cytosines converting them to uracils. [00405] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises enzymatic conversion of the first nucleobase using a non-specific, modification-sensitive double-stranded DNA deaminase, e.g., as in SEM-seq. See, e.g., Vaisvila et al. (2023) Discovery of novel DNA cytosine deaminase activities enables a nondestructive single-enzyme methylation sequencing method for base resolution high-coverage methylome mapping of cell-free and ultra-low input DNA. bioRxiv; DOI: 10.1101/2023.06.29.547047, available at https://www.biorxiv.org/content/10.1101/2023.06.29.547047v1. SEM-Seq employs a non-specific, modification-sensitive double-stranded DNA deaminase (MsddA) in a nondestructive single-enzyme 5-methylctyosine sequencing (SEM-seq) method that deaminates unmodified cytosines. Accordingly, SEM-seq does not require the TET2 and T4-0GT or 5-hydroxymethylcytosine carbamoyltransferase protection and denaturing steps that are of use, e.g., in APOEC3A-based protocols. Additionally, MsddA does not deaminate 5-formylated cytosines (5fC) or 5-carboxylated cytosines (5caC). In SEM-seq, unmodified cytosines in the DNA are deaminated to uracil and is read as “T” during sequencing. Modified cytosines (e.g., 5mC) are not converted and are read as “C” during sequencing. Cytosines that are read as thymines are identified as unmodified (e.g., unmethylated) cytosines or as thymines in the DNA. Performing SEM-seq conversion thus facilitates identifying positions containing 5mC using the sequence reads obtained. In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises enzymatic conversion of the first nucleobase using MsddA.

[00406] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA of the first subsample converts a modified nucleoside. In some embodiments, the conversion procedure which converts a modified nucleosides comprises enzymatic conversion, such as DM-seq, for example, as described in WO2023/288222A1 . In DM-seq, unmodified cytosines in the DNA are enzymatically protected from a subsequent deamination step wherein 5mC in 5mCpG is converted to T. The enzymatically protected unmodified (e.g., unmethylated) cytosines are not converted and are read as “C” during sequencing. Cytosines that are read as thymines (in a CpG context) are identified as methylated cytosines in the DNA. Thus, when this type of conversion is used, the first nucleobase comprises unmodified (such as unmethylated) cytosine, and the second nucleobase comprises modified (such as methylated) cytosine. Sequencing of the converted DNA identifies positions that are read as cytosine as being unmodified C positions. Meanwhile, positions that are read as T are identified as being T or 5mC. Performing DM-seq conversion thus facilitates identifying positions containing 5mC using the sequence reads obtained.

[00407] Exemplary cytosine deaminases for use herein include APOBEC enzymes, for example, APOBEC3A. Generally, AID/APOBEC family DNA deaminase enzymes such as APOBEC3A (A3A) are used to deaminate (unprotected) unmodified cytosine and 5mC. For an exemplary description of APOBEC conversion, see, e.g., Schutsky et al., Nature Biotechnology 2018; 36: 1083-1090. [00408] The enzymatic protection of unmodified cytosines in the DNA comprises addition of a protective group to the unmodified cytosines. Such protective groups can comprise an alkyl group, an alkyne group, a carboxyl group, a carboxyalkyl group, an amino group, a hydroxymethyl group, a glucosyl group, a glucosylhydroxymethyl group, an isopropyl group, or a dye. For example, DNA can be treated with a methyltransferase, such as a CpG-specific methyltransferase, which adds the protective group to unmodified cytosines. The term methyltransferase is used broadly herein to refer to enzymes capable of transferring a methyl or substituted methyl (e.g., carboxymethyl) to a substrate (e.g., a cytosine in a nucleic acid). In some embodiments, the DNA is contacted with a CpG- specific DNA methyltransferase (MTase), such as a CpG-specific carboxymethyltransferase (CxMTase), and a substituted methyl donor, such as a carboxymethyl donor (e.g., carboxymethyl-S-adenosyl-L-methionine). See, e.g., WO2021/236778A2. In particular embodiments, the CxMTase can facilitate the addition of a protective carboxymethyl group to an unmethylated cytosine. In some embodiments, the unmethylated cytosine is unmodified cytosine. The carboxymethyl group can prevent deamination of the cytosine during a deamination step (such as a deamination step using an APOBEC enzyme, such as A3A). Substituted methyl or carboxymethyl donors useful in the disclosed methods include but are not limited to, S-adenosyl-L-methionine (SAM) analogs, optionally wherein the SAM analog is carboxy-S-adenosyl-L-methionine (CxSAM). SAM analogs are described, for example, in WO2022/197593A1 . The MTase may be, for example, a CpG methyltransferase from Spiroplasma sp. strain MQ1 (M.Sssl), DNA-methyltransferase 1 (DNMT1 ), DNA-methyltransferase 3 alpha (DNMT3A), DNA-methyltransferase 3 beta (DNMT3B), or DNA adenine methyltransferase (Dam). The CxMTase may be a CpG methyltransferase from Mycoplasma penetrans (M.Mpel). In a particular embodiment, the methyltransferase enzyme is a variant of M.Mpel, wherein the amino acid corresponding to position 374 is R or K.

[00409] In one embodiment, the methyltransferase enzyme is a variant of M.Mpel having an N374R substitution or an N374K substitution. The methyltransferase variant can further comprise one or more amino acid substitutions selected from a) substitution of one or both residues T300 and E305 with S, A, G, Q, D, or N; b) substitution of one or more residues A323, N306, and Y299 with a positively charged amino acid selected from K, R or H; and/or c) substitution of S323 with A, G, K, R or H, which may enhance the activity of the enzyme.

[00410] Optionally, the conversion procedure further includes enzymatic protection of 5hmCs, such as by glucosylation of the 5hmCs (e.g., using 0GT) or by carbamoylation of the 5hmCs (e.g., using 5-hydroxymethylcytosine carbamoyltransferase), in the DNA prior to the deamination of unprotected modified cytosines. In this method, 5hmC can be protected from conversion, for example through glucosylation using p-glucosyl transferase (0GT), forming (5-glucosylhydroxymethylcytosine) 5ghmC, or through carbamoylation using 5-hydroxymethylcytosine carbamoyltransferase, forming 5cmC. This is described, for example, in Yu et al., Cell 2012; 149: 1368-80, and in Yang et al., Bio-protocol, 2023; 12(17): e4496. Glucosylation or carbamoylation of 5hmC can reduce or eliminate deamination of 5hmC by a deaminase such as APOBEC3A. Treatment with an MTase or CxMTase then adds a protecting group to unmodified (unmethylated) cytosines in the DNA. 5mC (but not protected, unmodified cytosine and not 5ghmC or 5cmC) is then deaminated (converted to T in the case of 5mC) by treatment with a deaminase, for example, an APOBEC enzyme (such as APOBEC3A). Sequencing of the converted DNA identifies positions that are read as cytosine as being either 5hmC or unmodified C positions. Meanwhile, positions that are read as T are identified as being T or 5mC. Performing DM-seq conversion with glucosylation of 5hmC on a sample as described herein thus facilitates distinguishing positions containing unmodified C or 5hmC on the one hand from positions containing 5mC using the sequence reads obtained.

[00411] Also provided herein are methods in which alternative base conversion schemes are used. For example, unmethylated cytosines can be left intact while methylated cytosines and hydroxymethylcytosines are converted to a base read as a thymine (e.g., uracil, thymine, or dihydrouracil).

[00412] In some embodiments, methylating a cytosine in at least one first complementary strand or second complementary strand comprises contacting the cytosine with a methyltransferase such as DNMT1 or DNMT5. In such embodiments, the step of oxidizing a 5-hydroxymethylated cytosine to 5-formylcytosine (such as by contacting the 5-hydroxymethyl cytosine in a first strand and a second strand with KRuO4) can be optional.

[00413] In some embodiments, converting the modified cytosine in at least one first or second strand to a thymine or a base read as thymine comprises oxidizing a hydroxymethyl cytosine, e.g., the hydroxymethyl cytosine is oxidized to formylcytosine. In some embodiments, oxidizing the hydroxymethyl cytosine to formylcytosine comprises contacting the hydroxymethyl cytosine with a ruthenate, such as potassium ruthenate (KRuO4).

[00414] In some embodiments, the modified cytosine is converted to thymine, uracil, or dihydrouracil. In any such embodiments, amplification methods may comprise uracil- and/or dihydrouracil-tolerant amplification methods, such as PCR using a uracil- and/or dihydrouracil-tolerant DNA polymerase.

[00415] In some embodiments, the method comprises converting a formylcytosine and/or a methylcytosine to carboxylcytosine as part of converting the modified cytosine in at least one first or second strand to a thymine or a base read as thymine. For example, converting the formylcytosine and/or the methylcytosine to carboxylcytosine can comprise contacting the formylcytosine and/or the methylcytosine with a TET enzyme, such as TET1 , TET2, TET3, or a TET2 comprising a T1372S mutation. In some embodiments, the method comprises reducing the carboxylcytosine as part of converting the modified cytosine in at least one first or second strand to a thymine or a base read as thymine, and/or the carboxylcytosine is reduced to dihydrouracil. In some embodiments, reducing the carboxylcytosine comprises contacting the carboxylcytosine with a borane or borohydride reducing agent.

[00416] In some embodiments, the borane or borohydride reducing agent comprises pyridine borane, 2-picoline borane, borane, tert-butylamine borane, ammonia borane, sodium borohydride, sodium cyanoborohydride (NaBH3CN), lithium borohydride (LiBH4), ethylenediamine borane, dimethylamine borane, sodium triacetoxyborohydride, morpholine borane, 4-methylmorpholine borane, trimethylamine borane, dicyclohexylamine borane, or a salt thereof. In other embodiments, the reducing agent comprises lithium aluminum hydride, sodium amalgam, amalgam, sulfur dioxide, dithionate, thiosulfate, iodide, hydrogen peroxide, hydrazine, diisobutylaluminum hydride, oxalic acid, carbon monoxide, cyanide, ascorbic acid, formic acid, dithiothreitol, beta- mercaptoethanol, or any combination thereof.

[00417] Various TET enzymes may be used in the disclosed methods as appropriate. In some embodiments, the one or more TET enzymes comprise TETv. TETv is described in US Patent 10,260,088. In some embodiments, the one or more TET enzymes comprise TETcd. TETcd is described in US Patent 10,260,088. In some embodiments, the one or more TET enzymes comprise TET 1 . In some embodiments, the one or more TET enzymes comprise TET2. TET2 may be expressed and used as a fragment comprising TET2 residues 1129-1480 joined to TET2 residues 1844-1936 by a linker as described, e.g., in US Patent 10,961 ,525. In some embodiments, the one or more TET enzymes comprise TET1 and TET2. In some embodiments, the one or more TET enzymes comprise a V1900 TET mutant, such as a V1900A, V1900C, V1900G, V1900I, or V1900P TET mutant. In some embodiments, the one or more TET enzymes comprise a V1900 TET2 mutant, such as a V1900A, V1900C, V1900G, V1900I, or V1900P TET2 mutant. It can be beneficial to use a TET enzyme that maximizes formation of 5-carboxylcytosine (5-caC) relative to less oxidized modified cytosines, particularly 5- formylcytosine, because 5-caC is not a substrate for enzymatic deamination, e.g., by APOBEC enzymes such as APOBEC3A. Maximizing formation of 5-caC thus reduces the risk of false calls in which a base is identified as unmethylated because it underwent deamination even though it was methylated (or hydroxymethylated) in the original sample. Accordingly, in some embodiments, the TET enzyme comprises a mutation that increases formation of 5-caC. In some embodiments, the one or more TET enzymes comprise a TET2 enzyme comprising a T1372S mutation, such as TET2-CS-T1372S and TET2-CD- T1372S. A TET2 comprising a T1372S mutation is described in US Patent 10,961 ,525 and may be expressed and used as a fragment comprising TET2 residues 1129-1480 joined to TET2 residues 1844-1936 by a linker. Position 1372 of TET2 corresponds to position 258 of SEQ ID NO: 21 (wild type TET2 catalytic domain) of US Patent 10,961 ,525. Thus, the sequence of a T1372S TET2 catalytic domain may be obtained by changing the threonine at position 258 of SEQ ID NO: 21 of US Patent 10,961 ,525 to serine. TET2 comprising a T 1372S mutation is also described in Liu et al., Nat Chem Biol. 2017 February; 13(2): 181-187. As demonstrated in Liu et al., TET2 comprising a T1372S mutation can more efficiently oxidize 5mC to produce 5-carboxylcytosine (5caC) than other versions of TET2 such as TET2 lacking a T1372S mutation. In some embodiments, the TET2 enzyme is a human TET2 enzyme comprising a T1372S mutation. Exemplary mutations are set forth above. “A mutation that increases formation of 5-caC” means that the TET enzyme having the mutation produces more 5-caC than a TET enzyme that lacks the mutation but is otherwise identical. 5-caC production can be measured as described, e.g., in Liu et al., Nat Chem Biol 13:181-187 (2017) (see Online Methods section, TET reactions in vitro subsection, “driving” conditions). Any variants and/or mutants described in Liu et al. (2017) can be used in the disclosed methods as appropriate.

[00418] Provided herein is a method comprising contacting DNA contacting DNA with a mutant TET2 enzyme (e.g. comprising a V1900A, V1900C, V1900G, V1900I, V1900P, or T1372S mutation) to oxidize 5-methylcytosine (5mC) and/or 5- hydroxymethylcytosine (5hmC) present in the DNA to 5-carboxycytosine (5caC), subsequently contacting at least a portion of the DNA with a substituted borane reducing agent, thereby converting 5-caC in the DNA to dihydrouracil (DHU), thereby producing treated DNA, and sequencing at least a portion of the treated DNA.

[00419] In some embodiments, the procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA comprises separating DNA originally comprising the first nucleobase from DNA not originally comprising the first nucleobase. In some such embodiments, the first nucleobase is hmC. DNA originally comprising the first nucleobase may be separated from other DNA using a labeling procedure comprising biotinylating positions that originally comprised the first nucleobase. In some embodiments, the first nucleobase is first derivatized with an azide- containing moiety, such as a glucosyl-azide containing moiety. The azide-containing moiety then may serve as a reagent for attaching biotin, e.g., through Huisgen cycloaddition chemistry. Then, the DNA originally comprising the first nucleobase, now biotinylated, can be separated from DNA not originally comprising the first nucleobase using a biotin-binding agent, such as avidin, neutravidin (deglycosylated avidin with an isoelectric point of about 6.3), or streptavidin. An example of a procedure for separating DNA originally comprising the first nucleobase from DNA not originally comprising the first nucleobase is hmC-seal, which labels hmC to form p-6-azide-glucosyl-5- hydroxymethylcytosine and then attaches a biotin moiety through Huisgen cycloaddition, followed by separation of the biotinylated DNA from other DNA using a biotin-binding agent. For an exemplary description of hmC-seal, see, e.g., Han et al., Mol. Cell 2016; 63: 711-719. This approach is useful for identifying fragments that include one or more hmC nucleobases.

[00420] In some embodiments, following such a separation, the method further comprises differentially tagging each of the DNA originally comprising the first nucleobase, the DNA not originally comprising the first nucleobase. The method may further comprise pooling the DNA originally comprising the first nucleobase and the DNA not originally comprising the first nucleobase following differential tagging. The DNA originally comprising the first nucleobase and the DNA not originally comprising the first nucleobase may then be used in downstream analyses. For example, the pooled DNA originally comprising the first nucleobase and the DNA not originally comprising the first nucleobase may be sequenced in the same sequencing cell (such as after being subjected to further treatments, such as those described herein) while retaining the ability to resolve whether a given read came from a molecule of DNA originally comprising the first nucleobase or DNA not originally comprising the first nucleobase using the differential tags.

[00421] In some embodiments, the first nucleobase is a modified or unmodified adenine, and the second nucleobase is a modified or unmodified adenine. In some embodiments, the modified adenine is N6-methyladenine (mA). In some embodiments, the modified adenine is one or more of N6-methyladenine (mA), N6- hydroxymethyladenine (hmA), or N6-formyladenine (fA).

[00422] Techniques comprising partitioning based on methylation status or methylated DNA immunoprecipitation (MeDIP) can be used to separate DNA containing modified bases such as mC, mA, caC (which may be generated by oxidation of mC or hmC with Tet2, e.g., before enzymatic conversion of unmodified C to U, e.g., using a deaminase such as APOBEC3A), or dihydrouracil from other DNA. See, e.g., Kumar et al., Frontiers Genet. 2018; 9: 640; Greer et al., Cell 2015; 161 : 868-878. An antibody specific for mA is described in Sun et al., Bioessays 2015; 37:1155-62. Antibodies for various modified nucleobases, such as mC, caC, and forms of thymine/uracil including dihydrouracil or halogenated forms such as 5-bromouracil, are commercially available. Various modified bases can also be detected based on alterations in their base pairing specificity. For example, hypoxanthine is a modified form of adenine that can result from deamination and is read in sequencing as a G. See, e.g., US Patent 8,486,630; Brown, Genomes, 2nd Ed., John Wiley & Sons, Inc., New York, N.Y., 2002, chapter 14, “Mutation, Repair, and Recombination.”

G. Captured Set; Target Regions

[00423] In some embodiments, nucleic acids captured or enriched using a method described herein comprise captured DNA, such as one or more captured sets of DNA. In some embodiments, the captured DNA comprise target regions that are differentially methylated in different immune cell types. In some embodiments, the immune cell types comprise rare or closely related immune cell types, such as activated and naive lymphocytes or myeloid cells at different stages of differentiation.

[00424] In some embodiments, a captured epigenetic target region set captured from a sample or first subsample comprises hypermethylation target regions. In some embodiments, the hypermethylation target regions are differentially or exclusively hypermethylated in one cell type or in one immune cell type, or in one immune cell type within a cluster. In some embodiments, the hypermethylation target regions are hypermethylated to an extent that is distinguishably higher or exclusively present in one cell type or one immune cell type or one immune cell type within a cluster. Such hypermethylation target regions may be hypermethylated in other cell types but not to the extent observed in the one cell type. In some embodiments, the hypermethylation target regions show lower methylation in healthy cfDNA than in at least one other tissue type.

[00425] In some embodiments, a captured epigenetic target region set captured from a sample or second subsample comprises hypomethylation target regions. In some embodiments, the hypomethylation target regions are exclusively hypomethylated in one cell type or in one immune cell type or in one immune cell type within a cluster. In some embodiments, the hypomethylation target regions are hypomethylated to an extent that is exclusively present in one cell type or one immune cell type or in one immune cell type within a cluster. [00426] Such hypomethylation target regions may be hypomethylated in other cell types but not to the extent observed in the one cell type. In some embodiments, the hypomethylation target regions show higher methylation in healthy cfDNA than in at least one other tissue type. [0248] Without wishing to be bound by any particular theory, in an individual with cancer, proliferating or activated immune cells (and potentially also cancer cells) may shed more DNA into the bloodstream than immune cells in a healthy individual (and healthy cells of the same tissue type, respectively). As such, the distribution of cell type and/or tissue of origin of cfDNA may change upon carcinogenesis. For example, the distribution of immune cell type of origin may change in a subject having cancer, precancer, infection, transplant rejection, or other disease or disorder directly or indirectly affecting the immune system. The status of epigenetic target regions of certain immune cell types likewise may change in a subject having such a disease relative to a healthy subject or relative to the same subject prior to having the disease or disorder. Thus, variations in hypermethylation and/or hypomethylation can be an indicator of disease. For example, an increase in the level of hypermethylation target regions and/or hypomethylation target regions in a subsample following a partitioning step can be an indicator of the presence (or recurrence, depending on the history of the subject) of cancer.

[00427] Exemplary hypermethylation target regions and hypomethylation target regions useful for distinguishing between various cell types, including but not limited to immune cell types, have been identified by analyzing DNA obtained from various cell types via whole genome bisulfite sequencing, as described, e.g., in Stunnenberg, H. G. et. al., “The International Human Epigenome Consortium: A Blueprint for Scientific Collaboration and Discovery,” Cell 167, 1145 (2016) (doi.org/10.1186/sl3059-020-02065- 5). Whole-genome bisulfite sequencing data is available from the Blueprint consortium, available on the internet at dcc.blueprint-epigenome.eu.

[00428] In some embodiments, first and second captured target region sets comprise, respectively, DNA corresponding to a sequence-variable target region set and DNA corresponding to an epigenetic target region set, for example, as described in WO 2020/160414. The first and second captured sets may be combined to provide a combined captured set. [00429] Where DNA (e.g., a sample or subsample) has been subjected to a procedure such as bisulfite conversion, treatment with a deaminase, or any of the other such procedures mentioned herein that alter the base-pairing specificity of certain bases, enrichment or capture may use oligonucleotides (e.g., primers or probes) specific for the altered or unaltered sequence, as desired.

[00430] In some embodiments in which a captured set comprising DNA corresponding to the sequence-variable target region set and the epigenetic target region set includes a combined captured set as discussed above, the DNA corresponding to the sequence-variable target region set may be present at a greater concentration than the DNA corresponding to the epigenetic target region set, e.g., a 1.1 to 1.2-fold greater concentration, a 1.2- to 1.4-fold greater concentration, a 1.4- to 1 .6-fold greater concentration, a 1.6- to 1.8-fold greater concentration, a 1.8- to 2.0-fold greater concentration, a 2.0- to 2.2-fold greater concentration, a 2.2- to 2.4-fold greater concentration a 2.4- to 2.6-fold greater concentration, a 2.6- to 2.8-fold greater concentration, a 2.8- to 3.0-fold greater concentration, a 3.0- to 3.5-fold greater concentration, a 3.5- to 4.0, a 4.0- to 4.5-fold greater concentration, a 4.5- to 5.0-fold greater concentration, a 5.0- to 5.5-fold greater concentration, a 5.5- to 6.0-fold greater concentration, a 6.0- to 6.5-fold greater concentration, a 6.5- to 7.0-fold greater, a 7.0- to 7.5-fold greater concentration, a 7.5- to 8.0-fold greater concentration, an 8.0- to 8.5-fold greater concentration, an 8.5- to 9.0-fold greater concentration, a 9.0- to 9.5-fold greater concentration, 9.5- to 10.0-fold greater concentration, a 10- to 11 -fold greater concentration, an 11- to 12-fold greater concentration a 12- to 13-fold greater concentration, a 13- to 14-fold greater concentration, a 14- to 15-fold greater concentration, a 15- to 16-fold greater concentration, a 16- to 17-fold greater concentration, a 17- to 18-fold greater concentration, an 18- to 19-fold greater concentration, a 19- to 20-fold greater concentration, a 20- to 30-fold greater concentration, a 30- to 40-fold greater concentration, a 40- to 50-fold greater concentration, a 50- to 60-fold greater concentration, a 60- to 70-fold greater concentration, a 70- to 80-fold greater concentration, a 80- to 90-fold greater concentration, or a 90- to 100-fold greater concentration. The degree of difference in concentrations accounts for normalization for the footprint sizes of the target regions, as discussed in the definition section.

1. Epigenetic Target Region Set

[00431] In some embodiments, an epigenetic target region set may comprise one or more types of target regions likely to differentiate DNAfrom different immune cell types and other non- immune cell types and/or to differentiate neoplastic (e.g., tumor or cancer) cells and from healthy cells, e.g., non-neoplastic circulating cells. Exemplary types of such regions are discussed in detail herein. The epigenetic target region set may also comprise one or more control regions, e.g., as described herein.

[00432] In some embodiments, the epigenetic target region set has a footprint of at least 100 kb, e.g., at least 200 kb, at least 300 kb, or at least 400 kb. In some embodiments, the epigenetic target region set has a footprint in the range of 100-1000 kb, e.g., 100-200 kb, 200-300 kb, 300- 400 kb, 400-500 kb, 500-600 kb, 600-700 kb, 700- 800 kb, 800-900 kb, and 900-1 ,000 kb. a. Hypermethylation Target Regions

[00433] In some embodiments, the epigenetic target region set comprises one or more hypermethylation target regions. In some embodiments, hypermethylation target regions are exclusively hypermethylated in one immune cell type or hypermethylated to a greater extent in one immune cell type than in any other immune cell type or than in any other immune cell type within the same immune cell cluster. In some such embodiments, hypermethylation target regions indicate the levels of particular immune cell types from which the DNA originated, including rare immune cell types such as activated B cells (including memory B cells and plasma cells), activated T cells (including regulatory T cells (Tregs), CD4 effector memory T cells, CD4 central memory T cells, CD8 effector memory T cells, and CD8 central memory T cells), and natural killer (NK) cells. Methylation patterns of hypermethylation target regions that are useful for deconvoluting immune cell types may further change in certain disease states, such as cancer. Thus, in some embodiments, hypermethylation target regions that are useful for deconvoluting immune cell types are also useful for determining the likelihood that the subject from which the sample was obtained has cancer or precancer. In some such embodiments, hypermethylation target regions are useful for determining whether levels of particular immune cell types are abnormal and whether such abnormal levels are likely related to the presence of cancer or precancer, or if they are related to a different disease or condition other than cancer or precancer.

[00434] In some embodiments, certain hypermethylation target regions exhibit an increase in the level of observed methylation, e.g., are hypermethylated, in DNA produced by neoplastic cells, such as tumor or cancer cells. Detection of such hypermethylation target regions, e.g., in conjunction with detection of hypermethylation target regions indicative of immune cell types, may further increase the specificity and/or sensitivity of methods described herein. In some embodiments, such increases in observed methylation in hypermethylated target regions indicate an increased likelihood that a sample (e.g., of cfDNA) was obtained from a subject having cancer. For example, hypermethylation of promoters oftumor suppressor genes has been observed repeatedly. See, e.g., Kang et ah, Genome Biol. 18:53 (2017) and references cited therein. In another example, as discussed above, hypermethylation target regions can include regions that do not necessarily differ in methylation in cancerous tissue relative to DNA from healthy tissue of the same type, but do differ in methylation (e.g., have more methylation) relative to cfDNA that is typical in healthy subjects. Where, for example, the presence of a cancer results in increased cell death such as apoptosis of cells of the tissue type corresponding to the cancer, such a cancer can be detected at least in part using such hypermethylation target regions. In some embodiments, hypermethylation target regions useful for determining the likelihood that a subject has cancer are different than the hypermethylation target regions useful for determining the levels of particular immune cell types. In some embodiments, at least some of the hypermethylation target regions useful for determining the likelihood that a subject has cancer are the same as the hypermethylation target regions useful for determining the levels of particular immune cell types.

[00435] An extensive discussion of methylation variable target regions in colorectal cancer is provided in Lam et al., Biochim Biophys Acta. 1866:106-20 (2016). These include VIM, SEPT9, ITGA4, OSM4, GATA4 and NDRG4. An exemplary set of hypermethylation target regions based on colorectal cancer (CRC) studies is provided in Table 1 . Many of these genes likely have relevance to cancers beyond colorectal cancer; for example, TP53 is widely recognized as a critically important tumor suppressor and hypermethylation-based inactivation of this gene may be a common oncogenic mechanism.

Table 1. Exemplary Hypermethylation Target Regions based on CRC studies.

[00436] In some embodiments, the hypermethylation target regions comprise a plurality of loci listed in Table 1 , e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the loci listed in Table 1. For example, for each locus included as a target region, there may be one or more probes with a hybridization site that binds between the transcription start site and the stop codon (the last stop codon for genes that are alternatively spliced) of the gene, or in the promoter region of the gene. In some embodiments, the one or more probes bind within 300 bp of the transcription start site of a gene in Table 1 , e.g., within 200 or 100 bp.

[00437] Methylation variable target regions in various types of lung cancer are discussed in detail, e.g., in Ooki et al., Clin. Cancer Res. 23:7141-52 (2017); Belinksy, Annu. Rev. Physiol. 77:453- 74 (2015); Hulbert et al., Clin. Cancer Res. 23:1998-2005 (2017); Shi et al., BMC Genomics 18:901 (2017); Schneider et al., BMC Cancer. 11 :102 (2011 ); Lissa et al., Transl Lung Cancer Res 5(5):492-504 (2016); Skvortsova et aL, Br. J. Cancer. 94(10): 1492-1495 (2006); Kim et al., Cancer Res. 61 :3419-3424 (2001); Furonaka et aL, Pathology International 55:303-309 (2005); Gomes et al., Rev. Port. Pneumol. 20:20-30 (2014); Kim et al., Oncogene. 20:1765-70 (2001); Hopkins-Donaldson et al., Cell Death Differ. 10:356-64 (2003); Kikuchi et aL, Clin. Cancer Res. 11 :2954-61 (2005); Heller et aL, Oncogene 25:959-968 (2006); Licchesi et aL, Carcinogenesis. 29:895-904 (2008); Guo et aL, Clin. Cancer Res. 10:7917-24 (2004); Palmisano et al., Cancer Res. 63:4620-4625 (2003); and Toyooka et al., Cancer Res. 61 :4556-4560, (2001 ).

[00438] An exemplary set of hypermethylation target regions based on lung cancer studies is provided in Table 2. Many of these genes likely have relevance to cancers beyond lung cancer; for example, Casp8 (Caspase 8) is a key enzyme in programmed cell death and hypermethylation-based inactivation of this gene may be a common oncogenic mechanism not limited to lung cancer. Additionally, a number of genes appear in both Tables 1 and 2, indicating generality.

Table 2. Exemplary Hypermethylation Target Regions based on Lung Cancer studies.

[00439] Any of the foregoing embodiments concerning target regions identified in Table 2 may be combined with any of the embodiments described above concerning target regions identified in Table 1. In some embodiments, the hypermethylation target regions comprise a plurality of loci listed in Table 1 or Table 2, e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the loci listed in Table 1 or Table 2. [00440] In some embodiments, the hypermethylation target regions comprise regions of one or more genes listed in Table 2b, e.g. at least 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050,

[00441] 1000, 1100, 1150 or 1200 genes listed in Table 3. Hypermethylation of these genes can be useful for detecting contributions from immune cells to a DNA sample. In some embodiments, the hypermethylation target regions comprise regions of a plurality of genes listed in Table 2b, e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the genes listed in Table 3. In some embodiments, the hypermethylation target regions comprise regions of all of the genes listed in Table 3.

Table 3. Exemplary genes comprising exemplary hypermethylation target regions.

[00442] Additional hypermethylation target regions may be obtained, e.g., from the Cancer Genome Atlas. Kang et al., Genome Biology 18:53 (2017), describe construction of a probabilistic method called CancerLocator using hypermethylation target regions from breast, colon, kidney, liver, and lung. In some embodiments, the hypermethylation target regions can be specific to one or more types of cancer. Accordingly, in some embodiments, the hypermethylation target regions include one, two, three, four, or five subsets of hypermethylation target regions that collectively show hypermethylation in one, two, three, four, or five of breast, colon, kidney, liver, and lung cancers.

[00443] In some embodiments, where different epigenetic target regions are captured from first and second subsamples, the epigenetic target regions captured from the first subsample comprise hypermethylation target regions. b. Hypomethylation target regions

[00444] In some embodiments, the epigenetic target region set comprises one or more hypomethylation target regions. In some embodiments, hypomethylation target regions are exclusively hypomethylated in one immune cell type or hypomethylated to a greater extent in one immune cell type than in any other immune cell type or in any other immune cell type within the same immune cell cluster. In some such embodiments, hypomethylation target regions indicate the levels of particular immune cell types from which the DNA originated, including rare immune cell types such as activated B cells (including memory B cells and plasma cells), activated T cells (including regulatory T cells (Tregs), CD4 effector memory T cells, CD4 central memory T cells, CD8 effector memory T cells, and CD8 central memory T cells), and natural killer (NK) cells. Methylation patterns of hypomethylation target regions that are useful for deconvoluting immune cell types may further change in certain disease states, such as cancer. Thus, in some embodiments, hypomethylation target regions that are useful for deconvoluting immune cell types are also useful for determining the likelihood that the subject from which the sample was obtained has cancer or precancer. In some such embodiments, hypomethylation target regions are useful for determining whether levels of particular immune cell types are abnormal and whether such abnormal levels are likely related to the presence of cancer or precancer, or if they are related to a different disease or condition other than cancer or precancer.

[00445] Additionally, global hypomethylation is a commonly observed phenomenon in various cancers. See, e.g., Hon et al., Genome Res. 22:246-258 (2012) (breast cancer); Ehrlich, Epigenomics 1 :239-259 (2009) (review article noting observations of hypomethylation in colon, ovarian, prostate, leukemia, hepatocellular, and cervical cancers). For example, regions such as repeated elements, e.g., LINE1 elements, Alu elements, centromeric tandem repeats, pericentromeric tandem repeats, and satellite DNA, and intergenic regions that are ordinarily methylated in healthy cells may show reduced methylation in tumor cells. Accordingly, in some embodiments, the epigenetic target region set includes hypomethylation target regions in which a decrease in the level of observed methylation indicates an increased likelihood of the presence of cancer. Detection of such hypomethylation target regions, e.g., in conjunction with detection of hypomethylation target regions indicative of immune cell types, may further increase the specificity and/or sensitivity of methods described herein. In another example, as discussed above, hypomethylation target regions can include regions that do not necessarily differ in methylation in cancerous tissue relative to DNA from healthy tissue of the same type, but do differ in methylation (e.g., are less methylated) relative to cfDNA that is typical in healthy subjects. Where, for example, the presence of a cancer results in increased cell death such as apoptosis of cells of the tissue type corresponding to the cancer, such a cancer can be detected at least in part using such hypomethylation target regions. In some embodiments, hypomethylation target regions useful for determining the likelihood that a subject has cancer are different than the hypomethylation target regions useful for determining the levels of particular immune cell types. In some embodiments, at least some of the hypomethylation target regions useful for determining the likelihood that a subject has cancer are the same as the hypomethylation variable target regions useful for determining the levels of particular immune cell types.

[00446] In some embodiments, hypomethylation target regions include repeated elements and/or intergenic regions. In some embodiments, repeated elements include one, two, three, four, or five of LINE1 elements, Alu elements, centromeric tandem repeats, pericentromeric tandem repeats, and/or satellite DNA.

[00447] Exemplary specific genomic regions that show cancer-associated hypomethylation include nucleotides 8403565-8953708 and 151104701-151106035 of human chromosome 1. In some embodiments, the hypomethylation target regions overlap or comprise one or both of these regions.

[00448] Additionally, hypomethylation target regions may be obtained, e.g., from Fox-Fisher et al., ElifeNov 29; 10 (2021), EpiDISH R package, Moss et al., Nat Commun 9:1 (2018), and Loyfer et al. bioRxiv https://doi.org/10.1101/2022.01.24.477547 (2022). In some embodiments, the hypomethylation target regions can be specific to one or more types of immune cells.

[00449] In some embodiments, where different epigenetic target regions are captured from first and second subsamples, the epigenetic target regions captured from the second subsample comprise hypomethylation target regions. In some embodiments, the epigenetic target regions captured from the second subsample comprise hypomethylation target regions and the epigenetic target regions captured from the first subsample comprise hypermethylation target regions. c. CTCF binding regions

[00450] CTCF is a DNA-binding protein that contributes to chromatin organization and often colocalizes with cohesin. Perturbation of CTCF binding sites has been reported in a variety of different cancers. See, e.g., Katainen et al., Nature Genetics, doi:10.1038/ng.3335, published online 8 June 2015; Guo et al., Nat. Commun. 9:1520 (2018). CTCF binding results in recognizable patterns in cfDNA that can be detected by sequencing, e.g., through fragment length analysis. Details regarding sequencing-based fragment length analysis are provided in Snyder et aL, Cell 164:57-68 (2016); WO 2018/009723; and US20170211143A1 , each of which are incorporated herein by reference.

[00451] Thus, perturbations of CTCF binding result in variation in the fragmentation patterns of cfDNA. As such, CTCF binding sites are a type of fragmentation variable target regions.

[00452] There are many known CTCF binding sites. See, e.g., the CTCFBSDB (CTCF Binding Site Database), available on the Internet at insulatordb.uthsc.edu/; Cuddapah et aL, Genome Res. 19:24-32 (2009); Martin et aL, Nat. Struct. MoL BioL 18:708-14 (2011 ); Rhee et aL, Cell. 147:1408-19 (2011 ), each of which are incorporated by reference. Exemplary CTCF binding sites are at nucleotides 56014955-56016161 on chromosome 8 and nucleotides 95359169-95360473 on chromosome 13.

[00453] Accordingly, in some embodiments, the epigenetic target region set includes CTCF binding regions. In some embodiments, the CTCF binding regions comprise at least 10, 20, 50, 100, 200, or 500 CTCF binding regions, or 10-20, 20-50, 50- 100, 100-200, 200-500, or 500-1000 CTCF binding regions, e.g., such as CTCF binding regions described above or in one or more of CTCFBSDB or the Cuddapah et aL, Martin et aL, or Rhee et al. articles cited above.

[00454] In some embodiments, at least some of the CTCF sites can be methylated or unmethylated, wherein the methylation state is correlated with the whether or not the cell is a cancer cell. In some embodiments, the epigenetic target region set comprises at least 100 bp, at least 200 bp, at least 300 bp, at least 400 bp, at least 500 bp, at least 750 bp, at least 1000 bp upstream and downstream regions of the CTCF binding sites. d. Transcription start sites.

[00455] Transcription start sites may also show perturbations in neoplastic cells. For example, nucleosome organization at various transcription start sites in healthy cells of the hematopoietic lineage — which contributes substantially to cfDNA in healthy individuals — may differ from nucleosome organization at those transcription start sites in neoplastic cells. This results in different cfDNA patterns that can be detected by sequencing, as discussed generally in Snyder et aL, Cell 164:57-68 (2016); WO 2018/009723; and US20170211143A1. In another example, transcription start sites may not necessarily differ epigenetically in cancerous tissue relative to DNA from healthy tissue of the same type, but do differ epigenetically (e.g., with respect to nucleosome organization) relative to cfDNA that is typical in healthy subjects. Where, for example, the presence of a cancer results in increased cell death, such as apoptosis, of cells of the tissue type corresponding to the cancer, such a cancer can be detected at least in part using such differences in transcription start sites.

[00456] Thus, perturbations of transcription start sites also result in variation in the fragmentation patterns of cfDNA. As such, transcription start sites are also a type of fragmentation variable target regions.

[00457] Human transcriptional start sites are available from DBTSS (DataBase of Human Transcription Start Sites), available on the Internet at dbtss.hgc.jp and described in Yamashita et al., Nucleic Acids Res. 34(Database issue): D86-D89 (2006), which is incorporated herein by reference.

[00458] Accordingly, in some embodiments, the epigenetic target region set includes transcriptional start sites. In some embodiments, the transcriptional start sites comprise at least 10, 20, 50, 100, 200, or 500 transcriptional start sites, or 10-20, 20-50, 50-100, 100-200, 200-500, or 500-1000 transcriptional start sites, e.g., such as transcriptional start sites listed in DBTSS. In some embodiments, at least some of the transcription start sites can be methylated or unmethylated, wherein the methylation state is correlated with whether or not the cell is a cancer cell. In some embodiments, the epigenetic target region set comprises at least 100 bp, at least 200 bp, at least 300 bp, at least 400 bp, at least 500 bp, at least 750 bp, at least 1000 bp upstream and downstream regions of the transcription start sites. e. Focal amplifications

[00459] Although focal amplifications are somatic mutations, they can be detected by sequencing based on read frequency in a manner analogous to approaches for detecting certain epigenetic changes such as changes in methylation. As such, regions that may show focal amplifications in cancer can be included in the epigenetic target region set and may comprise one or more of AR, BRAF, CCND1 , CCND2, CCNE1 , CDK4, CDK6, EGFR, ERBB2, FGFR1 , FGFR2, KIT, KRAS, MET, MYC, PDGFRA, PIK3CA, and RAF1 . For example, in some embodiments, the epigenetic target region set comprises at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, or 18 of the foregoing targets. f. Methylation control regions or control regions

[00460] It can be useful to include control regions to facilitate data validation. In some embodiments, the epigenetic target region set includes control regions that are expected to be methylated or unmethylated in essentially all samples, regardless of whether the DNA is derived from a cancer cell or a normal cell. In some embodiments, the epigenetic target region set includes negative control regions that are expected to be hypomethylated or unmethylated in essentially all samples. In some embodiments, the epigenetic target region set includes positive control regions that are expected to be hypermethylated in essentially all samples.

2. Sequence-variable target region set.

[00461] In some embodiments, the sequence-variable target region set comprises a plurality of regions known to undergo somatic mutations (e.g., single nucleotide variations and/or indels) in cancer. The single nucleotide variations and/or indels may be relative to a reference sequence, e.g., a published human genome sequence, such as the GRCh38 human genome assembly.

[00462] In some aspects, the sequence-variable target region set targets a plurality of different genes or genomic regions (“panel”) selected such that a determined proportion of subjects having a cancer exhibits a genetic variant or tumor marker in one or more different genes or genomic regions in the panel. The panel may be selected to limit a region for sequencing to a fixed number of base pairs. The panel may be selected to sequence a desired amount of DNA, e.g., by adjusting the affinity and/or amount of the probes as described elsewhere herein. The panel may be further selected to achieve a desired sequence read depth. The panel may be selected to achieve a desired sequence read depth or sequence read coverage for an amount of sequenced base pairs. The panel may be selected to achieve a theoretical sensitivity, a theoretical specificity, and/or a theoretical accuracy for detecting one or more genetic variants in a sample. [0284] Probes for detecting the panel of regions can include those for detecting genomic regions of interest (hotspot regions). Information about chromatin structure can be taken into account in designing probes, and/or probes can be designed to maximize the likelihood that particular sites (e.g., KRAS codons 12 and 13) can be captured, and may be designed to optimize capture based on analysis of cfDNA coverage and fragment size variation impacted by nucleosome binding patterns and GC sequence composition. Regions used herein can also include non-hotspot regions optimized based on nucleosome positions and GC models.

[00463] Examples of listings of genomic locations of interest may be found in Table 4 and Table 5. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least a portion of at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, or 70 of the genes of Table 3. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, or 70 of the SNVs of Table 4. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least 1 , at least 2, at least 3, at least 4, at least 5, or 6 of the fusions of Table 4. In some embodiments, a sequence- variable target region set used in the methods of the present disclosure comprise at least a portion of at least 1 , at least 2, or 3 of the indels of Table 4. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least a portion of at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, at least 70, or 73 of the genes of Table 5. In some embodiments, a sequence- variable target region set used in the methods of the present disclosure comprises at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, at least 70, or 73 of the SNVs of Table 5. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least 1 , at least 2, at least 3, at least 4, at least 5, or 6 of the fusions of Table 5. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least a portion of at least 1 , at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, or 18 of the indels of Table 5. Each of these genomic locations of interest may be identified as a backbone region or hot-spot region for a given panel. An example of a listing of hot-spot genomic locations of interest may be found in Table 6. In some embodiments, a sequence-variable target region set used in the methods of the present disclosure comprises at least a portion of at least 1 , at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, or at least 20 of the genes of Table 6. Each hot-spot genomic region is listed with several characteristics, including the associated gene, chromosome on which it resides, the start and stop position of the genome representing the gene’s locus, the length of the gene’s locus in base pairs, the exons covered by the gene, and the critical feature (e.g., type of mutation) that a given genomic region of interest may seek to capture.

Table 4

Table 5

Table 6

[00464] Additionally, or alternatively, suitable target region sets are available from the literature. For example, Gale et al., PLoS One 13: e0194630 (2018), which is incorporated herein by reference, describes a panel of 35 cancer-related gene targets that can be used as part or all of a sequence-variable target region set. These 35 targets are AKTI, ALK, BRAF, CCND1 , CDK2A, CTNNB1 , EGFR, ERBB2, ESR1 , FGFR1 , FGFR2, FGFR3, F0XL2, GAT A3, GNA11 , GNAQ, GNAS, HRAS, IDH1 , IDH2, KIT, KRAS, MED 12, MET, MYC, NFE2L2, NRAS, PDGFRA, PIK3CA, PPP2R1A, PTEN, RET, STK11 , TP53, and U2AF1 .

[00465] In some embodiments, the sequence-variable target region set comprises target regions from at least 10, 20, 30, or 35 cancer-related genes, such as the cancer- related genes listed above.

H. Subjects

[00466] In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject having a cancer or a precancer, an infection, transplant rejection, or other disease directly or indirectly affecting the immune system. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject suspected of having a cancer or a precancer, an infection, transplant rejection, or other disease directly or indirectly affecting the immune system. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject having a tumor. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject suspected of having a tumor. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject having neoplasia. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject suspected of having neoplasia. In some embodiments, the DNA (e.g., cfDNA) is obtained from a subject in remission from a tumor, cancer, or neoplasia (e.g., following chemotherapy, surgical resection, radiation, or a combination thereof). In any of the foregoing embodiments, the cancer, tumor, or neoplasia or suspected cancer, tumor, or neoplasia may be of the lung, colon, rectum, kidney, breast, prostate, or liver. In some embodiments, the cancer, tumor, or neoplasia or suspected cancer, tumor, or neoplasia is of the lung. In some embodiments, the cancer, tumor, or neoplasia or suspected cancer, tumor, or neoplasia is of the colon or rectum. In some embodiments, the cancer, tumor, or neoplasia or suspected cancer, tumor, or neoplasia is of the breast. In some embodiments, the cancer, tumor, or neoplasia or suspected cancer, tumor, or neoplasia is of the prostate. In any of the foregoing embodiments, the subject may be a human subject. I. Pooling of DNA from samples or subsamples or portions thereof

[00467] In some embodiments, the methods herein comprise preparing one or more pools comprising tagged DNA from a plurality of partitioned subsamples. In some embodiments, a pool comprises at least a portion of the DNA of a hypomethylated partition and at least a portion of the DNA of a hypermethylated partition. Target regions, e.g., including epigenetic target regions and/or sequence-variable target regions, may be captured from a pool. The steps of capturing a target region set from at least an aliquot or portion of a sample or subsample described elsewhere herein encompass capture steps performed on a pool comprising DNA from first and second subsamples. A step of amplifying DNA in a pool may be performed before capturing target regions from the pool. The capturing step may have any of the features described for capturing steps elsewhere herein.

[00468] In some embodiments, the methods comprise preparing a first pool comprising at least a portion of the DNA of a hypomethylated partition. In some embodiments, the methods comprise preparing a second pool comprising at least a portion of the DNA of a hypermethylated partition. In some embodiments, the methods comprise capturing at least a first set of target regions from the first pool, wherein the first set comprises sequence-variable target regions. A step of amplifying DNA in the first pool may be performed before this capture step. In some embodiments, capturing the first set of target regions from the first pool comprises contacting the DNA of the first pool with a first set of target-specific probes, wherein the first set of target- specific probes comprises target-binding probes specific for the sequence-variable target regions. In some embodiments, the methods comprise capturing a second plurality of sets of target regions from the second pool, wherein the second plurality comprises sequence-variable target regions and epigenetic target regions. A step of amplifying DNA in the second pool may be performed before this capture step. In some embodiments, capturing the second plurality of sets of target regions from the second pool comprises contacting the DNA of the first pool with a second set of target-specific probes, wherein the second set of target- specific probes comprises target-binding probes specific for the sequence-variable target regions and target-binding probes specific for the epigenetic target regions. [00469] In some embodiments, sequence-variable target regions are captured from a second portion of a partitioned subsample. The second portion may include some, a majority, substantially all, or all of the DNA of the subsample that was not included in the pool. The regions captured from the pool and from the subsample may be combined and analyzed in parallel.

[00470] The epigenetic target regions may show differences in methylation levels and/or fragmentation patterns depending on whether they originated from a particular cell or tissue type or from a tumor or from healthy cells, as discussed elsewhere herein. The sequence-variable target regions may show differences in sequence depending on whether they originated from a tumor or from healthy cells. [0293] Analysis of epigenetic target regions from a hypomethylated partition may be less informative in some applications than analysis of sequence-variable target regions from hypermethylated and hypomethylated partitions and epigenetic target regions from a hypermethylated partition. As such, in methods where sequence-variable target regions and epigenetic target regions are being captured, the latter may be captured to a lesser extent than one or more of the sequence-variable target regions are captured from the hypermethylated and hypomethylated partitions and/or to a lesser extent that epigenetic target regions are captured from a hypermethylated partition. For example, sequence-variable target regions can be captured from a portion of a hypomethylated partition that is not pooled with a hypermethylated partition, and the pool can be prepared with some (e.g., a majority, substantially all, or all) of the DNA from a hypermethylated partition and none or some (e.g., a minority) of the DNA from a hypomethylated partition. Such approaches can reduce or eliminate sequencing of epigenetic target regions from hypomethylated partitions, thereby reducing the amount of sequencing data that suffices for further analysis.

[00471] In some embodiments, including a minority of the DNA of a hypomethylated partition in the pool facilitates quantification of one or more epigenetic features (e.g., methylation or other epigenetic feature(s) discussed in detail elsewhere herein), e.g., on a relative basis.

[00472] In some embodiments, the pool comprises a minority of the DNA of a hypomethylated partition, e.g., less than about 50% of the DNA of a hypomethylated partition, such as less than or equal to about 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, or 5% of the DNA of a hypomethylated partition. In some embodiments, the pool comprises about 5%-25% of the DNA of a hypomethylated partition. In some embodiments, the pool comprises about 10%-20% of the DNA of a hypomethylated partition. In some embodiments, the pool comprises about 10% of the DNA of a hypomethylated partition. In some embodiments, the pool comprises about 15% of the DNA of a hypomethylated partition. In some embodiments, the pool comprises about 20% of the DNA of a hypomethylated partition.

[00473] In some embodiments, the pool comprises a portion of a hypermethylated partition, which may be at least about 50% of the DNA of a hypermethylated partition. For example, the pool may comprise at least about 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, or 95% of the DNA of a hypermethylated partition. In some embodiments, the pool comprises 50-55%, 55- 60%, 60-65%, 65-70%, 70-75%, 75-80%, 80-85%, 85-90%, 90- 95%, or 95-100% of the DNA of a hypermethylated partition. In some embodiments, the second pool comprises all or substantially all of the DNA of a hypermethylated partition.

[00474] In some embodiments, a first pool comprises substantially all or all of the DNA of a hypomethylated partition (e.g., wherein a second pool does not comprise DNA of a hypomethylated partition. In some embodiments, the second pool does not comprise DNA of a hypomethylated partition (e.g., wherein the first pool comprises substantially all or all of the DNA of a hypomethylated partition).

[00475] In some embodiments, a second pool comprises a portion of a hypermethylated partition, which may be any of the values and ranges set forth above with respect to a hypomethylated partition. In some embodiments, the second pool comprises all or substantially all of the DNA of a hypermethylated partition.

[00476] In an exemplary embodiment, after partitioning, the partitions separately undergo end repair and ligation to adapters comprising molecular barcodes and are then amplified separately. After the amplification, amplified molecules are enriched (still keeping the partitions separate). Post-enrichment, the enriched DNA are pooled according to any of the embodiments described herein, and then amplified again. After amplification, the molecules are sequenced. [00477] In various embodiments, the methods further comprise sequencing the captured DNA, e.g., to different degrees of sequencing depth for the epigenetic and sequence-variable target region sets, consistent with the discussion above.

J. Sequencing

[00478] In general, sample nucleic acids, including nucleic acids flanked by adapters, with or without prior amplification can be subject to sequencing. Sequencing methods include, for example, Sanger sequencing, high-throughput sequencing, pyrosequencing, sequencing-by synthesis, single-molecule sequencing, nanopore sequencing, semiconductor sequencing, sequencing-by-ligation, sequencing-by- hybridization, Digital Gene Expression (Helicos), Next generation sequencing (NGS), Single Molecule Sequencing by Synthesis (SMSS) (Helicos), massively-parallel sequencing, Clonal Single Molecule Array (Solexa), shotgun sequencing, Ion Torrent, Oxford Nanopore, Roche Genia, Maxim-Gilbert sequencing, primer walking, and sequencing using PacBio, SOLID, Ion Torrent, or Nanopore platforms.

[00479] In some embodiments, sequencing comprises detecting and/or distinguishing unmodified and modified nucleobases. For example, PacBio sequencing (e.g., single-molecule real-time (SMRT) sequencing) offers the ability to directly detect of, e.g., 5-methylcytosine and 5- hydroxymethylcytosine as well as unmodified cytosine. See, e.g., Schatz., Nature Methods. 14(4): 347-348 (2017); and US 9,150,918. Also, Oxford nanopore sequencing systems (e.g., MinlON sequencer) that can directly detect methylation of DNA (for example: 5-methylcytosine and 5-hydroxymethylcytosine) can be used here. Sequencing reactions can be performed in a variety of sample processing units, which may multiple lanes, multiple channels, multiple wells, or other mean of processing multiple sample sets substantially simultaneously. Sample processing unit can also include multiple sample chambers to enable processing of multiple runs simultaneously. Similarly, Ion Torrent sequencing may also be used to directly detect methylation. Thus, in some embodiments, methylation status can be determined during sequencing, e.g., without or independently of a partitioning step or a conversion procedure such as bisulfite treatment. [00480] The sequencing reactions can be performed on one or more forms of nucleic acids, such as those known to contain markers of cancer or of other disease. The sequencing reactions can also be performed on any nucleic acid fragments present in the sample. In some embodiments, sequence coverage of the genome may be less than 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%, 99%, 99.9% or 100%. In some embodiments, the sequence reactions may provide for sequence coverage of at least 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, or 80% of the genome. Sequence coverage can be performed on at least 5, 10, 20, 70, 100, 200 or 500 different genes, or at most 5000, 2500, 1000, 500 or 100 different genes. [0304] Simultaneous sequencing reactions may be performed using multiplex sequencing. In some cases, cell-free nucleic acids may be sequenced with at least 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 50000, 100,000 sequencing reactions. In other cases, cell-free nucleic acids may be sequenced with less than 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 50000, 100,000 sequencing reactions. Sequencing reactions may be performed sequentially or simultaneously. Subsequent data analysis may be performed on all or part of the sequencing reactions. In some cases, data analysis may be performed on at least 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 50000, 100,000 sequencing reactions. In other cases, data analysis may be performed on less than 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 50000, 100,000 sequencing reactions. An exemplary read depth is 1000- 50000 reads per locus (base). 1.

1. Differential depth of sequencing

[00481] In some embodiments, nucleic acids corresponding to a sequence-variable target region set are sequenced to a greater depth of sequencing than nucleic acids corresponding to an epigenetic target region set. For example, the depth of sequencing for nucleic acids corresponding to sequence variant target region sets may be at least 1.25-, 1.5-, 1.75-, 2-, 2.25-, 2.5-, 2.75-, 3-, 3.5-, 4-, 4.5-, 5-, 6-, 7-, 8-, 9-, 10-, 11-, 12-, 13- , 14-, or 15 -fold greater, or 1.25- to 1.5-, 1.5- to 1.75-, 1.75- to 2-, 2- to 2.25-, 2.25- to 2.5-, 2.5- to 2.75-, 2.75- to 3-, 3- to 3.5-, 3.5- to 4-, 4- to 4.5-, 4.5- to 5-, 5- to 5.5-, 5.5- to 6-, 6- to 7-, 7- to 8-, 8- to 9-, 9- to 10-, 10- to 11-, 11- to 12-, 13- to 14-, 14- to 15-fold, or 15- to 100-fold greater, than the depth of sequencing for nucleic acids corresponding to an epigenetic target region set. In some embodiments, said depth of sequencing is at least 2-fold greater. In some embodiments, said depth of sequencing is at least 5-fold greater. In some embodiments, said depth of sequencing is at least 10-fold greater. In some embodiments, said depth of sequencing is 4- to 10-fold greater. In some embodiments, said depth of sequencing is 4- to 100-fold greater.

[00482] In some embodiments, DNA corresponding to a sequence-variable target region set, and/or to an epigenetic target region set are sequenced concurrently, e.g., in the same sequencing cell (such as the flow cell of an Illumina sequencer) and/or in the same composition, which may be a combined or pooled composition resulting from recombining separately captured sets or a composition obtained by, e.g., capturing the cfDNA corresponding to the sequence-variable target region set, and/or the captured cfDNA corresponding to an epigenetic target region set in the same vessel.

K. Analysis

[00483] In some embodiments, any of the methods disclosed herein comprises determining a likelihood that the subject from which the DNA was obtained has a disease or disorder related to the immune system, such as an infection, transplant rejection, or cancer or precancer, an indication of cancer

[00484] In some embodiments, any of the methods disclosed herein comprises identifying the presence of DNA produced by a tumor (or neoplastic cells, or cancer cells) or by precancer cells. In some embodiments, a method described herein comprises determining an indication of cancer in the subject. In some such embodiments, determination of the indication of cancer facilitates detection or diagnosis or cancer or precancer, or determination of cancer prognosis or cancer treatment options. For example, determining the metrics from the one or more classification regions and the one or more control regions can help in determining the indication of cancer. In some embodiments, the metrics can be used to determine the tumor fraction of a sample.

[00485] The present methods can be used to diagnose presence of conditions, particularly cancer or precancer, in a subject, to characterize conditions (e.g., staging cancer or determining heterogeneity of a cancer), monitor response to treatment of a condition, effect prognosis risk of developing a condition or subsequent course of a condition. The present disclosure can also be useful in determining the efficacy of a particular treatment option. For example, the change in the tumor fraction or determining the methylation status of one or regions can be useful in determining whether the patient is responding to the treatment or not. In another example, perhaps certain treatment options may be correlated with methylation profiles of cancers over time. This correlation may be useful in selecting a therapy.

[00486] Additionally, if a cancer is observed to be in remission after treatment, the present methods can be used to monitor residual disease or recurrence of disease.

[00487] The types and number of cancers that may be detected may include blood cancers, brain cancers, lung cancers, skin cancers, nose cancers, throat cancers, liver cancers, bone cancers, lymphomas, pancreatic cancers, skin cancers, bowel cancers, rectal cancers, thyroid cancers, bladder cancers, kidney cancers, mouth cancers, stomach cancers, solid state tumors, heterogeneous tumors, homogenous tumors and the like. Type and/or stage of cancer can be detected from genetic variations including mutations, rare mutations, indels, copy number variations, transversions, translocations, recombination, inversion, deletions, aneuploidy, partial aneuploidy, polyploidy, chromosomal instability, chromosomal structure alterations, gene fusions, chromosome fusions, gene truncations, gene amplification, gene duplications, chromosomal lesions, DNA lesions, abnormal changes in nucleic acid chemical modifications, abnormal changes in epigenetic patterns, and abnormal changes in nucleic acid 5-methylcytosine. [00488] Genetic data can also be used for characterizing a specific form of cancer. Cancers are often heterogeneous in both composition and staging. Genetic profile data may allow characterization of specific sub-types of cancer that may be important in the diagnosis or treatment of that specific sub-type. This information may also provide a subject or practitioner clues regarding the prognosis of a specific type of cancer and allow either a subject or practitioner to adapt treatment options in accord with the progress of the disease. Some cancers can progress to become more aggressive and genetically unstable. Other cancers may remain benign, inactive or dormant. The system and methods of this disclosure may be useful in determining disease progression.

[00489] Further, the methods of the disclosure may be used to characterize the heterogeneity of an abnormal condition in a subject. Such methods can include, e.g., generating a genetic profile of extracellular polynucleotides derived from the subject, wherein the genetic profile comprises a plurality of data resulting from copy number variation and rare mutation analyses. In some embodiments, an abnormal condition is cancer or precancer. In some embodiments, the abnormal condition may be one resulting in a heterogeneous genomic population. In the example of cancer, some tumors are known to comprise tumor cells in different stages of the cancer. In other examples, heterogeneity may comprise multiple foci of disease. Again, in the example of cancer, there may be multiple tumor foci, perhaps where one or more foci are the result of metastases that have spread from a primary site.

[00490] The present methods can be used to generate or profile, fingerprint or set of data that is a summation of genetic information derived from different cells in a heterogeneous disease. This set of data may comprise copy number variation, epigenetic variation, or other mutation analyses alone or in combination.

[00491] The present methods can be used to diagnose, prognose, monitor or observe cancers, or other diseases. In some embodiments, the methods herein do not involve the diagnosing, prognosing or monitoring a fetus and as such are not directed to non-invasive prenatal testing. In other embodiments, these methodologies may be employed in a pregnant subject to diagnose, prognose, monitor or observe cancers or other diseases in an unborn subject whose DNA and other polynucleotides may co- circulate with maternal molecules.

[00492] An exemplary method for determining an indication of cancer through NGS comprises the following steps:

1 . Extracting cfDNA from a blood sample

2. Partitioning cfDNA into a plurality of partitions by contacting the DNA with an agent that recognizes a modified cytosine, such as methyl cytosine, in the DNA

3. Ligating the partitions with adapters comprising molecular barcodes

4. Treating the hyper and/or intermediate partitions with one or more MSREs and/or treating the hypo partition with one or more MDREs

5. Amplifying the partitions post digestion via PCR amplification

6. Capturing DNA comprising hypermethylated target regions, hypomethylated target regions and control regions using target-specific probes. 7. Amplifying the captured DNA and assaying in multiplex on an NGS instrument.

8. Analyzing NGS data using one or more methods disclosed herein to determine the indication of cancer.

[00493] Another exemplary method for determining an indication of cancer through NGS comprises the following steps:

1. Extracting cfDNA from a blood sample.

2. Ligating the cfDNA with adapters comprising molecular barcodes

3. Subjecting the ligated cfDNA to a methylation-sensitive conversion method

4. Capturing DNA comprising hypermethylated target regions, hypomethylated target regions and control regions using target-specific probes, wherein the probes are designed such that they can be targeted to capture converted or unconverted molecules depending on the type of methylation-sensitive conversion method and the target regions (whether hypermethylated target regions or hypomethylated target regions) being captured.

5. Amplifying the captured DNA and assaying in multiplex on an NGS instrument.

6. Analyzing NGS data using one or more methods disclosed herein to determine the indication of cancer.

[00494] Another exemplary method for determining methylation status of a target region (e.g., promoter region) through NGS comprises the following steps:

1 . Extracting cfDNA from a blood sample

2. Partitioning cfDNA into a plurality of partitions by contacting the DNA with an agent that recognizes a modified cytosine, such as methyl cytosine, in the DNA

3. Ligating the partitions with adapters comprising molecular barcodes

4. Treating the hyper and/or intermediate partitions with one or more MSREs and/or treating the hypo partition with one or more MDREs

5. Amplifying the partitions post digestion via PCR amplification

6. Capturing DNA comprising hypermethylated target regions, hypomethylated target regions and control regions using target-specific probes.

7. Amplifying the captured DNA and assaying in multiplex on an NGS instrument.

8. Analyzing NGS data using one or more methods disclosed herein to determine whether the target region (e.g., promoter region) is methylated or not. [00495] Another exemplary method for determining an indication of cancer or for determining methylation status of a target region (e.g., promoter region) through NGS comprises the following steps:

1 . Extracting cfDNA from a blood sample

2. Partitioning cfDNA into a plurality of partitions by contacting the DNA with an agent that recognizes a modified cytosine, such as methyl cytosine, in the DNA

3. Ligating the partitions with adapters comprising molecular barcodes

4. Treating the hyper and/or intermediate partitions with a procedure that affect a first nucleobase in the cfDNA differently from a second nucleobase (e.g., bisulfite method, EM-seq)

5. Amplifying the partitions post -treating the procedure via PCR amplification

6. Capturing DNA comprising hypermethylated target regions, hypomethylated target regions and control regions using target-specific probes.

7. Amplifying the captured DNA and assaying in multiplex on an NGS instrument.

8. Analyzing NGS data using one or more methods disclosed herein to determine whether the target region (e.g., promoter region) is methylated or not.

[00496] In some embodiments, instead of using cfDNA from a blood sample, the exemplary methods discussed above can also be used with DNA samples obtained from tissue sample, stool sample or bodily fluids like urine sample. In these embodiments, the DNA can be a whole genomic DNA. In instances, where whole genomic DNA is used, an additional step of fragmenting the DNA (after DNA extraction, but prior to step 2) is performed to the methods discussed above. In some embodiments of methods described herein, molecular barcodes consist of nucleotides that are not altered by a procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA, such as any of those described herein (e.g., mC along with A, T, and G where the procedure is bisulfite conversion or any other conversion that does not affect mC; hmC along with A, T, and G where the procedure is a conversion that does not affect hmC; etc.). In some embodiments of methods described herein, the molecular tags do not comprise nucleotides that are altered by a procedure that affects a first nucleobase in the DNA differently from a second nucleobase in the DNA, such as any of those described herein (e.g., the tags do not comprise unmodified C where the procedure is bisulfite conversion or any other conversion that affects C; the tags do not comprise mC where the procedure is a conversion that affects mC; the tags do not comprise hmC where the procedure is a conversion that affects hmC; etc.).

Additional features of certain disclosed methods

A. Samples

[00497] A sample can be any biological sample isolated from a subject. A sample can be a bodily sample. Samples can include body tissues, such as known or suspected solid tumors, whole blood, platelets, serum, plasma, stool, red blood cells, white blood cells or leucocytes, endothelial cells, tissue biopsies, cerebrospinal fluid synovial fluid, lymphatic fluid, ascites fluid, interstitial or extracellular fluid, the fluid in spaces between cells, including gingival crevicular fluid, bone marrow, pleural effusions, cerebrospinal fluid, saliva, mucous, sputum, semen, sweat, urine. Samples are preferably body fluids, particularly blood and fractions thereof, and urine. A sample can be in the form originally isolated from a subject or can have been subjected to further processing to remove or add components, such as cells, or enrich for one component relative to another. Thus, a preferred body fluid for analysis is plasma or serum containing cell-free nucleic acids.

[00498] In some embodiments, a population of nucleic acids is obtained from a serum, plasma or blood sample from a subject suspected of having neoplasia, a tumor, precancer, or cancer or previously diagnosed with neoplasia, a tumor, precancer, or cancer. The population includes nucleic acids having varying levels of sequence variation, epigenetic variation, and/or post replication or transcriptional modifications. Post- replication modifications include modifications of cytosine, particularly at the 5-position of the nucleobase, e.g., 5-methylcytosine, 5- hydroxymethylcytosine, 5-formylcytosine and 5-ca rboxy I cytosi n e .

[00499] A sample can be isolated or obtained from a subject and transported to a site of sample analysis. The sample may be preserved and shipped at a desirable temperature, e.g., room temperature, 4°C, -20°C, and/or -80°C. A sample can be isolated or obtained from a subject at the site of the sample analysis. The subject can be a human, a mammal, an animal, a companion animal, a service animal, or a pet. The subject may have a cancer, precancer, infection, transplant rejection, or other disease or disorder related to changes in the immune system. The subject may not have cancer or a detectable cancer symptom. The subject may have been treated with one or more cancer therapy, e.g., any one or more of chemotherapies, antibodies, vaccines or biologies. The subject may be in remission. The subject may or may not be diagnosed of being susceptible to cancer or any cancer-associated genetic mutations/disorders.

[00500] In some embodiments, the sample comprises plasma. The volume of plasma obtained can depend on the desired read depth for sequenced regions. Exemplary volumes are 0.4-40 ml, 5-20 ml, 10-20 ml. For examples, the volume can be 0.5 mL, 1 mL, 5 ml_ 10 ml_, 20 ml_, 30 ml_, or 40 ml_. A volume of sampled plasma may be 5 to 20 mL.

[00501] A sample can comprise various amount of nucleic acid that contains genome equivalents. For example, a sample of about 30 ng DNA can contain about 10,000 (10⁴) haploid human genome equivalents and, in the case of cfDNA, about 200 billion (2xlOⁿ) individual polynucleotide molecules. Similarly, a sample of about 100 ng of DNA can contain about 30,000 haploid human genome equivalents and, in the case of cfDNA, about 600 billion individual molecules.

[00502] A sample can comprise nucleic acids from different sources, e.g., from cells and cell-free of the same subject, from cells and cell-free of different subjects. A sample can comprise nucleic acids carrying mutations. For example, a sample can comprise DNA carrying germline mutations and/or somatic mutations. Germline mutations refer to mutations existing in germline DNA of a subject. Somatic mutations refer to mutations originating in somatic cells of a subject, e.g., precancer cells or cancer cells. A sample can comprise DNA carrying cancer-associated mutations (e.g., cancer-associated somatic mutations). A sample can comprise an epigenetic variant (i.e., a chemical or protein modification), wherein the epigenetic variant associated with the presence of a genetic variant such as a cancer-associated mutation. In some embodiments, the sample comprises an epigenetic variant associated with the presence of a genetic variant, wherein the sample does not comprise the genetic variant.

[00503] Exemplary amounts of cell-free nucleic acids in a sample before amplification range from about 1 fg to about 1 pg, e.g., 1 pg to 200 ng, 1 ng to 100 ng, 10 ng to 1000 ng. For example, the amount can be up to about 600 ng, up to about 500 ng, up to about 400 ng, up to about 300 ng, up to about 200 ng, up to about 100 ng, up to about 50 ng, or up to about 20 ng of cell-free nucleic acid molecules. The amount can be at least 1 fg, at least 10 fg, at least 100 fg, at least 1 pg, at least 10 pg, at least 100 pg, at least 1 ng, at least 10 ng, at least 100 ng, at least 150 ng, or at least 200 ng of cell-free nucleic acid molecules. The amount can be up to 1 femtogram (fg), 10 fg, 100 fg, 1 picogram (pg), 10 pg, 100 pg, 1 ng, 10 ng, 100 ng, 150 ng, or 200 ng of cell-free nucleic acid molecules. The method can comprise obtaining 1 femtogram (fg) to 200 ng- [0326] Cell-free nucleic acids are nucleic acids not contained within or otherwise bound to a cell or in other words nucleic acids remaining in a sample after removing intact cells. Cell- free nucleic acids include DNA, RNA, and hybrids thereof, including genomic DNA, mitochondrial DNA, siRNA, miRNA, circulating RNA (cRNA), tRNA, rRNA, small nucleolar RNA (snoRNA), Piwi-interacting RNA (piRNA), long non-coding RNA (long ncRNA), or fragments of any of these. Cell-free nucleic acids can be double-stranded, single- stranded, or a hybrid thereof. A cell-free nucleic acid can be released into bodily fluid through secretion or cell death processes, e.g., cellular necrosis and apoptosis. Some cell-free nucleic acids are released into bodily fluid from cancer cells e.g., circulating tumor DNA, (ctDNA). Others are released from healthy cells. In some embodiments, cfDNA is cell-free fetal DNA (cffDNA) In some embodiments, cell free nucleic acids are produced by tumor cells. In some embodiments, cell free nucleic acids are produced by a mixture of tumor cells and non-tumor cells.

[00504] Cell-free nucleic acids have an exemplary size distribution of about 100-500 nucleotides, with molecules of 110 to about 230 nucleotides representing about 90% of molecules, with a mode of about 168 nucleotides and a second minor peak in a range between 240 to 440 nucleotides.

[00505] Cell-free nucleic acids can be isolated from bodily fluids through a fractionation step in which cell-free nucleic acids, as found in solution, are separated from intact cells and other non-soluble components of the bodily fluid. Partitioning may include techniques such as centrifugation or filtration. Alternatively, cells in bodily fluids can be lysed and cell-free and cellular nucleic acids processed together. Generally, after addition of buffers and wash steps, nucleic acids can be precipitated with an alcohol. Further clean up steps may be used such as silica-based columns to remove contaminants or salts. Non-specific bulk carrier nucleic acids, such as C 1 DNA, DNA or protein for bisulfite sequencing, hybridization, and/or ligation, may be added throughout the reaction to optimize certain aspects of the procedure such as yield. [0329] After such processing, samples can include various forms of nucleic acid including double stranded DNA, single stranded DNA, and single stranded RNA. In some embodiments, single stranded DNA and RNA can be converted to double stranded forms so they are included in subsequent processing and analysis steps. [0330] DNA molecules can be linked to adapters at either one end or both ends. Typically, double-stranded molecules are blunt ended by treatment with a polymerase with a 5'-3' polymerase and a 3 '-5' exonuclease (or proof-reading function), in the presence of all four standard nucleotides. Klenow large fragment and T4 polymerase are examples of suitable polymerase. The blunt ended DNA molecules can be ligated with at least partially double stranded adapter (e.g., a Y shaped or bell-shaped adapter). Alternatively, complementary nucleotides can be added to blunt ends of sample nucleic acids and adapters to facilitate ligation. Contemplated herein are both blunt end ligation and sticky end ligation. In blunt end ligation, both the nucleic acid molecules and the adapter tags have blunt ends. In sticky-end ligation, typically, the nucleic acid molecules bear an “A” overhang and the adapters bear a “T” overhang.

B. Tags

[00506] Tags comprising barcodes can be incorporated into or otherwise joined to adapters. Tags can be incorporated by ligation, overlap extension PCR among other methods. i) Molecular tagging strategies

[00507] Molecular tagging refers to a tagging practice that allows one to differentiate among DNA molecules from which sequence reads originated. Tagging strategies can be divided into unique tagging and non-unique tagging strategies. In unique tagging, all or substantially all of the molecules in a sample bear a different tag, so that reads can be assigned to original molecules based on tag information alone. Tags used in such methods are sometimes referred to as “unique tags”. In non-unique tagging, different molecules in the same sample can bear the same tag, so that other information in addition to tag information is used to assign a sequence read to an original molecule. Such information may include start and stop coordinate, coordinate to which the molecule maps, start or stop coordinate alone, etc. Tags used in such methods are sometimes referred to as “non-unique tags”. Accordingly, it is not necessary to uniquely tag every molecule in a sample. It suffices to uniquely tag molecules falling within an identifiable class within a sample. Thus, molecules in different identifiable families can bear the same tag without loss of information about the identity of the tagged molecule.

[00508] In certain embodiments of non-unique tagging, the number of different tags used can be sufficient that there is a very high likelihood (e.g., at least 99%, at least 99.9%, at least 99.99% or at least 99.999% that all DNA molecules of a particular group bear a different tag. It is to be noted that when barcodes are used as tags, and when barcodes are attached, e.g., randomly, to both ends of a molecule, the combination of barcodes, together, can constitute a tag. This number, in term, is a function of the number of molecules falling into the calls. For example, the class may be all molecules mapping to the same start-stop position on a reference genome. The class may be all molecules mapping across a particular genetic locus, e.g., a particular base or a particular region (e.g., up to 100 bases or a gene or an exon of a gene). In certain embodiments, the number of different tags used to uniquely identify a number of molecules, z, in a class can be between any of 2*z, 3*z, 4*z, 5*z, 6*z, 7*z, 8*z, 9*z, 10*z, 11 *z, 12*z, 13*z, 14*z, 15*z, 16*z, 17*z, 18*z, 19*z, 20*z or 100*z (e.g., lower limit) and any of 100,000*z, 10,000*z, 1000*z or 100*z (e.g., upper limit).

[00509] For example, in a sample of about 5 ng to 30 ng of cell free DNA, one expects around 3000 molecules to map to a particular nucleotide coordinate, and between about 3 and 10 molecules having any start coordinate to share the same stop coordinate. Accordingly, about 50 to about 50,000 different tags (e.g., between about 6 and 220 barcode combinations) can suffice to uniquely tag all such molecules. To uniquely tag all 3000 molecules mapping across a nucleotide coordinate, about 1 million to about 20 million different tags would be required. [0336] Generally, assignment of unique or non-unique tags barcodes in reactions follows methods and systems described by US patent applications 20010053519, 20030152490, 20110160078, and U.S. Pat. No. 6,582,908 and U.S. Pat. No. 7,537,898 and US Pat. No. 9,598,731. Tags can be linked to sample nucleic acids randomly or non-randomly. [0337] The unique tags may be loaded so that more than about 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, 100, 500, 1000, 5000, 10000, 50,000, 100,000, 500,000, 1 ,000,000, 10,000,000, 50,000,000 or 1 ,000,000,000 unique tags are loaded per genome sample. In some cases, the unique tags may be loaded so that less than about 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, 100, 500, 1000, 5000, 10000, 50,000, 100,000, 500,000, 1 ,000,000, 10,000,000, 50,000,000 or 1 ,000,000,000 unique tags are loaded per genome sample. In some cases, the average number of unique tags loaded per sample genome is less than, or greater than, about 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, 100, 500, 1000, 5000, 10000, 50,000, 100,000, 500,000, 1 ,000,000, 10,000,000, 50,000,000 or 1 ,000,000,000 unique tags per genome sample.

[00510] A preferred format uses 20-50 different tags (e.g., barcodes) ligated to both ends of target nucleic acids. For example, 35 different tags (e.g., barcodes) ligated to both ends of target molecules creating 35 x 35 permutations, which equals 1225 for 35 tags. Such numbers of tags are sufficient so that different molecules having the same start and stop points have a high probability (e.g., at least 94%, 99.5%, 99.99%, 99.999%) of receiving different combinations of tags. Other barcode combinations include any number between 10 and 500, e.g., about 15x15, about 35x35, about 75x75, about 100x100, about 250x250, about 500x500.

[00511] In some cases, unique tags may be predetermined or random or semi- random sequence oligonucleotides. In other cases, a plurality of barcodes may be used such that barcodes are not necessarily unique to one another in the plurality. In this example, barcodes may be ligated to individual molecules such that the combination of the barcode and the sequence it may be ligated to creates a unique sequence that may be individually tracked. As described herein, detection of non-unique barcodes in combination with sequence data of beginning (start) and end (stop) portions of sequence reads may allow assignment of a unique identity to a particular molecule. The length or number of base pairs, of an individual sequence read may also be used to assign a unique identity to such a molecule. As described herein, fragments from a single strand of nucleic acid having been assigned a unique identity, may thereby permit subsequent identification of fragments from the parent strand. C. Amplification

[00512] Sample nucleic acids flanked by adapters can be amplified by PCR and other amplification methods. Amplification is typically primed by primers that anneal or bind to primer binding sites in adapters flanking a DNA molecule to be amplified. Amplification methods can involve cycles of denaturation, annealing and extension, resulting from thermocycling or can be isothermal as in transcription-mediated amplification. Other amplification methods include the ligase chain reaction, strand displacement amplification, nucleic acid sequence-based amplification, and self- sustained sequence-based replication.

[00513] In some embodiments, the present methods perform dsDNA ligations with T-tailed and C-tailed adapters, which result in amplification of at least 50, 60, 70 or 80% of double stranded nucleic acids before linking to adapters. Preferably the present methods increase the amount or number of amplified molecules relative to control methods performed with T-tailed adapters alone by at least 10, 15 or 20%.

D. Capture moieties.

[00514] As discussed above, nucleic acids in a sample can be subject to a capture step, in which molecules having target regions are captured for subsequent analysis. Target capture can involve use of probes (e.g., oligonucleotides) labeled with a capture moiety, such as biotin, and a second moiety or binding partner that binds to the capture moiety, such as streptavidin. In some embodiments, a capture moiety and binding partner can have higher and lower capture yields for different sets of target regions, such as those of the sequence-variable target region set and the epigenetic target region set, respectively, as discussed elsewhere herein. Methods comprising capture moieties are further described in, for example, U.S. patent 9,850,523, issuing December 26, 2017, which is incorporated herein by reference.

[00515] Capture moieties include, without limitation, biotin, avidin, streptavidin, a nucleic acid comprising a particular nucleotide sequence, a hapten recognized by an antibody, and magnetically attractable particles. The extraction moiety can be a member of a binding pair, such as biotin/ streptavidin or hapten/antibody. In some embodiments, a capture moiety that is attached to an analyte is captured by its binding pair which is attached to an isolatable moiety, such as a magnetically attractable particle or a large particle that can be sedimented through centrifugation. The capture moiety can be any type of molecule that allows affinity separation of nucleic acids bearing the capture moiety from nucleic acids lacking the capture moiety. Exemplary capture moieties are biotin which allows affinity separation by binding to streptavidin linked or linkable to a solid phase or an oligonucleotide, which allows affinity separation through binding to a complementary oligonucleotide linked or linkable to a solid phase.

E. Collections of target-specific probes

[00516] In some embodiments, a collection of target-specific probes is used in a method comprising an epigenetic target region set and/or a sequence-variable target region set, as described herein. In some embodiments, the collection of target-specific probes comprises target binding probes specific for a sequence-variable target region set and target-binding probes specific for an epigenetic target region set. In some embodiments, the capture yield of the target binding probes specific for the sequence- variable target region set is higher (e.g., at least 2-fold higher) than the capture yield of the target-binding probes specific for the epigenetic target region set. In some embodiments, the collection of target-specific probes is configured to have a capture yield specific for the sequence-variable target region set higher (e.g., at least 2-fold higher) than its capture yield specific for the epigenetic target region set.

[00517] In some embodiments, the capture yield of the target-binding probes specific for the sequence-variable target region set is at least 1.25-, 1.5-, 1.75-, 2-, 2.25- , 2.5-, 2.75-, 3-, 3.5-, 4-, 4.5-, 5-, 6-, 7-, 8-, 9-, 10-, 11 -, 12-, 13-, 14-, or 15-fold higher than the capture yield of the target-binding probes specific for the epigenetic target region set. In some embodiments, the capture yield of the target-binding probes specific for the sequence-variable target region set is 1 .25- to 1.5-, 1 .5- to 1 .75-, 1 .75- to 2-, 2- to 2.25-, 2.25- to 2.5-, 2.5- to 2.75-, 2.75- to 3-, 3- to 3.5-, 3.5- to 4-, 4- to 4.5-, 4.5- to 5-, 5- to 5.5- , 5.5- to 6-, 6- to 7-, 7- to 8-, 8- to 9-, 9- to 10-, 10- to 11 -, 11- to 12-, 13- to 14-, or 14- to 15-fold higher than the capture yield of the target-binding probes specific for the epigenetic target region set. [00518] In some embodiments, the collection of target-specific probes is configured to have a capture yield specific for the sequence-variable target region set at least 1 .25-, 1.5-, 1.75-, 2-, 2.25-, 2.5-, 2.75-, 3-, 3.5-, 4-, 4.5-, 5-, 6-, 7-, 8-, 9-, 10-, 11-, 12-, 13-, 14-, or 15-fold higher than its capture yield for the epigenetic target region set. In some embodiments, the collection of target-specific probes is configured to have a capture yield specific for the sequence-variable target region set is 1 .25- to 1 .5-, 1 .5- to 1 .75-, 1 .75- to 2-, 2- to 2.25-, 2.25- to 2.5-, 2.5- to 2.75-, 2.75- to 3-, 3- to 3.5-, 3.5- to 4-, 4- to 4.5-, 4.5- to 5-, 5- to 5.5-, 5.5- to 6-, 6- to 7-, 7- to 8-, 8- to 9-, 9- to 10-, 10- to 11 -, 11 - to 12-, 13- to 14-, or 14- to 15-fold higher than its capture yield specific for the epigenetic target region set.

[00519] The collection of probes can be configured to provide higher capture yields for the sequence-variable target region set in various ways, including concentration, different lengths and/or chemistries (e.g., that affect affinity), and combinations thereof. Affinity can be modulated by adjusting probe length and/or including nucleotide modifications as discussed below.

[00520] In some embodiments, the target-specific probes specific for the sequence- variable target region set are present at a higher concentration than the target-specific probes specific for the epigenetic target region set. In some embodiments, concentration of the target-binding probes specific for the sequence-variable target region set is at least 1.25-, 1.5-, 1.75-, 2-, 2.25-, 2.5-, 2.75-, 3-, 3.5-, 4-, 4.5-, 5-, 6-, 7-, 8-, 9-, 10-, 11 -, 12-, 13- , 14-, or 15-fold higher than the concentration of the target-binding probes specific for the epigenetic target region set. In some embodiments, the concentration of the target- binding probes specific for the sequence-variable target region set is 1 .25- to 1 .5-, 1 .5- to 1 .75-, 1 .75- to 2-, 2- to 2.25-, 2.25- to 2.5-, 2.5- to 2.75-, 2.75- to 3-, 3- to 3.5-, 3.5- to 4-, 4- to 4.5-, 4.5- to 5-, 5- to 5.5-, 5.5- to 6-, 6- to 7-, 7- to 8-, 8- to 9-, 9- to 10-, 10- to 11-, 11- to 12-, 13- to 14-, or 14- to 15-fold higher than the concentration of the target-binding probes specific for the epigenetic target region set. In such embodiments, concentration may refer to the average mass per volume concentration of individual probes in each set. [00521] In some embodiments, the target-specific probes specific for the sequence- variable target region set have a higher affinity for their targets than the target-specific probes specific for the epigenetic target region set. Affinity can be modulated in any way known to those skilled in the art, including by using different probe chemistries. For example, certain nucleotide modifications, such as cytosine 5-methylation (in certain sequence contexts), modifications that provide a heteroatom at the T sugar position, and LNA nucleotides, can increase stability of double-stranded nucleic acids, indicating that oligonucleotides with such modifications have relatively higher affinity for their complementary sequences. See, e.g., Severin et ah, Nucleic Acids Res. 39: 8740-8751 (2011 ); Freier et ah, Nucleic Acids Res. 25: 4429-4443 (1997); US Patent No. 9,738,894. Also, longer sequence lengths will generally provide increased affinity. Other nucleotide modifications, such as the substitution of the nucleobase hypoxanthine for guanine, reduce affinity by reducing the amount of hydrogen bonding between the oligonucleotide and its complementary sequence. In some embodiments, the target-specific probes specific for the sequence-variable target region set have modifications that increase their affinity for their targets. In some embodiments, alternatively or additionally, the target- specific probes specific for the epigenetic target region set have modifications that decrease their affinity for their targets. In some embodiments, the target-specific probes specific for the sequence- variable target region set have longer average lengths and/or higher average melting temperatures than the target-specific probes specific for the epigenetic target region set. These embodiments may be combined with each other and/or with differences in concentration as discussed above to achieve a desired fold difference in capture yield, such as any fold difference or range thereof described above. [00522] In some embodiments, the target-specific probes comprise a capture moiety. The capture moiety may be any of the capture moieties described herein, e.g., biotin. In some embodiments, the target-specific probes are linked to a solid support, e.g., covalently or non-covalently such as through the interaction of a binding pair of capture moieties. In some embodiments, the solid support is a bead, such as a magnetic bead.

[00523] In some embodiments, the target-specific probes specific for the sequence- variable target region set and/or the target-specific probes specific for the epigenetic target region set comprise a capture moiety as discussed above, e.g., probes comprising capture moieties and sequences selected to tile across a panel of regions, such as genes. [00524] In some embodiments, the target-specific probes are provided in a single composition. [00525] The single composition may be a solution (liquid or frozen). Alternatively, it may be a lyophilizate.

[00526] Alternatively, the target-specific probes may be provided as a plurality of compositions, e.g., comprising a first composition comprising probes specific for the epigenetic target region set and a second composition comprising probes specific for the sequence-variable target region set. These probes may be mixed in appropriate proportions to provide a combined probe composition with any of the foregoing fold differences in concentration and/or capture yield. Alternatively, they may be used in separate capture procedures (e.g., with aliquots of a sample or sequentially with the same sample) to provide first and second compositions comprising captured epigenetic target regions and sequence-variable target regions, respectively. i) Probes specific for epigenetic target regions.

[00527] The probes for the epigenetic target region set may comprise probes specific for one or more types of target regions likely to differentiate DNA originating from different types of immune cells, including rare immune cell types, and/or to differentiate DNA from precancerous or neoplastic (e.g., tumor or cancer) cells from healthy cells, e.g., non-neoplastic circulating cells. Exemplary types of such regions are discussed in detail herein. The probes for the epigenetic target region set may also comprise probes for one or more control regions, e.g., as described herein.

[00528] In some embodiments, the probes for the epigenetic target region probe set have a footprint of at least 100 kb, e.g., at least 200 kb, at least 300 kb, or at least 400 kb. In some embodiments, the probes for the epigenetic target region set have a footprint in the range of 100- 1000 kb, e.g., 100-200 kb, 200-300 kb, 300-400 kb, 400-500 kb, 500- 600 kb, 600-700 kb, 700- 800 kb, 800-900 kb, and 900-1 ,000 kb. In some embodiments, the probes for the epigenetic target region probe set have a footprint of at least 5 kb, e.g., at least 10, 20, or 50 kb. a. Hypermethylation target regions.

[00529] In some embodiments, for the methods using methylation-sensitive conversion (e.g., bisulfite or EM-seq), the probes can be designed to target either the converted molecules or unconverted molecules depending on the type of methylation- sensitive conversion and the target region being enriched. For example, if bisulfite treatment is used, the unmethylated cytosines in the DNA molecules will be converted to dihydrouracil and methylated cytosines will remain unconverted as cytosine. For capturing DNA molecules in the hypermethylated target regions (where the molecules of interest to cancer or any other disease under investigation will be hypermethylated), the probes can be designed to capture the unconverted molecules, whereas for capturing molecules in the hypomethylated target regions (where the molecules of interest to cancer or any other disease under investigation will be hypomethylated or unmethylated), the probes can be designed to capture the converted molecules

[00530] In some embodiments, the probes for the epigenetic target region set comprise probes specific for one or more hypermethylation target regions. The hypermethylation target regions may be any of those set forth above. For example, in some embodiments, the probes specific for hypermethylation target regions comprise probes specific for a plurality of loci that are differentially methylated in different immune cell types. In some embodiments, each immune cell type specific hypermethylation target region comprises at least one CpG site that is methylated with a frequency greater than or equal to 0.3, 0.4, 0.5, or 0.6 in one immune cell type and with a frequency less than or equal to 0.1 , 0.2, or 0.3 in all other immune cell types. In some embodiments, each immune cell type specific hypermethylation target region comprises at least two CpG sites within 100 base pairs of each other that are each methylated with a frequency greater than or equal to 0.3, 0.4, 0.5, or 0.6 in one immune cell type and with a frequency less than or equal to 0.1 , 0.2, or 0.3 in all other immune cell types. In some such embodiments, each immune cell type specific hypermethylation target region comprises a total of at least 2, 3, 4, 5, 6, 7, 8, 9, or 10 CpG sites within 150 base pairs or within 200 base pairs, wherein fewer than three of the at least 2, 3, 4, 5, 6, 7, 8, 9, or 10 CpG sites are methylated with a frequency greater than 0.1 , 0.2, or 0.3 in any normal tissue type. In some embodiments, each immune cell type specific epigenetic target region set comprises at least 3, at least 5, at least 10, at least 20, or at least 30 hypermethylation target regions that are uniquely hypermethylated in each one of the immune cell types that are identified in the method.

[00531] In some embodiments, the probes specific for hypermethylation target regions comprise probes specific for a plurality of loci listed in Table 1 , e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the loci listed in Table 1. In some embodiments, the probes specific for hypermethylation target regions comprise probes specific for a plurality of loci listed in Table 2, e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the loci listed in Table 2. In some embodiments, the probes specific for hypermethylation target regions comprise probes specific for a plurality of loci listed in Table 1 or Table 2, e.g., at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 100% of the loci listed in Table 1 or Table 2.

[00532] In some embodiments, for each locus included as a target region, there may be one or more probes with a hybridization site that binds between the transcription start site and the stop codon (the last stop codon for genes that are alternatively spliced) of the gene. In some embodiments, the one or more probes bind within 300 bp of the listed position, e.g., within 200 or 100 bp. In some embodiments, a probe has a hybridization site overlapping the position listed above. In some embodiments, the probes specific for the hypermethylation target regions include probes specific for one, two, three, four, or five subsets of hypermethylation target regions that collectively show hypermethylation in one, two, three, four, or five of breast, colon, kidney, liver, and lung cancers, b. Hypomethylation target regions.

[00533] In some embodiments, the probes for the epigenetic target region set comprise probes specific for one or more hypomethylation target regions. The hypomethylation target regions may be any of those set forth above. For example, in some embodiments, the probes specific for hypomethylation target regions comprise probes specific for a plurality of loci that are differentially methylated in different immune cell types. In some embodiments, each immune cell type specific hypomethylation target region comprises at least one CpG site that is methylated with a frequency less than or equal to 0.1 , 0.2, or 0.3 in one immune cell type and with a frequency greater than or equal to 0.3, 0.4, 0.5, or 0.6 in all other immune cell types. In some embodiments, each immune cell type specific hypomethylation target region comprises at least two CpG sites within 100 base pairs of each other that are each methylated with a frequency less than or equal to 0.1 , 0.2, or 0.3 in one immune cell type and with a frequency greater than or equal to 0.3, 0.4, 0.5, or 0.6 in all other immune cell types. In some such embodiments, each immune cell type specific hypomethylation target region comprises a total of at least 2, 3, 4, 5, 6, 7, 8, 9, or 10 CpG sites within 150 base pairs or within 200 base pairs, wherein fewer than three of the at least 2, 3, 4, 5, 6, 7, 8, 9, or 10 CpG sites are methylated with a frequency less than 0.1 , 0.2, or 0.3 in any normal tissue type. In some embodiments, each immune cell type specific epigenetic target region set comprises at least 3, at least 5, at least 10, at least 20, or at least 30 hypomethylation target regions that are uniquely hypomethylated in each one of the immune cell types that are identified in the method.

[00534] In some embodiments, the probes specific for one or more hypomethylation target regions may include probes for regions such as repeated elements, e.g., LINE1 elements, Alu elements, centromeric tandem repeats, pericentromeric tandem repeats, and satellite DNA, and intergenic regions that are ordinarily methylated in healthy cells may show reduced methylation in tumor cells.

[00535] In some embodiments, probes specific for hypomethylation target regions include probes specific for repeated elements and/or intergenic regions. In some embodiments, probes specific for repeated elements include probes specific for one, two, three, four, or five of LINE1 elements, Alu elements, centromeric tandem repeats, pericentromeric tandem repeats, and/or satellite DNA.

[00536] Exemplary probes specific for genomic regions that show cancer- associated hypomethylation include probes specific for nucleotides 8403565-8953708 and/or 151104701 - 151106035 of human chromosome 1. In some embodiments, the probes specific for hypomethylation target regions include probes specific for regions overlapping or comprising nucleotides 8403565-8953708 and/or 151104701-151106035 of human chromosome 1 .

[00537] In some embodiments, the probes for the epigenetic target region set include probes specific for CTCF binding regions. In some embodiments, the probes specific for CTCF binding regions comprise probes specific for at least 10, 20, 50, 100, 200, or 500 CTCF binding regions, or 10-20, 20-50, 50-100, 100-200, 200-500, or 500- 1000 CTCF binding regions, e.g., such as CTCF binding regions described above or in one or more of CTCFBSDB or the Cuddapah et al., Martin et al., or Rhee et al. articles cited above. In some embodiments, the probes for the epigenetic target region set comprise at least 100 bp, at least 200 bp at least 300 bp, at least 400 bp, at least 500 bp, at least 750 bp, or at least 1000 bp upstream and downstream regions of the CTCF binding sites, d. Transcription start sites.

[00538] In some embodiments, the probes for the epigenetic target region set include probes specific for transcriptional start sites. In some embodiments, the probes specific for transcriptional start sites comprise probes specific for at least 10, 20, 50, 100, 200, or 500 transcriptional start sites, or 10-20, 20-50, 50-100, 100-200, 200-500, or 500- 1000 transcriptional start sites, e.g., such as transcriptional start sites listed in DBTSS. In some embodiments, the probes for the epigenetic target region set comprise probes for sequences at least 100 bp, at least 200 bp, at least 300 bp, at least 400 bp, at least 500 bp, at least 750 bp, or at least 1000 bp upstream and downstream of the transcriptional start sites.

[00539] As noted above, although focal amplifications are somatic mutations, they can be detected by sequencing based on read frequency in a manner analogous to approaches for detecting certain epigenetic changes such as changes in methylation. As such, regions that may show focal amplifications in cancer can be included in the epigenetic target region set, as discussed above. In some embodiments, the probes specific for the epigenetic target region set include probes specific for focal amplifications. In some embodiments, the probes specific for focal amplifications include probes specific for one or more of AR, BRAF, CCND1 , CCND2, CCNE1 , CDK4, CDK6, EGFR, ERBB2, FGFR1 , FGFR2, KIT, KRAS, MET, MYC, PDGFRA, PIK3CA, and RAFI. For example, in some embodiments, the probes specific for focal amplifications include probes specific for one or more of at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, or 18 of the foregoing targets.

Control regions

[00540] In some embodiments, the probes specific for the epigenetic target region set include probes specific for positive control regions that are expected to be methylated in essentially all samples. In some embodiments, the probes specific for the epigenetic target region set include probes specific for negative control regions that are expected to be hypomethylated or unmethylated in essentially all samples.

2) Probes specific for sequence-variable target regions. [00541] The probes for the sequence-variable target region set may comprise probes specific for a plurality of regions known to undergo somatic mutations in cancer. The probes may be specific for any sequence-variable target region set described herein. Exemplary sequence-variable target region sets are discussed in detail herein, e.g., in the sections above concerning captured sets. [0366] In some embodiments, the sequence-variable target region probe set has a footprint of at least 0.5 kb, e.g., at least 1 kb, at least 2 kb, at least 5 kb, at least 10 kb, at least 20 kb, at least 30 kb, or at least 40 kb. In some embodiments, the epigenetic target region probe set has a footprint in the range of 0.5-100 kb, e.g., 0.5-2 kb, 2-10 kb, 10-20 kb, 20-30 kb, 30-40 kb, 40-50 kb, 50- 60 kb, 60-70 kb, 70-80 kb, 80-90 kb, and 90-100 kb.

[00542] In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least a portion of at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, or at 70 of the genes of Table 4. In some embodiments, probes specific for the sequence- variable target region set comprise probes specific for the at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, or 70 of the SNVs of Table 3. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least 1 , at least 2, at least 3, at least 4, at least 5, or 6 ofthe fusions of Table 3. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least a portion of at least 1, at least 2, or 3 of the indels of Table 4. In some embodiments, probes specific for the sequence- variable target region set comprise probes specific for at least a portion of at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, at least 70, or 73 of the genes of Table 5. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 35, at least 40, at least 45, at least 50, at least 55, at least 60, at least 65, at least 70, or 73 of the SNVs of Table 5. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least 1 , at least 2, at least 3, at least 4, at least 5, or 6 of the fusions of Table 5. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least a portion of at least 1 , at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, or 18 of the indels of Table 5. In some embodiments, probes specific for the sequence-variable target region set comprise probes specific for at least a portion of at least 1 , at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 13, at least 14, at least 15, at least 16, at least 17, at least 18, at least 19, or at least 20 of the genes of Table 6.

[00543] In some embodiments, the probes specific for the sequence-variable target region set comprise probes specific for target regions from at least 10, 20, 30, or 35 cancer-related genes, such as AKTI, ALK, BRAF, CCND1 , CDK2A, CTNNB1 , EGFR, ERBB2, ESR1, FGFR1 , FGFR2, FGFR3, FOXL2, GAT A3, GNA11, GNAQ, GNAS, HRAS, IDH1 , IDH2, KIT, KRAS, MED 12, MET, MYC, NFE2L2, NRAS, PDGFRA, PIK3CA, PPP2R1A, PTEN, RET, STK11 , TP53, and U2AF 1.

Precision Treatments

[00544] The precision diagnostics provided by the improved computer system 110 may result in precision treatment plans, which may be identified by the computer system 110 (and/or curated by health professionals). For example, one type of precision diagnostic and treatment may relate to genes in the homologous recombination repair (HRR) pathway.

[00545] Homologous recombination is a type of genetic recombination in which nucleotide sequences are exchanged between two similar or identical molecules of DNA. It is most widely used by cells to accurately repair harmful breaks that occur on both strands of DNA, known as double-strand breaks (DSB). HRR provides a mechanism for the error-free removal of damage present in DNA that has replicated (S and G2 phases), to eliminate chromosomal breaks before the cell division occurs. The primary model for how homologous recombination repairs double-strand breaks in DNA is homologous recombination repair pathway which mediates the double-strand break repair (DSBR) pathway and the synthesis-dependent strand annealing (SDSA) pathway. Germline and somatic deficiencies in homologous recombination genes have been strongly linked to breast, ovarian and prostate cancers.

[00546] The number and types of variant nucleotides in a sample can provide an indication of the amenability of the subject providing the sample to treatment, i.e., therapeutic intervention. For example, various poly ADP ribose polymerase (PARP) inhibitors have been shown to stop the growth of tumors from breast, ovarian and prostate cancers caused by hereditary mutations in the BRCA1 or BRCA2 genes. Some of these therapeutic agents may inhibit base excision repair (BER), which may compensate for the deficiency of HRR.

[00547] On the other hand, certain BRCA and HRR wildtype patients may not achieve clinical benefit from treatment with a PARP inhibitor. Furthermore, not all ovarian cancer patients with a BRCA mutation will respond to a PARP inhibitor. Moreover, different types of mutations may indicate different therapies. For example, somatic heterozygous deletions in HRR genes may indicate a different therapy than somatic homozygous deletions. Thus, the state of genetic material may influence therapy. In one example, a PARP inhibitor may be administered to an individual harboring a somatic homozygous deletion in a HRR gene, but not to an individual harboring a wildtype allele or somatic heterozygous deletions in the HRR gene.

[00548] In some implementations, a subject having HRD as determined by any of the methods disclosed may be administered a targeted therapy. The targeted therapy may comprise a PARP inhibitor. Examples of PARP inhibitors that may be administered include one or more of: VELIPARIB, OLAPARIB, TALAZOPARIB, RUCAPARIB, NIRAPARIB, PAMIPARIB, CEP 9722 (Cephalon), E7016 (Eisai), E7449 (Eisai, a PARP 1/2 and tankyrase 1/2 inhibitor), or 3-Aminobenzamide. In some implementations, the targeted therapy may comprise at least one base excision repair (BER) inhibitor. For example, OLAPARIB may inhibit BER. In certain implementations, the targeted therapy may comprise combination of a PARP inhibitor and radiotherapy. In an implementation, the combination of a PARP inhibitor and radiotherapy would permit the PARP inhibitor to lead to formation of double strand breaks from the single-strand breaks generated by the radiotherapy in tumor tissue (e.g., tissue with BRCA1/BRCA2 mutations). This combination can provide more powerful therapy per radiation dose. Related Therapies

[00549] In certain embodiments, the methods disclosed herein relate to identifying and administering therapies, such as customized therapies, to patients or subjects based on the determination of the presence or absence or levels of epigenomic and/or genetic variation. In some embodiments, the patient or subject has a given disease, disorder or condition, e.g., any of the cancers or other conditions described elsewhere herein. Essentially any cancer therapy (e.g., surgical therapy, radiation therapy, chemotherapy, immunotherapy, and/or the like) may be included as part of these methods.

[00550] Typically, the disease under consideration is a type of cancer. Non-limiting examples of such cancers include biliary tract cancer, bladder cancer, transitional cell carcinoma, urothelial carcinoma, brain cancer, gliomas, astrocytomas, breast cancer, metaplastic carcinoma, cervical cancer, cervical squamous cell carcinoma, rectal cancer, colorectal carcinoma, colon cancer, hereditary nonpolyposis colorectal cancer, colorectal adenocarcinomas, gastrointestinal stromal tumors (GISTs), endometrial carcinoma, endometrial stromal sarcomas, esophageal cancer, esophageal squamous cell carcinoma, esophageal adenocarcinoma, ocular melanoma, uveal melanoma, gallbladder carcinomas, gallbladder adenocarcinoma, renal cell carcinoma, clear cell renal cell carcinoma, transitional cell carcinoma, urothelial carcinomas, Wilms tumor, leukemia, acute lymphocytic leukemia (ALL), acute myeloid leukemia (AML), chronic lymphocytic leukemia (CLL), chronic myeloid leukemia (CML), chronic myelomonocytic leukemia (CMML), liver cancer, liver carcinoma, hepatoma, hepatocellular carcinoma, cholangiocarcinoma, hepatoblastoma, Lung cancer, non-small cell lung cancer (NSCLC), mesothelioma, B-cell lymphomas, non-Hodgkin lymphoma, diffuse large B-cell lymphoma, Mantle cell lymphoma, T cell lymphomas, non- Hodgkin lymphoma, precursor T-lymphoblastic lymphoma/leukemia, peripheral T cell lymphomas, multiple myeloma, nasopharyngeal carcinoma (NPC), neuroblastoma, oropharyngeal cancer, oral cavity squamous cell carcinomas, osteosarcoma, ovarian carcinoma, pancreatic cancer, pancreatic ductal adenocarcinoma, pseudopapillary neoplasms, acinar cell carcinomas, Prostate cancer, prostate adenocarcinoma, skin cancer, melanoma, malignant melanoma, cutaneous melanoma, small intestine carcinomas, stomach cancer, gastric carcinoma, gastrointestinal stromal tumor (GIST), uterine cancer, or uterine sarcoma.

[00551] Non-limiting examples of other genetic-based diseases, disorders, or conditions that are optionally evaluated using the methods and systems disclosed herein include achondroplasia, alpha- 1 antitrypsin deficiency, antiphospholipid syndrome, autism, autosomal dominant polycystic kidney disease, Charcot-Marie-Tooth (CMT), cri du chat, Crohn's disease, cystic fibrosis, Dercum disease, down syndrome, Duane syndrome, Duchenne muscular dystrophy, Factor V Leiden thrombophilia, familial hypercholesterolemia, familial mediterranean fever, fragile X syndrome, Gaucher disease, hemochromatosis, hemophilia, holoprosencephaly, Huntington's disease, Klinefelter syndrome, Marfan syndrome, myotonic dystrophy, neurofibromatosis, Noonan syndrome, osteogenesis imperfecta, Parkinson's disease, phenylketonuria, Poland anomaly, porphyria, progeria, retinitis pigmentosa, severe combined immunodeficiency (scid), sickle cell disease, spinal muscular atrophy, Tay-Sachs, thalassemia, trimethylaminuria, Turner syndrome, velocardiofacial syndrome, WAGR syndrome, Wilson disease, or the like.

[00552] In certain embodiments, the therapies can include one or more of treatments for target therapies, including abemaciclib (Verzenio), abiraterone acetate (Zytiga), acalabrutinib (Calquence), adagrasib (Krazati), ado-trastuzumab emtansine (Kadcyla), afatinib dimaleate (Gilotrif), alectinib (Alecensa), alemtuzumab (Campath), alitretinoin (Panretin), alpelisib (Piqray), amivantamab- vmjw (Rybrevant), anastrozole (Arimidex), apalutamide (Erleada), asciminib hydrochloride (Scemblix), atezolizumab (Tecentriq), atezolizumab (Tecentriq), avapritinib (Ayvakit), avelumab (Bavencio), axicabtagene ciloleucel (Yescarta), axitinib (Inlyta), belinostat (Beleodaq), belzutifan (Welireg), bevacizumab (Avastin), bexarotene (Targretin), binimetinib (Mektovi), blinatumomab (Blincyto), bortezomib (Velcade), bosutinib (Bosulif), brentuximab vedotin (Adcetris), brexucabtagene autoleucel (Tecartus), brigatinib (Alunbrig), cabazitaxel (Jevtana), cabozantinib-s-malate (Cabometyx), cabozantinib-s-malate (Cometriq), capmatinib hydrochloride (Tabrecta), carfilzomib (Kyprolis), cemiplimab-rwlc (Libtayo), ceritinib (Zykadia), cetuximab (Erbitux), ciltacabtagene autoleucel (Carvykti), cobimetinib fumarate (Cotellic), copanlisib hydrochloride (Aliqopa), crizotinib (Xalkori), dabrafenib (Tafmlar), dabrafenib mesylate (Tafmlar), dacomitinib (Vizimpro), daratumumab (Darzalex), daratumumab and hyaluronidase-fihj (Darzalex Faspro), darolutamide (Nubeqa), dasatinib (Sprycel), denileukin diftitox (Ontak), denosumab (Xgeva), dinutuximab (Unituxin), dostarlimab-gxly (Jemperli), durvalumab (Imfinzi), duvelisib (Copiktra), elacestrant dihydrochloride (Orserdu), elotuzumab (Empliciti), enasidenib mesylate (Idhifa), encorafenib (Braftovi), enfortumab vedotin-ejfv (Padcev), entrectinib (Rozlytrek), enzalutamide (Xtandi), erdafitinib (Balversa), erlotinib hydrochloride (Tarceva), everolimus (Afinitor), exemestane (Aromasin), fam-trastuzumab deruxtecan- nxki (Enhertu), fam-trastuzumab deruxtecan-nxki (Enhertu), fedratinib hydrochloride (Inrebic), fulvestrant (Faslodex), futibatinib (Lytgobi), gefitinib (Iressa), gemtuzumab ozogamicin (Mylotarg), gilteritinib fumarate (Xospata), glasdegib maleate (Daurismo), ibritumomab tiuxetan (Zevalin), ibrutinib (Imbruvica), idecabtagene vicleucel (Abecma), idelalisib (Zydelig), imatinib mesylate (Gleevec), infigratinib phosphate (Truseltiq), inotuzumab ozogamicin (Besponsa), iobenguane 1 131 (Azedra), ipilimumab (Yervoy), isatuximab-irfc (Sarclisa), ivosidenib (Tibsovo), ixazomib citrate (Ninlaro), lanreotide acetate (SomatulineDepot), lapatinib ditosylate (Tykerb), larotrectinib sulfate (Vitrakvi), lenvatinib mesylate (Lenvima), letrozole (Femara), lisocabtagene maraleucel (Breyanzi), loncastuximab tesirine-lpyl (Zynlonta), lorlatinib (Lorbrena), lutetium Lu 177 vipivotide tetraxetan (Pluvicto), lutetium Lu 177-dotatate (Lutathera), margetuximab-cmkb (Margenza), midostaurin (Rydapt), mirvetuximab soravtansine-gynx (Elahere), mobocertinib succinate (Exkivity), mogamulizumab-kpkc (Poteligeo), mosunetuzumab- axgb (Lunsumio), moxetumomab pasudotox-tdfk(Lumoxiti), naxitamab-gqgk (Danyelza), necitumumab (Portrazza), neratinib maleate (Nerlynx), nilotinib (Tasigna), niraparib tosylate monohydrate (Zejula), nivolumab (Opdivo), nivolumab and relatlimab-rmbw (Opdualag), obinutuzumab (Gazyva), ofatumumab (Arzerra), olaparib (Lynparza), olutasidenib (Rezlidhia), osimertinib mesylate (Tagrisso), pacritinib citrate (Vonjo), palbociclib (Ibrance), panitumumab (Vectibix), pazopanib hydrochloride(Votrient), pembrolizumab (Keytruda), pemigatinib(Pemazyre), pertuzumab (Perjeta), pertuzumab, trastuzumab, and hyaluronidase-zzxf (Phesgo), pexidartinib hydrochloride (Turalio), pirtobrutinib (Jaypirca), polatuzumab vedotin-piiq (Polivy), ponatinib hydrochloride (Iclusig), pralatrexate (Folotyn), pralsetinib (Gavreto), radium 223 dichloride (Xofigo), ramucirumab (Cyramza), regorafenib (Stivarga), retifanlimab-dlwr (Zynyz), ribociclib (Kisqali), ripretinib (Qinlock), rituximab (Rituxan), rituximab and hyaluronidase human (Rituxan Hycela), romidepsin (Istodax), rucaparib camsylate(Rubraca), ruxolitinib phosphate (Jakafi), sacituzumab govitecan-hziy (Trodelvy), selinexor (Xpovio), selpercatinib (Retevmo), selumetinib sulfate (Koselugo), siltuximab (Sylvant), sirolimus protein-bound particles (Fyarro), sonidegib (Odomzo), sorafenib tosylate (Nexavar), sotorasib (Lumakras), sunitinib malate (Sutent), tafasitamab-cxix (Monjuvi), tagraxofusp- erzs (Elzonris), talazoparib tosylate (Talzenna), tamoxifen citrate (Soltamox), tazemetostat hydrobromide (Tazverik), tebentafusp-tebn (Kimmtrak), teclistamab-cqyv (Tecvayli), temsirolimus (Torisel), tepotinib hydrochloride (Tepmetko), tisagenlecleucel (Kymriah), tisotumab vedotin-tftv (Tivdak), tivozanib hydrochloride (Fotivda), toremifene (Fareston), trametinib (Mekinist), trametinib dimethyl sulfoxide (Mekinist), trastuzumab (Herceptin), tremelimumab-actl (Imjudo), tretinoin (Vesanoid), tucatinib (Tukysa), vandetanib (Caprelsa), vemurafenib (Zelboraf), venetoclax (Venclexta), vismodegib (Erivedge), vorinostat (Zolinza), zanubrutinib (Brukinsa), ziv-aflibercept (Zaltrap).

[00553] In certain embodiments, the therapy administered to a subject comprises at least one chemotherapy drug. In some embodiments, the chemotherapy drug may comprise alkylating agents (for example, but not limited to, Chlorambucil, Cyclophosphamide, Cisplatin and Carboplatin), nitrosoureas (for example, but not limited to, Carmustine and Lomustine), anti-metabolites (for example, but not limited to, Fluorauracil, Methotrexate and Fludarabine), plant alkaloids and natural products (for example, but not limited to, Vincristine, Paclitaxel and Topotecan), anti- tumor antibiotics (for example, but not limited to, Bleomycin, Doxorubicin and Mitoxantrone), hormonal agents (for example, but not limited to, Prednisone, Dexamethasone, Tamoxifen and Leuprolide) and biological response modifiers (for example, but not limited to, Herceptin and Avastin, Erbitux and Rituxan). In some embodiments, the chemotherapy administered to a subject may comprise FOLFOX or FOLFIRI. In certain embodiments, a therapy may be administered to a subject that comprises at least one PARP inhibitor. In certain embodiments, the PARP inhibitor may include OLAPARIB, TALAZOPARIB, RUCAPARIB, NIRAPARIB (trade name ZEJULA), among others. In some embodiments, the methods comprise administering a therapy comprising a PARP inhibitor, such as olaparib, to a subject determined to have homologous recombination repair (HRR) gene or deficiency (HRD), such as with BRCA1 , BRCA2, ATM, BARD1 , BRIP1 , CDK12, CHEK1 , CHEK2, FANCL, PALB2, RAD51 B, RAD51C, RAD51 D, and RAD54L alterations. In some embodiments, the subject has a metastatic castrate resistant prostate cancer (mCRPC). In some embodiments, the PARP inhibitor, such as olaprib is used to treat a subject having ovarian cancer, breast cancer, pancreatic cancer, or mCRPC, wherein the subject is determined to have alterations in BRCA1 , BRCA2, and/or ATM.

[00554] In some embodiments, essentially any cancer therapy (e.g., surgical therapy, radiation therapy, chemotherapy, immunotherapy, and/or the like) may be included as part of these methods. Customized therapies can include at least one immunotherapy (or an immunotherapeutic agent). Immunotherapy refers generally to methods of enhancing an immune response against a given cancer type. In certain embodiments, immunotherapy refers to methods of enhancing a T cell response against a tumor or cancer.

[00555] In some embodiments, the immunotherapy or immunotherapeutic agent targets an immune checkpoint molecule. Certain tumors are able to evade the immune system by co-opting an immune checkpoint pathway. Thus, targeting immune checkpoints has emerged as an effective approach for countering a tumor’s ability to evade the immune system and activating anti-tumor immunity against certain cancers. Pardoll, Nature Reviews Cancer, 2012, 12:252-264.

[00556] In certain embodiments, the immune checkpoint molecule is an inhibitory molecule that reduces a signal involved in the T cell response to antigen. For example, CTLA4 is expressed on T cells and plays a role in downregulating T cell activation by binding to CD80 (aka B7.1 ) or CD86 (aka B7.2) on antigen presenting cells. PD-1 is another inhibitory checkpoint molecule that is expressed on T cells. PD-1 limits the activity of T cells in peripheral tissues during an inflammatory response. In addition, the ligand for PD-1 (PD-L1 or PD-L2) is commonly upregulated on the surface of many different tumors, resulting in the downregulation of anti-tumor immune responses in the tumor microenvironment. In certain embodiments, the inhibitory immune checkpoint molecule is CTLA4 or PD-1. In other embodiments, the inhibitory immune checkpoint molecule is a ligand for PD-1, such as PD-L1 or PD-L2. In other embodiments, the inhibitory immune checkpoint molecule is a ligand for CTLA4, such as CD80 or CD86. In other embodiments, the inhibitory immune checkpoint molecule is lymphocyte activation gene 3 (LAG3), killer cell immunoglobulin like receptor (KIR), T cell membrane protein 3 (TIM3), galectin 9 (GAL9), or adenosine A2a receptor (A2aR).

[00557] Antagonists that target these immune checkpoint molecules can be used to enhance antigen-specific T cell responses against certain cancers. Accordingly, in certain embodiments, the immunotherapy or immunotherapeutic agent is an antagonist of an inhibitory immune checkpoint molecule. In certain embodiments, the inhibitory immune checkpoint molecule is PD-1. In certain embodiments, the inhibitory immune checkpoint molecule is PD-L1. In certain embodiments, the antagonist of the inhibitory immune checkpoint molecule is an antibody (e.g., a monoclonal antibody). In certain embodiments, the antibody or monoclonal antibody is an anti-CTLA4, anti-PD-1 , anti-PD- L1 , or anti-PD-L2 antibody. In certain embodiments, the antibody is a monoclonal anti- PD-1 antibody. In some embodiments, the antibody is a monoclonal anti-PD-L1 antibody. In certain embodiments, the monoclonal antibody is a combination of an anti-CTLA4 antibody and an anti-PD-1 antibody, an anti-CTLA4 antibody and an anti-PD-L1 antibody, or an anti-PD-L1 antibody and an anti-PD-1 antibody. In certain embodiments, the anti- PD-1 antibody is one or more of pembrolizumab (Keytruda®) or nivolumab (Opdivo®). In certain embodiments, the anti-CTLA4 antibody is ipilimumab (Yervoy®). In certain embodiments, the anti-PD-L1 antibody is one or more of atezolizumab (Tecentriq®), avelumab (Bavencio®), or durvalumab (Imfinzi®). In certain embodiments, immunotherapy, such as pembrolizumab, is used to treat a subject determined to have a high microsatellite instability status (MSI-H). In certain embodiments, the immunotherapy, such as pembrolizumab, is used to treat a subject determined to have a high tumor mutational burden (TMB), for example, then the TMB status is greater than or equal to 10 mutations per megabase. In certain embodiment, the immunotherapy, such as pembrolizumab, is used to treat a subject determined to a have a mismatch repair deficiency (dMMR), such as in genes comprising MLH1 , PMS2, MSH2 and MSH6.

[00558] In certain embodiments, the immunotherapy or immunotherapeutic agent is an antagonist (e.g., antibody) against CD80, CD86, LAG3, KIR, TIM3, GAL9, or A2aR. In other embodiments, the antagonist is a soluble version of the inhibitory immune checkpoint molecule, such as a soluble fusion protein comprising the extracellular domain of the inhibitory immune checkpoint molecule and an Fc domain of an antibody. In certain embodiments, the soluble fusion protein comprises the extracellular domain of CTLA4, PD-1 , PD-L1 , or PD-L2. In some embodiments, the soluble fusion protein comprises the extracellular domain of CD80, CD86, LAG3, KIR, TIM3, GAL9, or A2aR. In one embodiment, the soluble fusion protein comprises the extracellular domain of PD-L2 or LAG3.

[00559] In certain embodiments, the immune checkpoint molecule is a co- stimulatory molecule that amplifies a signal involved in a T cell response to an antigen. For example, CD28 is a co-stimulatory receptor expressed on T cells. When a T cell binds to antigen through its T cell receptor, CD28 binds to CD80 (aka B7.1) or CD86 (aka B7.2) on antigen-presenting cells to amplify T cell receptor signaling and promote T cell activation. Because CD28 binds to the same ligands (CD80 and CD86) as CTLA4, CTLA4 is able to counteract or regulate the co-stimulatory signaling mediated by CD28. In certain embodiments, the immune checkpoint molecule is a co-stimulatory molecule selected from CD28, inducible T cell co-stimulator (ICOS), CD137, 0X40, or CD27. In other embodiments, the immune checkpoint molecule is a ligand of a co-stimulatory molecule, including, for example, CD80, CD86, B7RP1 , B7-H3, B7-H4, CD137L, OX40L, or CD70. [00560] Agonists that target these co-stimulatory checkpoint molecules can be used to enhance antigen-specific T cell responses against certain cancers. Accordingly, in certain embodiments, the immunotherapy or immunotherapeutic agent is an agonist of a co-stimulatory checkpoint molecule. In certain embodiments, the agonist of the co- stimulatory checkpoint molecule is an agonist antibody and preferably is a monoclonal antibody. In certain embodiments, the agonist antibody or monoclonal antibody is an anti- CD28 antibody. In other embodiments, the agonist antibody or monoclonal antibody is an anti-ICOS, anti-CD137, anti-OX40, or anti-CD27 antibody. In other embodiments, the agonist antibody or monoclonal antibody is an anti-CD80, anti-CD86, anti-B7RP1 , anti- B7-H3, anti-B7-H4, anti-CD137L, anti-OX40L, or anti-CD70 antibody.

[00561] In certain embodiments, the status of a nucleic acid variant from a sample from a subject as being of somatic or germline origin may be compared with a database of comparator results from a reference population to identify customized or targeted therapies for that subject. Typically, the reference population includes patients with the same cancer or disease type as the subject and/or patients who are receiving, or who have received, the same therapy as the subject. A customized or targeted therapy (or therapies) may be identified when the nucleic variant and the comparator results satisfy certain classification criteria (e.g., are a substantial or an approximate match).

[00562] In certain embodiments, the customized therapies described herein are typically administered parenterally (e.g., intravenously or subcutaneously). Pharmaceutical compositions containing an immunotherapeutic agent are typically administered intravenously. Certain therapeutic agents are administered orally. However, customized therapies (e.g., immunotherapeutic agents, etc.) may also be administered by any method known in the art, for example, buccal, sublingual, rectal, vaginal, intraurethral, topical, intraocular, intranasal, and/or intraauricular, which administration may include tablets, capsules, granules, aqueous suspensions, gels, sprays, suppositories, salves, ointments, or the like.

[00563] In certain embodiments, the present methods are also useful in determining the efficacy of particular treatment options. For example, the number of variations detected, irrespective of their precise identity, is a predictor of amenability to immunotherapy because the mutations create neoepitopes that can be subject of immune attack (see e.g., US20200370129).

[00564] Other variations or copy number variations indicate suitability of a particular drug. Some examples of such variations are as follows:

Table 1 : List of cancer types with associated biomarker target and drug

[00565] In certain embodiments, the therapy comprises administrating a treatment to a subject determined to have a copy number amplification. In some embodiments, the treatment may comprise trastuzumab, ado-trastuzumab emtansine, or pertuzumab where the subject was determined to have an ERBB2 (HER2) gene amplification. In some embodiments, the subject has breast cancer or gastric cancer.

[00566] In some embodiments, the therapy comprises administering one or more drugs to the subject. For example, patients with non-small lung cancer determined to have either an EGFR exon 19 deletion or an EGFR exon 21 L858R alteration may be treated with amivantamab in combination with lazertinib.

[00567] The present methods can be used to generate or profile, fingerprint or set of data that is a summation of genetic information derived from different cells in a heterogeneous disease. This set of data may comprise copy number variation, nucleotide variation, epigenomic information, and/or tumor fraction. In some embodiments, the methods disclosed herein are used to monitor the efficacy or responsiveness of a treatment to the subject. In some embodiments, the methods disclosed herein can be used to determine whether the subject is a candidate for a therapy to treat the cancer or disease.

[00568] The present methods can be used to diagnose, prognose, monitor or observe cancers or other diseases of fetal origin. That is, these methodologies can be employed in a pregnant subject to diagnose, prognose, monitor or observe cancers or other diseases in an unborn subject whose DNA and other nucleic acids may co-circulate with maternal molecules.

[00569] In certain embodiments, the present methods can be used to determine minimal residual disease (MRD) of a subject, for example, based on a tumor fraction determination. In some embodiments, the methods may be directed to determining MRD by using a tissue-informed assay (i.e., using a tissue sample collected from a patient to determine a personalized panel to enrich for one or more genomic and/or epigenomic variants in a subsequent blood sample from the patient) or a tissue-naive assay.

[00570] In certain embodiments, the present methods can integrate genomic and/or epigenomic data with proteomic (proteins and their post-translational modifications), transcriptomic, fragmentomic, immunological, histological, and/or other analyte-specific data to determine disease initiation, progression, malignant transformation, and therapeutic outcomes.

[00571] Figure 9 is a block diagram illustrating components of a machine 900, according to some example implementations, able to read instructions from a machine- readable medium (e.g., a machine-readable storage medium) and perform any one or more of the methodologies discussed herein. Specifically, Figure 9 shows a diagrammatic representation of the machine 900 in the example form of a computer system, within which instructions 902 (e.g., software, a program, an application, an applet, an app, or other executable code) for causing the machine 900 to perform any one or more of the methodologies discussed herein may be executed. As such, the instructions 902 may be used to implement modules or components described herein. The instructions 902 transform the general, non-programmed machine 900 into a particular machine 900 programmed to carry out the described and illustrated functions in the manner described. In alternative implementations, the machine 900 operates as a standalone device or may be coupled (e.g., networked) to other machines. In a networked deployment, the machine 900 may operate in the capacity of a server machine or a client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The machine 900 may comprise, but not be limited to, a server computer, a client computer, a personal computer (PC), a tablet computer, a laptop computer, a netbook, a set-top box (STB), a personal digital assistant (PDA), an entertainment media system, a cellular telephone, a smart phone, a mobile device, a wearable device (e.g., a smart watch), a smart home device (e.g., a smart appliance), other smart devices, a web appliance, a network router, a network switch, a network bridge, or any machine capable of executing the instructions 902, sequentially or otherwise, that specify actions to be taken by machine 900. Further, while only a single machine 900 is illustrated, the term "machine" shall also be taken to include a collection of machines that individually or jointly execute the instructions 902 to perform any one or more of the methodologies discussed herein.

[00572] The machine 900 may include processors 904, memory/storage 906, and I/O components 908, which may be configured to communicate with each other such as via a bus 910. In an example implementation, the processors 904 (e.g., a central processing unit (CPU), a reduced instruction set computing (RISC) processor, a complex instruction set computing (CISC) processor, a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a radio- frequency integrated circuit (RFIC), another processor, or any suitable combination thereof) may include, for example, a processor 912 and a processor 914 that may execute the instructions 902. The term “processor" is intended to include multi-core processors 904 that may comprise two or more independent processors (sometimes referred to as “cores”) that may execute instructions 902 contemporaneously. Although Figure 9 shows multiple processors 904, the machine 900 may include a single processor 912 with a single core, a single processor 912 with multiple cores (e.g., a multi-core processor), multiple processors 912, 914 with a single core, multiple processors 912, 914 with multiple cores, or any combination thereof.

[00573] The memory/storage 906 may include memory, such as a main memory 916, or other memory storage, and a storage unit 918, both accessible to the processors 904 such as via the bus 910. The storage unit 918 and main memory 916 store the instructions 902 embodying any one or more of the methodologies or functions described herein. The instructions 902 may also reside, completely or partially, within the main memory 916, within the storage unit 918, within at least one of the processors 904 (e.g., within the processor’s cache memory), or any suitable combination thereof, during execution thereof by the machine 900. Accordingly, the main memory 916, the storage unit 918, and the memory of processors 904 are examples of machine-readable media.

[00574] The I/O components 908components 908 may include a wide variety of components to receive input, provide output, produce output, transmit information, exchange information, capture measurements, and so on. The specific I/O components 908 that are included in a particular machine 900 will depend on the type of machine. For example, portable machines such as mobile phones will likely include a touch input device or other such input mechanisms, while a headless server machine will likely not include such a touch input device. It will be appreciated that the I/O components 908components 908 may include many other components that are not shown in Figure 9. The I/O components 908 are grouped according to functionality merely for simplifying the following discussion and the grouping is in no way limiting. In various example implementations, the I/O components 908components 908 may include user output components 920 and user input components 922. The user output components 920 may include visual components (e.g., a display such as a plasma display panel (PDP), a light emitting diode (LED) display, a liquid crystal display (LCD), a projector, or a cathode ray tube (CRT)), acoustic components (e.g., speakers), haptic components (e.g., a vibratory motor, resistance mechanisms), other signal generators, and so forth. The user input components 922 may include alphanumeric input components (e.g., a keyboard, a touch screen configured to receive alphanumeric input, a photo-optical keyboard, or other alphanumeric input components), point-based input components (e.g., a mouse, a touchpad, a trackball, a joystick, a motion sensor, or other pointing instrument), tactile input components (e.g., a physical button, a touch screen that provides location or force of touches or touch gestures, or other tactile input components), audio input components (e.g., a microphone), and the like.

[00575] In further example implementations, the I/O components 908components 908 may include biometric components 924, motion components 926, environmental components 928, or position components 930 among a wide array of other components. For example, the biometric components 924 may include components to detect expressions (e.g., hand expressions, facial expressions, vocal expressions, body gestures, or eye tracking), measure biosignals (e.g., blood pressure, heart rate, body temperature, perspiration, or brain waves), identify a person (e.g., voice identification, retinal identification, facial identification, fingerprint identification, or electroencephalogram based identification), and the like. The motion components 926 may include acceleration sensor components (e.g., accelerometer), gravitation sensor components, rotation sensor components (e.g., gyroscope), and so forth. The environmental components 928 may include, for example, illumination sensor components (e.g., photometer), temperature sensor components (e.g., one or more thermometer that detect ambient temperature), humidity sensor components, pressure sensor components (e.g., barometer), acoustic sensor components (e.g., one or more microphones that detect background noise), proximity sensor components (e.g., infrared sensors that detect nearby objects), gas sensors (e.g., gas detection sensors to detection concentrations of hazardous gases for safety or to measure pollutants in the atmosphere), or other components that may provide indications, measurements, or signals corresponding to a surrounding physical environment. The position components 930 may include location sensor components (e.g., a GPS receiver component), altitude sensor components (e.g., altimeters or barometers that detect air pressure from which altitude may be derived), orientation sensor components (e.g., magnetometers), and the like. [00576] Communication may be implemented using a wide variety of technologies. The I/O components 908 may include communication components 932 operable to couple the machine 900 to a network 934 or devices 936. For example, the communication components 932 may include a network interface component or other suitable device to interface with the network 934. In further examples, communication components 932 may include wired communication components, wireless communication components, cellular communication components, near field communication (NFC) components, Bluetooth® components (e.g., Bluetooth® Low Energy), Wi-Fi® components, and other communication components to provide communication via other modalities. The devices 936 may be another machine 900 or any of a wide variety of peripheral devices (e.g., a peripheral device coupled via a USB). [00577] Moreover, the communication components 932 may detect identifiers or include components operable to detect identifiers. For example, the communication components 932 may include radio frequency identification (RFID) tag reader components, NFC smart tag detection components, optical reader components (e.g., an optical sensor to detect one-dimensional bar codes such as Universal Product Code (UPC) bar code, multi-dimensional bar codes such as Quick Response (QR) code, Aztec code, Data Matrix, Dataglyph, MaxiCode, PDF417, Ultra Code, UCC RSS-2D bar code, and other optical codes), or acoustic detection components (e.g., microphones to identify tagged audio signals). In addition, a variety of information may be derived via the communication components 932, such as location via Internet Protocol (IP) geo-location, location via Wi-Fi® signal triangulation, location via detecting an NFC beacon signal that may indicate a particular location, and so forth.

[00578] As used herein, “component” refers to a device, physical entity, or logic having boundaries defined by function or subroutine calls, branch points, APIs, or other technologies that provide for the partitioning or modularization of particular processing or control functions. Components may be combined via their interfaces with other components to carry out a machine process. A component may be a packaged functional hardware unit designed for use with other components and a part of a program that usually performs a particular function of related functions. Components may constitute either software components (e.g., code embodied on a machine-readable medium) or hardware components. A "hardware component" is a tangible unit capable of performing certain operations and may be configured or arranged in a certain physical manner. In various example implementations, one or more computer systems (e.g., a standalone computer system, a client computer system, or a server computer system) or one or more hardware components of a computer system (e.g., a processor or a group of processors) may be configured by software (e.g., an application or application portion) as a hardware component that operates to perform certain operations as described herein.

[00579] A hardware component may also be implemented mechanically, electronically, or any suitable combination thereof. For example, a hardware component may include dedicated circuitry or logic that is permanently configured to perform certain operations. A hardware component may be a special-purpose processor, such as a field- programmable gate array (FPGA) or an ASIC. A hardware component may also include programmable logic or circuitry that is temporarily configured by software to perform certain operations. For example, a hardware component may include software executed by a general-purpose processor 904 or other programmable processor. Once configured by such software, hardware components become specific machines (or specific components of a machine 900) uniquely tailored to perform the configured functions and are no longer general-purpose processors 904. It will be appreciated that the decision to implement a hardware component mechanically, in dedicated and permanently configured circuitry, or in temporarily configured circuitry (e.g., configured by software) may be driven by cost and time considerations. Accordingly, the phrase "hardware component"(or "hardware-implemented component") should be understood to encompass a tangible entity, be that an entity that is physically constructed, permanently configured (e.g., hardwired), or temporarily configured (e.g., programmed) to operate in a certain manner or to perform certain operations described herein. Considering implementations in which hardware components are temporarily configured (e.g., programmed), each of the hardware components need not be configured or instantiated at any one instance in time. For example, where a hardware component comprises a general-purpose processor 904 configured by software to become a special-purpose processor, the general-purpose processor 904 may be configured as respectively different special-purpose processors (e.g., comprising different hardware components) at different times. Software accordingly configures a particular processor 912processor 912, 914 or processors 904, for example, to constitute a particular hardware component at one instance of time and to constitute a different hardware component at a different instance of time.

[00580] Hardware components can provide information to, and receive information from, other hardware components. Accordingly, the described hardware components may be regarded as being communicatively coupled. Where multiple hardware components exist contemporaneously, communications may be achieved through signal transmission (e.g., over appropriate circuits and buses) between or among two or more of the hardware components. In implementations in which multiple hardware components are configured or instantiated at different times, communications between such hardware components may be achieved, for example, through the storage and retrieval of information in memory structures to which the multiple hardware components have access. For example, one hardware component may perform an operation and store the output of that operation in a memory device to which it is communicatively coupled. A further hardware component may then, at a later time, access the memory device to retrieve and process the stored output.

[00581] Hardware components may also initiate communications with input or output devices, and can operate on a resource (e.g., a collection of information). The various operations of example methods described herein may be performed, at least partially, by one or more processors 904 that are temporarily configured (e.g., by software) or permanently configured to perform the relevant operations. Whether temporarily or permanently configured, such processors 904 may constitute processor- implemented components that operate to perform one or more operations or functions described herein. As used herein, "processor-implemented component" refers to a hardware component implemented using one or more processors 904. Similarly, the methods described herein may be at least partially processor-implemented, with a particular processor processor 912, 914 or processors 904 being an example of hardware. For example, at least some of the operations of a method may be performed by one or more processors 904 or processor-implemented components. Moreover, the one or more processors 904 may also operate to support performance of the relevant operations in a "cloud computing" environment or as a "software as a service" (SaaS). For example, at least some of the operations may be performed by a group of computers (as examples of machines 900 including processors 904), with these operations being accessible via a network 934 (e.g., the Internet) and via one or more appropriate interfaces (e.g., an API). The performance of certain of the operations may be distributed among the processors, not only residing within a single machine 900, but deployed across a number of machines. In some example implementations, the processors 904 or processor-implemented components may be located in a single geographic location (e.g., within a home environment, an office environment, or a server farm). In other example implementations, the processors 904 or processor-implemented components may be distributed across a number of geographic locations.

[00582] Figure 10 is a block diagram illustrating system 1000 that includes an example software architecture 1002, which may be used in conjunction with various hardware architectures herein described. Figure 10 is a non-limiting example of a software architecture, and it will be appreciated that many other architectures may be implemented to facilitate the functionality described herein. The software architecture 1002 may execute on hardware such as machine 900 of Figure 9 that includes, among other things, processors 904, memory/storage 906, and input/output (I/O) components 908. A representative hardware layer 1004 is illustrated and can represent, for example, the machine 900 of Figure 9. The representative hardware layer 1004 includes a processing unit 1006 having associated executable instructions 1008. Executable instructions 1008 represent the executable instructions of the software architecture 1002, including implementation of the methods, components, and so forth described herein. The hardware layer 1004 also includes at least one of memory or storage modules memory/storage 1010, which also have executable instructions 1008. The hardware layer 1004 may also comprise other hardware 1012.

[00583] In the example architecture of Figure 10, the software architecture 1002 may be conceptualized as a stack of layers where each layer provides particular functionality. For example, the software architecture 1002 may include layers such as an operating system 1014, libraries 1016, frameworks/middleware 101018, applications 1020, and a presentation layer 1022. Operationally, the applications 1020 or other components within the layers may invoke API calls 1024 through the software stack and receive messages 1026 in response to the API calls 1024. The layers illustrated are representative in nature and not all software architectures have all layers. For example, some mobile or special purpose operating systems may not provide a frameworks/middleware 1018, while others may provide such a layer. Other software architectures may include additional or different layers.

[00584] The operating system 1014 may manage hardware resources and provide common services. The operating system 1014 may include, for example, a kernel 1028, services 1030, and drivers 1032. The kernel 1028 may act as an abstraction layer between the hardware and the other software layers. For example, the kernel 1028 may be responsible for memory management, processor management (e.g., scheduling), component management, networking, security settings, and so on. The services 1030 may provide other common services for the other software layers. The drivers 1032 are responsible for controlling or interfacing with the underlying hardware. For instance, the drivers 1032 include display drivers, camera drivers, Bluetooth® drivers, flash memory drivers, serial communication drivers (e.g., Universal Serial Bus (USB) drivers), Wi-Fi® drivers, audio drivers, power management drivers, and so forth depending on the hardware configuration.

[00585] The libraries 1016 provide a common infrastructure that is used by at least one of the applications 1020, other components, or layers. The libraries 1016 provide functionality that allows other software components to perform tasks in an easier fashion than to interface directly with the underlying operating system 1014 functionality (e.g., kernel 1028, services 1030, drivers 1032). The libraries 1016 may include system libraries 1034 (e.g., C standard library) that may provide functions such as memory allocation functions, string manipulation functions, mathematical functions, and the like. In addition, the libraries 1016 may include API libraries 1036 such as media libraries (e.g., libraries to support presentation and manipulation of various media format such as MPEG4, H.264, MP3, AAC, AMR, JPG, PNG), graphics libraries (e.g., an OpenGL framework that may be used to render two-dimensional and three-dimensional in a graphic content on a display), database libraries (e.g., SQLite that may provide various relational database functions), web libraries (e.g., WebKit that may provide web browsing functionality), and the like. The libraries 1016 may also include a wide variety of other libraries 638 to provide many other APIs to the applications 1020 and other software components/modules.

[00586] The frameworks/middleware 1018 (also sometimes referred to as middleware) provide a higher-level common infrastructure that may be used by the applications 1020 or other software components/modules. For example, the frameworks/middleware 1018 may provide various graphical user interface functions, high-level resource management, high-level location services, and so forth. The frameworks/middleware 1018 may provide a broad spectrum of other APIs that may be utilized by the applications 1020 or other software components/modules, some of which may be specific to a particular operating system 1014 or platform.

[00587] The applications 1020 include built-in applications 1040 and third-party applications 1042. Examples of representative built-in applications 1040 may include, but are not limited to, a contacts application, a browser application, a book reader application, a location application, a media application, a messaging application, or a game application. Third-party applications 1042 may include an application developed using the ANDROID™ or IOS™ software development kit (SDK) by an entity other than the vendor of the particular platform, and may be mobile software running on a mobile operating system such as IOS™, ANDROID™, WINDOWS® Phone, or other mobile operating systems. The third-party applications 1042 may invoke the API calls 1024 provided by the mobile operating system (such as operating system 1014) to facilitate functionality described herein.

[00588] The applications 1020 may use built-in operating system functions (e.g., kernel 1028, services 1030, drivers 1032), libraries 1016, and frameworks/m id dieware 1018 to create Uls to interact with users of the system. Alternatively, or additionally, in some systems, interactions with a user may occur through a presentation layer, such as presentation layer 1022. In these systems, the application/component "logic" can be separated from the aspects of the application/component that interact with a user.

[00589] At least some of the processes described herein can be embodied in computer-readable instructions for execution by one or more processors such that the operations of the processes may be performed in part or in whole by the functional components of one or more computer systems. Accordingly, computer-implemented processes described herein are by way of example with reference thereto, in some situations. However, in other implementations, at least some of the operations of the computer-implemented processes described herein can be deployed on various other hardware configurations. The computer-implemented processes described herein are therefore not intended to be limited to the systems and configurations described with respect to Figures 9 and 10 and can be implemented in whole, or in part, by one or more additional system and/or components.

[00590] Although the flowcharts described herein can show operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations can be re-arranged. A process is terminated when its operations are completed. A process can correspond to a method, a procedure, an algorithm, etc. The operations of methods may be performed in whole or in part, can be performed in conjunction with some or all of the operations in other methods, and can be performed by any number of different systems, such as the systems described herein, or any portion thereof, such as a processor included in any of the systems.

EXAMPLES

Example 1 [00591] Circulating tumor DNA (ctDNA) in plasma exhibits methylation signatures distinct from that of cfDNA from non-tumor cells. Methyl binding domain (MBD) protein is used to partition DNA molecules allowing for downstream identification of differential methylation patterns. Briefly, after extraction, cell-free DNA (cfDNA) is separated into partitions based on the affinity of the cfDNA molecules to a methylated-DNA binding protein - i.e., methylated and unmethylated partitions. The DNA in each partition is then tagged with a distinct set of unique molecular barcodes. The DNA in the methylated partition is treated with methylation-sensitive restriction enzymes (MSREs) to digest unmethylated molecules. The partitions are then pooled and sequenced in parallel. Post- sequencing, each molecule is computationally assigned to a partition using its pair of molecular barcodes. The methylation caller has been developed to analyze the differential methylation between patients with and without neoplasms based on the partitions and the genomic locations of molecules.

[00592] A methylation panel of an assay contained regions in three main categories: classification regions (including differentially methylated regions or DMRs as well as regions associated with other analytes such as fragmentomics), positive control regions, and negative control regions. The regions of interest range can be upto around 2700 bp in size.

[00593] Positive control regions were selected based on their consistent pattern of hypermethylation across different cell types/tissues. As such, the cfDNA originating from these regions and found in the plasma is expected to be fully methylated (irrespective of the disease state or condition) and a quantitative measure of the number of molecules captured by the probes in these positive control regions is expected to be representative of the assay’s capability to capture all methylated molecules present in a sample in a corresponding region. Based on this property, these regions provide a basis for comparison between different samples/conditions, analogous to housekeeping genes in RNAseq; as such, they play the main role in normalization. Negative control regions on the other hand are consistently hypomethylated (irrespective of the disease state or condition) and have zero or few hyper methylated molecules, and thus the assay detects few to no molecules in these regions within the hyper or residual partitions. Negative control regions are primarily added as a QC measure. Besides their application in QC and normalization, the hypermethylation quantifications of all positive and negative control regions are also used as the input to the model.

[00594] Differentially methylated regions (DMRs), as their name suggests, are not consistently methylated between neoplasia cells and healthy cells. In general, these regions are hypermethylated in CRC tumor cells and hypomethylated in normal conditions (hyper DMR) or hypomethylated in CRC tumor cells and hypermethylated in normal conditions (hypo DMR). Therefore, for example, hyper DMRs get more methylated molecules in CRC samples compared to cancer-free samples; this difference makes them informative in detecting cancer. The quantitative measure of all but two of the DMRs on the panel - those located on chromosome X or chromosome Y - are used as input to the model.

[00595] The molecule counts of the classification and positive control regions are input to the methylation callers. Methylated partition molecule counts of a given sample are linearly correlated with cfDNA input. Thus, a way to normalize samples to remove the impact of cfDNA input on ctDNA quantification is needed. Almost all molecules from positive control regions end up in the methylated partition and therefore their quantity is also linearly correlated with cfDNA input. In addition, the total number of molecules observed in positive control regions at a fixed input reflects the per-sample efficacy of MBD partitioning. Normalizing to the total number of molecules present at positive control regions thus controls both for the amount of cfDNA input into the assay and the technical variance of MBD on a particular sample.

[00596] For the development of model, 7,587 cancer-free, 2,432 CRC, and 844 AA samples were gathered for training and performance assessment purposes. This dataset was generated across 253 batches and 58 different cohorts.

[00597] A first version of the model was training using cancer-free samples, as well as CRC positive samples having quantitative measures of mutant allele frequency across a number of ranges of values.

[00598] From the remaining CRCs samples which had i quantitative measures of MAF within a particular range were used in training alongside all 4,610 cancer-free samples. A second version of the model was trained differently from the first version of the model by using this second set of training data that included CRC samples having MAF values with the particular range and not across a number of ranges in conjunction with the set of 4,610 cancer-free samples.

[00599] The second version of the model is a regression model trained with the logit- transformed max variant MAF as the outcome variable (i.e., Y variable), and normalized per region molecule counts as the features (i.e., X Variable). Based on the known linear correlation between region scores and log transformed variant max MAF a linear regression model was used in training the model.

[00600] . The second version of the model assigns weights to each region, and the final score is calculated using these weights and the normalized molecule counts of the regions.

[00601] The second version of the model takes advantage of scores from the first version of the model to get an initial estimation of methylation signal for samples used in development. Later, this estimation determines which CRC samples are included in training the model.

[00602] The first version of the model outputs a score that can directly be converted into a methylation-based estimate of max MAF (methylMAF) by applying expit to the output from the first version of the model.

[00603] The methylMAF is well correlated with the somatic max MAF in the development set. Note that at lower somatic max MAF% the linear trend decays, resulting in methylMAF% and somatic max MAF% disagreeing.

[00604] The second version of the model was trained with cancer-free samples and the CRC samples from a number of cohorts from different ranges of MethylMAF%. A particular range of MethylMAF% was chosen based on the performance.

[00605] Based on the above observations, prior to training, CRC samples are filtered based on their methylMAF%, keeping only CRCs with methylMAF% equal to or within that particular range that resulted in a better performance of the model.

[00606] We first train a linear regression model using CRC samples within the methylMAF range with mutations detected, and Cancer Free samples, to predict the quantitative MAF of the samples. We then impute the MAF values for CRC samples without a mutation, and retrain the model using all CRCs within the methylMAF range and Cancer Frees. We repeat this process 5 times, each time updating the imputed values for MAF- CRCs. During each training process, cancer free values are set to a value far lower than CRCs, and an L2 penalty and robust regression techinque are leveraged; samples are weighted such that the entire cancer free class is greater than the CRC class, and hyper parameters into the model were tuned.

[00607] To avoid overfitting, cross-validation is done using ten random splits of the available data (70% training; 30% test). The model trained on the training portion of each split is used to assign a score to the samples in the testing subset. After all ten models are trained, the final score for each sample is calculated as the average of scores predicted by one or more of the models. For future samples, or those not included in any training split, the score is calculated as the average of the score from all 10 models.

[00608] Figure 11 shows the limits of detection in relation to the tumor fraction for the first version of the model and the second version of the model. Figure 12 shows the sensitivity for three models in relation to specificity. The bottom line shows results from a first model that does not implement regression model techniques described herein. The middle line shows results from a second model that corresponds to the first version of the regression model and the top line shows results from a third model that correspond to the second version of the regression.

Example 2

[00609] Circulating tumor DNA (ctDNA) in plasma exhibits methylation signatures distinct from that of cfDNA from non-tumor cells. Methyl binding domain (MBD) protein is used to partition DNA molecules allowing for downstream identification of differential methylation patterns. Briefly, after extraction, cell-free DNA (cfDNA) is separated into partitions based on the affinity of the cfDNA molecules to a methylated-DNA binding protein - i.e., methylated and unmethylated partitions. The DNA in each partition is then tagged with a distinct set of unique molecular barcodes. The DNA in the methylated partition is treated with methylation-sensitive restriction enzymes (MSREs) to digest unmethylated molecules. The partitions are then pooled and sequenced in parallel. Post- sequencing, each molecule is computationally assigned to a partition using its pair of molecular barcodes. The methylation caller has been developed to analyze the differential methylation between patients with and without neoplasms based on the partitions and the genomic locations of molecules.

[00610] A methylation panel of an assay contained regions in three main categories: classification regions (including differentially methylated regions or DMRs as well as regions associated with other analytes such as fragmentomics), positive control regions, and negative control regions. The regions of interest range can be upto around 2700 bp in size.

[00611] Positive control regions were selected based on their consistent pattern of hypermethylation across different cell types/tissues. As such, the cfDNA originating from these regions and found in the plasma is expected to be fully methylated (irrespective of the disease state or condition) and a quantitative measure of the number of molecules captured by the probes in these positive control regions is expected to be representative of the assay’s capability to capture all methylated molecules present in a sample in a corresponding region. Based on this property, these regions provide a basis for comparison between different samples/conditions, analogous to housekeeping genes in RNAseq; as such, they play the main role in normalization. Negative control regions on the other hand are consistently hypomethylated (irrespective of the disease state or condition) and have zero or few hyper methylated molecules, and thus the assay detects few to no molecules in these regions within the hyper or residual partitions. Negative control regions are primarily added as a QC measure. Besides their application in QC and normalization, the hypermethylation quantifications of all positive and negative control regions are also used as the input to the model.

[00612] Differentially methylated regions (DMRs), as their name suggests, are not consistently methylated between neoplasia cells and healthy cells. In general, these regions are hypermethylated in tumor cells and hypomethylated in normal conditions (hyper DMR) or hypomethylated in tumor cells and hypermethylated in normal conditions (hypo DMR). Therefore, for example, hyper DMRs get more methylated molecules in cancer samples compared to cancer-free samples; this difference makes them informative in detecting cancer. The quantitative measure of all but two of the DMRs on the panel - those located on chromosome X or chromosome Y - are used as input to the model. [00613] The molecule counts of the classification and positive control regions are input to the methylation callers. Methylated partition molecule counts of a given sample are linearly correlated with cfDNA input. Thus, a way to normalize samples to remove the impact of cfDNA input on ctDNA quantification is needed. Almost all molecules from positive control regions end up in the methylated partition and therefore their quantity is also linearly correlated with cfDNA input. In addition, the total number of molecules observed in positive control regions at a fixed input reflects the per-sample efficacy of MBD partitioning. Normalizing to the total number of molecules present at positive control regions thus controls both for the amount of cfDNA input into the assay and the technical variance of MBD on a particular sample.

[00614] For the development of A first version of models for detecting lung cancer and breast cancer, 2,166 cancer-free, 391 lung cancer, and 361 breast cancer samples were gathered for training. This dataset was generated across 72 batches and 54 different cohorts. A first version of the lung cancer model was training using cancer-free samples, as well as lung cancer positive samples using the logistic regression framework. A first version of the breast cancer model was training in a similar way of using cancer-free samples, as well as breast cancer positive samples using the logistic regression framework.

[00615] For the development of a second version of models for detecting lung cancer and breast cancer, 7,037 cancer-free, 752 lung cancer, and 985 breast cancer samples were gathered for training and performance assessment purposes. This dataset was generated across 247 batches and 18 different cohorts.

[00616] A second version of the lung cancer model was trained differently from the first version of the model by using this second set of training data that included lung cancer samples having MAF values with the particular range and not across a number of ranges in conjunction with the set of 7,037 cancer-free samples.

[00617] The second version of the model is a regression model trained with the logit- transformed max variant MAF as the outcome variable (i.e., Y variable), and normalized per region molecule counts as the features (i.e., X Variable). Based on the known linear correlation between region scores and log transformed variant max MAF a linear regression model was used in training the model. [00618] The second version of the model assigns weights to each region, and the final score is calculated using these weights and the normalized molecule counts of the regions.

[00619] We first train a linear regression model using lung cancer samples within a MAF range with mutations detected, and cancer-free samples, to predict the quantitative MAF of the samples. We then impute the MAF values for lung cancer samples without a mutation, and retrain the model using all lung cancer within the MAF range and cancer- free samples. We repeat this process 5 times, each time updating the imputed values for MAF- lung cancer samples. During each training process, cancer free values are set to a value far lower than lung cancer samples, and an L2 penalty and robust regression techniques are leveraged; samples are weighted such that the entire cancer free class is greater than the lung cancer class, and hyper parameters into the model were tuned.

[00620] To avoid overfitting, cross-validation is done to train 10 different models using ten random splits of the available data (70% training; 30% test). After all ten models are trained, for future test samples, the score is calculated as the average of the score from all 10 models.

[00621] A second version of the breast cancer model was trained similarly to the second version of the lung cancer by using this second set of training data that included breast cancer samples having MAF values with the particular range and not across a number of ranges in conjunction with a set of 4,149 cancer-free samples.

[00622] Figure 13 shows the limits of detection in relation to the tumor fraction for the first version of the model and the second version of the model.

Claims

CLAIMS WHAT IS CLAIMED IS:

1 . A method comprising: obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, wherein a tumor is detected in the first plurality of subjects; determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present; obtaining a second group of training samples derived from a second plurality of subjects, wherein a tumor is not detected with respect to the second plurality of subjects; performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model; analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

2. The method of claim 1 , wherein the training process for the second computational model includes a first iteration that comprises: determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values; determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples; and determining an initial version of the second computational model based on the first training data and the second training data.

3. The method of claim 2, comprising: analyzing the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent; and determining, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

4. The method of claim 3, comprising: obtaining third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples; and wherein the training process for the second computational model includes a second iteration that comprises: determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

5. The method of claim 4, comprising: determining, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure; determining a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples; determining that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value; and modifying the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

6. The method of any one of claims 1-5, comprising: determining, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, wherein the first weights are based on a first number of the plurality of samples; and determining, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, wherein the second weights are based on a second number of the second group of training samples and an additional weighting factor.

7. The method of any one of claims 1-6, wherein the training process of the second computational model comprises a loss function.

8. The method of claim 7, wherein the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

9. The method of claim 7, wherein the training process of the second computational model includes a plurality of iterations and individual iterations of the plurality of iterations are stopped before convergence of a Huber loss function.

10. The method of any one of claims 1 -9, wherein the second computational model comprises a linear regression model.

11. The method of any one of claims 1-10, wherein the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, the method comprising: determining a plurality of groupings of the training data, wherein individual groupings of the plurality of groupings of the training data include a training portion and a validation portion; and performing training processes for the plurality of computational models using the plurality of groupings of the training data.

12. The method of claim 11 , wherein determining indications of cancer being present in one or more subjects includes performing one or more statistical operations based on output from each computational model of the plurality of computational models.

13. The method of any one of claims 1-12, comprising: analyzing the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values; identifying one or more first samples from among the additional subset of the plurality of samples; and identifying one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

14. The method of claim 13, comprising: combining a first portion of the training sequence data that corresponds to the one or more first samples with a second portion of the training sequence data that corresponds to the one or more second samples to determine additional training sequence data for an additional training sample, wherein an additional sequence representation of the additional training sample includes an amount of first nucleotides corresponding to the one or more first samples and an amount of second nucleotides corresponding to the one or more second samples; and determining, by a third computational model and based on the additional sequence representation, an additional quantitative measure for the additional training sample, wherein a value of the additional quantitative measure is less than first values of the quantitative measure for the one or more first samples and greater than second values of the quantitative measure for the one or more second samples.

15. The method of any one of claims 1-14, wherein: a plurality of types of cancer are detected in the first plurality of subjects; and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

16. The method of any one of claims 1-15, wherein a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

17. The method of any one of claims 1-16, wherein the indication of cancer being present in the one or more test subjects includes a first result indicating a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

18. The method of any one of claims 1-17, wherein the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

19. The method of any one of claims 1-18, wherein individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the method comprises: analyzing the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content; analyzing the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected; and determining a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

20. The method of claim 19, wherein the individual values of the quantitative measure for individual samples of the plurality of samples are determined based on the metric for the individual classification regions.

21 . The method of any one of claims 1-20, wherein individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

22. The method of any one of claims 1-21 , wherein the training process for the second computational model comprises; performing a plurality of training processes for a plurality of instances of the second computational model using the training data; determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model; and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

23. The method of any one of claims 1-22, wherein the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

24. The method of claim 23, wherein the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

25. The method of claim 23 or 24, wherein the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.