Priority of U.S. provisional application No.61/316,174 entitled "Residual compensation including Underfill", filed on 22/3/2010, the entire contents of which are incorporated herein by reference.
Background
Biosensor systems provide for the analysis of samples of biological fluids such as whole blood, serum, plasma, urine, saliva, interstitial fluid (interstitial fluid) or intracellular fluid (intracellular fluid). Typically, the system includes a measurement device that analyzes the sample in the test sensor. The sample is usually present in liquid form and may be, in addition to a biological fluid, a derivative of a biological fluid, such as an extract, a dilution, a filtrate or a reconstituted precipitate (recombinant precipitate), and the like. The analysis performed by the biosensor system may determine the presence and/or concentration of one or more analytes, such as alcohol, glucose, uric acid, lactate, cholesterol, bilirubin, free fatty acids, triglycerides, proteins, ketones, phenylalanine, or enzymes, in the biological fluid. The above analysis is beneficial for the diagnosis and treatment of physiological abnormalities. For example, a diabetic patient may use a biosensor system to determine the glucose level in whole blood in order to regulate diet and/or medication.
Biosensor systems may be designed for analyzing one or more analytes, and may use different volumes of biological fluid. Some systems can analyze a single drop of whole blood, such as a volume of 0.25-15 microliters (μ L). The biosensor system may be implemented using a bench-top measuring device, a portable measuring device, and the like. The portable measuring device may be hand-held and can be used for the qualitative and/or quantitative determination of one or more analytes in a sample. Examples of portable measurement systems include Bayer HealthCare, Inc. (Bayer HealthCare, Inc.) of Tarrytown, New York, TalytownAn example of a meter, and a bench-top measurement system includes an electrochemical workstation available from CH instruments (CHInsmeters) of Austin, Tex.
The biosensor system may analyze the biological fluid using optical and/or electrochemical methods. In some optical systems, the analyte concentration is determined by measuring light that has interacted with or absorbed by a light-identifiable species, such as an analyte or a reaction product formed from a reaction of a chemical indicator with the analyte. In other optical systems, the chemical indicator fluoresces or emits light in response to the analyte when illuminated by the excitation beam. Such light may be converted into an electrical output signal, such as a current or potential, which may be processed similarly to the output signal from an electrochemical system. In any of the above optical systems, the system measures light and correlates the light to an analyte concentration of the sample.
In light absorbing optical systems, chemical indicators produce reaction products that absorb light. Chemical indicators such as tetrazolium (tetrazolium) may be used with enzymes such as diaphorase. Tetrazoles typically form formazans in response to redox reactions of analytes(formazan) (a chromogen (chromogen)). An incident input beam from a light source is directed at the sample. The light source may be a laser or a light emitting diode, etc. The incident light beam may have a wavelength selected for absorption by the reaction products. As the incident beam passes through the sample, the reaction products absorb a portion of the incident beam, thus attenuating or reducing the intensity of the incident beam. The incident beam may be reflected back to the detector by the sample or transmitted through the sample to the detector. The detector collects and measures the attenuated incident beam (output signal). The amount of light attenuated by the reaction product is an indicator of the concentration of analyte in the sample.
In a photogenerated optical system, a chemical indicator fluoresces or emits light in response to an analyte redox reaction. The detector collects and measures the generated light (output signal). The amount of light generated by the chemical indicator is an indicator of the concentration of the analyte in the sample.
In electrochemical biosensor systems, analyte concentration is determined from an electrical signal generated by an oxidation/reduction reaction or redox reaction of the analyte or by a substance responsive to the analyte when an input signal is applied to the sample. The input signal may be a potential or a current, and may be constant, varying, or a combination thereof (e.g., when a DC signal offset is applied to an AC signal). The input signal may be applied as a single pulse or may be applied in multiple pulses, sequences or periods. An enzyme or similar substance may be added to the sample in order to enhance the electron transport from the first substance to the second substance during the redox reaction. The enzyme or similar substance may react with a single analyte to provide specificity to a portion of the output signal generated. A mediator (mediator) may be used to maintain the oxidation state of the enzyme and/or to assist the transport of electrons from the analyte to the electrode.
Electrochemical biosensor systems generally comprise a measuring device with electrical contacts which are connected to electrical conductors of a detection sensor. The conductor may be made of a conductive material such as solid metal, metal paste, conductive carbon paste, and conductive polymer. The electrical conductors are typically connected to a working electrode, a counter electrode, a reference electrode and/or other electrodes that extend into the sample reservoir. One or more electrical conductors may also extend into the sample reservoir to provide functions not provided by those electrodes described above.
The measuring device applies an input signal to the electrical conductor of the detection sensor via the electrical contact. The electrical conductor transmits an input signal to the sample present in the sample reservoir via the electrode. The redox reaction of the analyte generates an electrical output signal in response to the input signal. The electrical output signal from the detection sensor may be a current (generated by amperometry (amperometry) or voltammetry (voltametry)), a potential (generated by potentiometry/amperometry (galvanometry)), or an accumulated charge (generated by coulometry). The measuring device may have the following processing capabilities: measuring the output signal and correlating the output signal with the presence and/or concentration of the one or more analytes in the sample.
In the coulometry method, a potential is applied to the sample to fully oxidize or reduce the analyte. A biosensor system using coulometry is disclosed in U.S. patent No.6,120,676. In amperometry, an electric signal of a constant potential (voltage) is applied to a conductor of a detection sensor, and an output signal to be measured is a current. Biosensor systems using amperometry are disclosed in U.S. patent nos. 5,620,579, 5,653,863, 6,153,069 and 6,413,411. In voltammetry, an electrical signal of varying potential is applied to a sample of the biological fluid, and the output measured is a current. In gated amperometry and gated voltammetry, pulsed inputs are used as disclosed in patent documents WO2007/013915 and WO 2007/040913, respectively.
In many biosensor systems, the detection sensor may be adapted for use outside or inside a living organism or partly inside a living organism for use. When used outside a living organism, a sample of biological fluid may be introduced into a sample reservoir in the detection sensor. The detection sensor may be placed in the measurement device before, after, or during introduction of the sample for analysis. When used in or partially within a living organism for use, the detection sensor may be continuously immersed in the sample or the sample may be intermittently introduced to the detection sensor. The detection sensor may include a reservoir (reservoir) as follows: the reservoir is partially isolated or open to a volume of sample. When open, the detection sensor may take the form of a fiber or other structure arranged to be in contact with the biological fluid. Similarly, for analysis, the sample may flow continuously past the detection sensor (e.g., continuously monitored) or be interrupted (e.g., intermittently monitored).
The measurement performance of a biosensor system is defined in terms of accuracy (accuracycacy) reflecting the combined effect of random and systematic error components. The systematic error, or accuracy (trueneness), is the difference between the average value of the analyte concentration determined by the biosensor system with respect to the biological fluid and one or more accepted reference values. Precision can be expressed in terms of mean bias, with a larger mean bias value representing lower precision and thus less accuracy. Precision (precision) is the degree of agreement of multiple analyte readings with respect to the mean. One or more errors in the analysis are in part a cause of bias and/or inaccuracy in the analyte concentration determined by the biosensor system. Thus, a reduction in the analysis error of the biosensor system may lead to an increase in accuracy and thus to an improvement in measurement performance.
Bias can be expressed in terms of "absolute bias" or "percent bias". The absolute bias may be expressed in measured units such as mg/dL, while the percent bias may be expressed as a percentage of the "absolute bias value compared to 100mg/dL or a reference analyte concentration for the sample". For glucose concentrations less than 100mg/dL, the percent bias was defined as "(100 mg/dL above absolute bias) 100". For glucose concentrations above 100mg/dL, the percent bias was defined as "absolute bias over reference analyte concentration 100". A recognized reference value for a glucose analyte in a whole blood sample may be obtained from a reference instrument, such as the YSI 2300 STAT PLUS available from YSI Inc. of Yellow Springs, OhioTM. For other analytes, other reference instruments and means can be used to determine percent bias.
Hematocrit (Hematocrit) bias refers to the average difference (systematic error) between the reference glucose concentration obtained by a reference instrument and the experimental glucose readings obtained by a biosensor system for samples containing different Hematocrit levels. The difference between the reference value and the value obtained from the above system is due to different hematocrit levels between specific whole blood samples, and can be generally expressed as a percentage by the following equation: % Hct-Bias =100% × (G)m-Gref)/GrefHere, GmIs the measured glucose concentration, G, at a particular hematocrit levelrefIs a reference glucose concentration at a reference hematocrit level. The greater the absolute value of% Hct-bias, the more the hematocrit level of the sample (expressed as% Hct, volume of red blood cells/volume of sample) will degrade the accuracy of the measured glucose concentration.
For example, if a whole blood sample containing the same glucose concentration but having 20%, 40%, and 60% hematocrit levels, respectively, is analyzed, the system will report three different glucose concentrations based on a set of calibration constants (e.g., slope and intercept for a whole blood sample containing 40% hematocrit). Thus, even though the total blood glucose concentration is the same, the system will report that the 20% hematocrit sample contains more glucose than the 40% hematocrit sample, and that the 60% hematocrit sample contains less glucose than the 40% hematocrit sample. "hematocrit sensitivity" is used to indicate the degree to which a change in the hematocrit level of a sample affects the bias value for analysis. Hematocrit sensitivity can be defined as the value of the percent bias (% -bias) per percent hematocrit (% Hct), i.e.,% bias per% Hct.
A biosensor system may provide an output signal that includes errors from multiple sources of error during analysis of a biological fluid. These sources of error result in gross errors that can be reflected in an abnormal output signal (e.g., when one or more portions or the entire portion of the output signal is not responsive or not properly responsive to the analyte concentration of the sample).
These errors may arise from one or more causes, such as physical characteristics of the sample, environmental factors of the sample, operating conditions of the system, manufacturing variations between test sensor batches, and the like. Physical characteristics of the sample include hematocrit (red blood cell) concentration, interfering substances such as lipids and proteins, and the like. Interfering substances include ascorbic acid, uric acid, and acetaminophen. Environmental factors of the sample include temperature, etc. The operating conditions of the system include: an underfill condition when the sample volume is not large enough, slow filling of the sample, intermittent electrical contact between the sample and one or more electrodes in the detection sensor, and early degradation of the reagent (reagent) that interacts with the analyte, among others. Detecting manufacturing variations between sensor lots includes: changes in the amount and/or activity of reagents, changes in electrode area and/or spacing, changes in the conductivity of conductors and electrodes, and the like. It is preferable to manufacture one lot of test sensors in a single production run, which greatly reduces or eliminates manufacturing variation from lot to lot. Manufacturing variations may also be introduced if the activity of the reagent changes or deteriorates between the time when the detection sensor is manufactured and the time when the detection sensor is used for analysis. There may be other causes or combinations of causes that cause errors in the analysis.
The percent bias limit, percent bias standard deviation, mean percent bias dispersion (mean percent bias spread), and hematocrit sensitivity are all independent means of expressing the measurement performance of the biosensor system. Additional means may also be used to represent the measurement performance of the biosensor system.
The percentage bias limit represents the accuracy of the biosensor system with respect to the reference analyte concentration, while the percentage bias standard deviation and the average percentage bias standard deviation reflect the accuracy obtained with multiple detection sensors of a single production lot or multiple production lots, respectively, with respect to errors caused by the physical characteristics of the sample, environmental factors of the sample, and operating conditions of the system. Considering manufacturing differences between different batches, the mean percent bias dispersion (the difference between the mean percent bias of a single batch and the mean of the mean percent bias of two or more batches of detection sensors) reflects the proximity of analyte concentrations determined by two or more batches of detection sensors for the same analyte concentration.
The percentage of each analysis that falls within the "percent bias limit" range of the selected percent bias boundary represents the percentage of the determined analyte concentration that is close to the reference concentration. Thus, the limit defines how close the determined analyte concentration is to the reference concentration. For example, 95 out of 100 analyses performed (95%) were within the ± 10% percent bias limits more accurate than 80 out of 100 analyses (80%) were within the ± 10% percent bias limits. Thus, an increase in the percentage of each analysis falling within the range of the selected percentage bias limit represents an improvement in the measurement performance of the biosensor system.
For the percent biases determined by multiple analyses using detection sensors from a single lot, the average of these percent biases can be determined to provide the "average percent bias" for the multiple analyses. The average percent bias of a single batch of detection sensors may be determined by using a subset of the batch (such as 100-140 detection sensors) in order to analyze multiple blood samples. Since the average percent bias of a single lot of detection sensors can be determined, "percent bias standard deviation" can also be determined to describe how much the percent bias of an individual analysis deviates from the average percent bias of that lot of detection sensors. The percent bias standard deviation can be considered an indicator of the accuracy of a single analysis in relation to the mean of multiple analyses of the same test sensor batch. These percentage-biased standard deviation values may be averaged (e.g., mathematically averaged) using root mean square or by other means in order to provide an indication of the accuracy of a single analysis in relation to the average of multiple analyses of multiple test sensor batches. Thus, a decrease in the percentage-biased standard deviation or the average percentage-biased standard deviation represents an increase in the measurement performance of the biosensor system associated with a single test sensor lot or multiple test sensor lots, respectively.
Multiple batches of detection sensors may be used to determine an average of the average percent bias determined from multiple analyses to provide a "total average percent bias" for multiple batches. This total average percent bias can be determined for more than two batches of detection sensors. Since the total average percent bias can be determined for multiple batches of detection sensors, the "average percent bias dispersion" can also be determined to describe the degree to which the average percent bias of an individual detection sensor batch deviates from the total average percent bias of multiple detection sensor batches. The average percent biased dispersion can be considered an indicator of the accuracy of a single test sensor lot in relation to the average of the mean of multiple analyses of multiple test sensor lots. Thus, a decrease in the average percent biased dispersion represents an increase in testing performance of the biosensor system associated with manufacturing variations across multiple test sensor lots, and represents an increase in accuracy associated with errors resulting from manufacturing variations across lots obtained with multiple test sensors across multiple production lots.
The improved measurement performance of biosensor systems by reducing errors from these or other sources means that patients can use more of the analyte concentration determined by the biosensor system for accurate treatment, for example when monitoring blood glucose. In addition, the need for the patient to discard the test sensors and repeat the analysis may also be reduced.
One test case is a collection (data population) of multiple analyses generated under substantially the same test conditions by using the same batch of detection sensors. For example, the determined analyte concentration values generally exhibit poorer measurement performance in the self-testing (self-testing) case than in the Health Care Professional (HCP) test case, whereas generally exhibit poorer measurement performance in the HCP test case than in the controlled environment test case. Such differences in measurement performance may be reflected in the following facts: the percent biased standard deviation of analyte concentration determined by the user self test is greater than the percent biased standard deviation of analyte concentration determined by the HCP test or by the controlled environment test. The controlled environment is an environment in which the physical properties and environmental factors of the sample can be controlled, preferably a laboratory environment. Thus, in a controlled environment, hematocrit concentration can be fixed and the actual sample temperature can be known and compensated for. In the case of HCP testing, errors in operating conditions can be reduced or eliminated. In the case of user-self-test testing, such as clinical trials, the determined analyte concentration is likely to contain errors from all types of sources of error.
The biosensor system may have a single source of uncorrected output values in response to a redox reaction of the analyte or a light-based reaction of the analyte, such as the counter electrode and the working electrode of an electrochemical system. The biosensor system may also have candidate capabilities to determine or estimate temperature, for example, by one or more thermocouples or other means. In addition to these systems, the biosensor system may also have the following capabilities: generating an additional output value in addition to the output value from the analyte or the output value from the mediator responsive to the analyte. For example, in an electrochemical detection sensor, one or more electrical conductors may also extend into the sample reservoir to provide functionality not provided by the working and counter electrodes. Such conductors may not have one or more working electrode reagents (such as mediators, etc.), thereby enabling subtraction of the background interferent signal from the working electrode signal.
Many biosensor systems include one or more methods of compensating for analysis-related errors in an attempt to improve the measurement performance of the biosensor system. The compensation method may improve the measurement performance of the biosensor system by providing the biosensor system with the ability to compensate for inaccurate analysis, thereby improving the accuracy and/or precision of concentration values obtained from the system. Conventional error compensation methods for physical error causes and environmental error causes have traditionally been developed in the laboratory because these types of errors can be reproduced in a controlled environment. However, because many operating condition errors are due to the way the user operates the biosensor system, these operating condition errors are not easily reproducible in the laboratory. Thus, errors resulting from operational errors can be difficult to reproduce in a laboratory environment and thus difficult to compensate with conventional compensation methods.
Accordingly, there is a continuing need for improved biosensor systems, particularly those that provide increasingly accurate determinations of sample analyte concentrations when user self-testing introduces errors in operating conditions into the analysis. The systems, devices, and methods of the present invention overcome at least one of the disadvantages associated with conventional biosensor systems.
Detailed Description
The analytical error and the resulting bias of the determined analyte concentration can be reduced by compensation of the residual error. By focusing on the residual error and finding the residual function related to the residual error, the total error of the analysis can be reduced. Errors from a biosensor system may have multiple sources of error or causes of error due to different processes/behaviors that are partially or completely independent. By compensating the main errors such as temperature and hematocrit with the main compensation function to remove at least 50% of the total error, the remaining residual errors can be determined and the residual function associated with these residual errors can be determined.
The residual error compensation may substantially compensate for the total error in the analysis until the error becomes a random error. The random error is such that: they are not ascribed to any cause of error and cannot be described by the residual function at a level statistically considered significant. The compensation from the combination of the main function and the residual function may improve the measurement performance of the biosensor system in more than one aspect. For example, the combined main and residual compensation may improve the measurement performance of the biosensor system with respect to one or more of the following aspects: percent bias limit, percent bias standard deviation, average percent bias dispersion, and/or other aspects.
Residual error compensation can provide the greatest benefit for samples that are analyzed by the user himself during the "self-test". Residual error compensation may also provide benefits for samples analyzed by a Health Care Professional (HCP). While not wishing to be bound by any particular theory, it is believed that self-test errors may originate from different behaviors or processes that are substantially independent of the controlled environment or HCP test errors.
FIG. 1A shows a method for determining the concentration of an analyte in a biological fluid sample. In step 142, the biosensor system generates an output signal in response to an oxidation/reduction (redox) reaction of a light identifiable substance or analyte in the biofluid sample. In step 144, the biosensor system measures the output signal. In step 146, the analyte concentration is determined according to a compensation method including at least one transfer function, at least one main function and at least one residual function, and the output signal. In step 148, the compensated analyte concentration may be displayed, stored for future reference, and/or used for additional calculations.
In step 142 of fig. 1A, the biosensor system generates an output signal in response to an oxidation/reduction (redox) reaction of a light identifiable substance or analyte in the biofluid sample. The output signal may be generated by an optical sensor system, an electrochemical sensor system, or the like.
In step 144 of fig. 1A, the biosensor system measures an output signal generated by the analyte in response to an input signal (e.g., according to a redox reaction of the analyte) applied to the sample. The system may measure the output signal continuously or intermittently. For example, the biosensor system may intermittently measure the output signal during the time period in which each pulse of the amperometric input signal is gated, resulting in a plurality of current values recorded during the time period of each pulse. The biosensor may measure the output signal from the analyte directly or indirectly via an electrochemical mediator. The biosensor system may display the output signal on a display and/or may store the output signal or some portion of the output signal in a storage device.
In step 146 of FIG. 1A, an error compensation method including at least one transfer function, at least one primary compensation, at least one residual compensation, and the output signal may be used to determine the analyte concentration of the sample.
Fig. 1B shows an error compensation method including a transfer function 110, main compensation, and residual compensation. The master compensation compensates the output from the transfer function 110 containing the total error 115 in the form of a master function 120. The residual compensation compensates the remaining residual error 125 in the form of at least a first residual function 130. The total error 115 includes a main error and a residual error. The total error 115 may also include random errors and/or other types of errors. The transfer function 110, the master function 120, and the first residual function 130 may be implemented as three separate mathematical equations, a single mathematical equation, or otherwise. For example, the transfer function 110 may be implemented as a first mathematical equation, and the primary function 120 and the first residual function 130 may be implemented in combination as a second mathematical equation.
In fig. 1B, the unmodified output value 105 may be an output current responsive to an amperometric, voltammetric, or other input signal for generating an output signal having a current component. The uncorrected output value may be an output potential in response to potentiometry, amperometry or other input signals for producing an output signal having a potential component. The unmodified output value may be an output signal having a current component or a potential component responsive to light detected by a detector of the optical system. The output signal is responsive to a measurable species in the sample. The measurable species may be an analyte of interest or may be a mediator whose concentration in the sample is responsive to the concentration of the analyte of interest.
The transfer function 110 is preferably a correlation between: one is an uncorrected output value 105 generated from the sample in response to an input signal from the measurement device; alternatively, one or more reference analyte concentrations are determined at known physical characteristics and environmental aspects of the sample. For example, the sample may be a whole blood sample with a known hematocrit content of 42%, and the analysis is performed at a known constant temperature of 25 ℃. The known correlation between the sample analyte concentration and the uncorrected output signal value can be represented in a curvilinear manner, a mathematical manner, or a combination of a curve and a mathematical manner, etc. The correlation may be represented by a Program Number (PNA) table or another look-up table (look-up table) or the like which is predetermined and stored in the measuring apparatus.
The master function 120 providing the master compensation may include: a slope-based function, a complex exponential function, or other compensation function that aims to reduce errors in the analysis such as temperature and hematocrit. For example, the total error observed for a biosensor system comprising a measurement device and a detection sensor may be expressed as Δ S/S (normalized slope deviation) or Δ G/G (relative glucose error). The master function 120 may compensate for at least 50% and preferably at least 60% of the total error 115. The remaining analytical errors in analyte concentration that are not compensated by the master function can be thought of as being due to operating conditions, manufacturing variations, and/or random errors. Suitable main compensation techniques can be found, for example, in PCT international publication WO2009/108239 and PCT international publication WO 2010/077660. The transfer function 110 may be mathematically combined with the master function 120.
When the sample is whole blood and the analyte is glucose, the compensation provided by the master function 120 may be substantially limited to compensation for analytical errors due to temperature and hematocrit. Thus, by characterizing the biosensor system with respect to temperature and hematocrit variation, the effects of temperature and hematocrit can be compensated for by the master function 120. Other sources of error that are independent of temperature and hematocrit (such as operating conditions of the system, etc.) are preferably not characterized and are therefore not included in the master function 120.
The preferred master function is an exponential function as follows: the exponential function may be determined using an error parameter value from an analysis result of the analyte (e.g., an intermediate signal from the analyte responsive output signal) or an error parameter value from a source independent of the analyte responsive output signal (e.g., thermocouple, additional electrode, etc.). The error parameter may be any value responsive to one or more errors in the output signal. The error parameter may be a value from an analysis result of the analyte (such as an intermediate signal from the output signal for analysis), or may be a value from a secondary output signal independent of the output signal for analysis (e.g., from a thermocouple current or a thermocouple voltage, an additional electrode current or an additional electrode current voltage, etc.). Thus, the error parameter may be extracted directly or indirectly from the output signal of the analysis result and/or may be obtained independently of the output signal for analysis. Other error parameters may be determined from these or other analytical output signals or secondary output signals. Any error parameter may be used to form the term(s) that make up the exponential function, such as those described in PCT international publication WO2009/108239 entitled "Slope-Based Compensation," filed on 12/6 2008, and so forth. A more detailed error correction process using an exponential function and a slope deviation value can also be found in this publication.
The exponential function is responsive to at least one error parameter. The exponential function may be a calculated number related to an error parameter, such as hematocrit or temperature, and represents the effect of the error parameter on bias. The exponential function may be experimentally determined as a regression equation or other equation of the curve between the error parameter and the deviation from the reference slope. Thus, the exponential function represents the effect of the error parameter on the slope deviation, the normalized slope deviation, or the percentage bias.
When the exponential function includes a combination of terms modified by the weighting coefficients, the exponential function is a complex number (complex). The above combination is preferably a linear combination, but other combination methods providing weighting coefficients for the terms may be used. Each term may include one or more error parameters. The terms included in the complex exponential function may be selected by one or more exclusion tests. More preferred main functions are complex exponential functions such as those disclosed in PCT international publication WO 2010/077660. Other primary compensation techniques may be used.
In addition to compensating for the main error with the main function 120, a first residual function 130 is employed that provides at least a portion of the residual compensation. Residual errors from error sources other than temperature and hematocrit may be correlated with one or more exponential functions and identified. The difference in error between an analysis performed in a controlled environment or an analysis performed by an HCP and a user self-test can be generally expressed by "residual error = total error observed-master function value". Thus, the residual error may be considered to be the non-random error and the manufacturing variation error minus the error to be compensated by the primary compensation (such as by a primary function, etc.).
The observed residual error is substantially free of errors that are removed from the total error by the value of the master function 120. The total error includes: errors from substantially different sources and/or test cases, such as temperature and hematocrit errors measured in a controlled environment (which are generally described by a primary function), and errors in operating conditions (which are generally described by a residual function) and manufacturing variations that relatively originate outside of the controlled environment. The first residual function 130 may compensate for at least 5%, preferably at least 10%, more preferably at least 20% of the total error 115. The master function 120 and the first residual function 130 together may compensate for at least 60%, and preferably at least 70%, of the total error 115.
The residual error can also be generically expressed by "residual error = (1+ total error observed)/(1 + main function value) -1". In this form, the residual error is the relative error of the analyte measurement values after the primary compensation function is applied. It therefore has the same form as the total error observed, but it is not applied to the original analyte (current (nA)/calibration slope), but is applied to increase the value of the main function. The combination of the main function and the residual function can compensate for the total non-random error in the analysis.
By focusing on residual errors in certain situations, such as user self-tests by inexperienced subjects, and finding at least one residual function related to these residual errors, the measurement performance of the biosensor system can be improved. If the second residual function is applied, the residual error remaining after the first residual function 130 is applied can be further reduced.
Although the error described by the second residual function may be from a controlled environment or an uncontrolled environment, such error is preferably a non-random error left after the main compensation and/or an error left after the main compensation and the first residual function compensation. For example, the second residual function can be selected to compensate for errors caused at extreme temperatures and/or extreme magenta hematocrit levels (such as at 5 ℃ and 70% Hct). Thus, the second residual function may be selected to compensate for errors outside the normal condition range of the main function or the main function and the first residual function. The second residual function may also be selected to compensate for system imperfections in the compensation provided by the main function or the main function and the first residual function. Since the residual error may also include an error that has not been fully compensated by the main function and the first residual function, the second residual error may be at least partially responsive to the main function and/or the first residual function. Thus, the second residual error may not be responsive to the main function and/or the first residual function, or the second residual error may be at least partially responsive to the main function and/or the first residual function.
In addition to including a main compensation and at least one residual compensation, the error compensation method shown in FIG. 1B may also include the ability to adjust the compensation provided by the main compensation in relation to the compensation provided by the residual compensation. When more than one residual function is used, the residual compensation may also include the ability to adjust the compensation provided by the first residual function and the second residual function. Since the function(s) constituting the residual compensation can be taken from predetermined values stored in the measuring device as a database of limited temperature and/or hematocrit ranges, etc., while the main function can be determined from the full range of temperatures and hematocrit, the error compensation provided by the main compensation in relation to the compensation provided by the residual compensation can be adjusted. Thus, the main function may be determined from the inputs obtained during the analysis of the sample, while a limited number of remaining functions may be predetermined and stored in the measuring device. Since there may be some overlap between the errors described by the main function and the one or more residual functions, it is also possible to adjust the error compensation provided by the main compensation in relation to the compensation provided by the residual compensation. There may be other reasons to adjust the error compensation provided by the main compensation in relation to the compensation provided by the residual compensation.
One method for adjusting the error compensation provided by the main compensation in relation to the compensation provided by the residual compensation includes weighting coefficients. The weighting factor may be a positive value, a negative value, or may be 0. The weighting coefficients may be determined by statistical processing of data collected from a combination of multiple analyte concentrations, different red blood cell pressure levels, different temperatures, and the like.
The general form of compensation used to adjust the error compensation provided by the main compensation in relation to the compensation provided by the residual compensation can be expressed as: the master function + WC residual function, where WC is the weighting factor. The weighting factor WC may be chosen as a function of the temperature and/or the hematocrit to be used to vary the compensation contribution of the remaining function. Similarly, the compensation comprising one or more residual functions (wherein each residual function is modified by a respective weighting coefficient) may take the following general form:
compensated analyte concentration = current nA/(slope)Cal(1+ master function + WC1 residual function 1+ WC2 residual function 2 … …)),
or take the following general form of alternative residual functions:
compensated analyte concentration = current nA/(slope)Cal(1+ master function) × (1+ WC1 × residual function 1) × (1+ WC2 × residual function 2) … …), wherein WC1 and WC2 are weighting coefficients having values between 0 and 1, and WC1 and WC2 are able to reduce or eliminate the effect of the residual function when conditions exceed those used to expand the residual function. Residual function 1 is the residual compensation of the first stage after the main compensation function and residual function 2 is the residual compensation of the next stage, but residual function 2 may not be obtained if no source of error/exponential function is found. The residual function 1 and the residual function 2 are preferably independent of each other and also independent of the main function.
The weighting coefficients for the main compensation-residual compensation and/or the weighting coefficients for the one or more residual functions may be predetermined and stored in the measuring device in table form or by other means. For example, WC1 values and WC2 values may be characterized in a two-dimensional table as a function of temperature and hematocrit. In this manner, the table of weighting coefficients can be constructed such that the measurement performance of the biosensor system is improved by reducing the effect of the residual function(s) on the determined analyte concentration when the hematocrit content of the sample and the temperature at which the analysis is performed are relatively close to the conditions used in obtaining the data used to determine the conversion function 110.
Table a below is an example of predetermined weighting coefficient values for a plurality of% -Hct values and temperatures presented in a two-dimensional table.
TABLE A
For example, as shown in table B below, the values of table a may be extended to additional% -Hct values and temperature values using linear interpolation (grading period) between two fixed WC values.
TABLE B
Tables a and B show that the weighting coefficient is 1 in the region from 30% -Hct to 55% -Hct and from 17 ℃ to 28 ℃, which means that the residual function provides a full contribution to the compensation method. However, for example, a weighting coefficient for 30% -Hct at 16 ℃ is a linear interpolation of two values at 15 ℃ and 17 ℃, which is 0.75 (i.e., (0.5+ 1)/2). Similarly, the values at 25% -Hct and 20 ℃ are a linear interpolation of the value at 20% -Hct and the value at 30% -Hct of 0.75 (i.e., (0.5+ 1)/2). The temperature may be obtained or estimated according to any means, including according to a thermocouple in a measuring device or according to a sample. The% -Hct may be calculated or estimated according to an equation, Hct sensing electrodes, a combination thereof, or other means.
Fig. 1C represents a general method for determining residual function(s) in response to an uncontrolled environment test case, such as a user self-test.
In step 162, the residual error is determined from analysis performed outside of the controlled environment (such as by user self-testing). The measurement can be performed by the following relationship:
residual error = total error-main function value
Wherein the total error is present in data collected from analyses performed outside of the controlled environment and may be collected from self-tests, HCP tests, and/or any other tests that introduce error from a test procedure that is substantially absent from controlled environment tests.
In step 164, one or more residual functions are determined. This determination step can be made by multivariate regression using the observed residual error as the response value (response) and the terms from the internal and external signals as the predictor. Other mathematical techniques may be used to determine the one or more residual functions.
In step 166, statistically insignificant terms are removed from the residual function as determined by one or more exclusion tests (such as with a p-value threshold or T-value), and the determination step 164 is repeated until the desired terms for the residual function are obtained.
Fig. 1D shows an iterative method for selecting terms to be included in the residual function. In step 152, a plurality of error parameters are selected as terms that may be included in the residual function. The error parameter may be derived directly or indirectly from an output signal in response to a light identifiable substance in the sample of the biological fluid or from an output signal from a redox reaction of an analyte in the sample. The error parameters described above may also be derived independently from an output signal such as the output signal of a thermocouple or other device. The term may include values other than error parameters (such as uncompensated analyte concentration values, etc.). Preferably, the selected term does not include terms and/or error parameters selected for total or primary compensation of the primary function. More preferably, the selected items do not include items that are eliminated by one or more exclusion tests. In this way, the error compensated by the residual function may be different from the error compensated by the main function. In addition, since the error in the determined analyte concentration can be described in different ways by more than two different error parameters or terms, the residual function can compensate for the error left by the master function in different ways by term selection by using one or more terms that are not present in the master function. Thus, the residual function preferably comprises a term that is different from the term of the main function.
In step 154, a first exclusion value for each option is determined using one or more mathematical techniques. The mathematical techniques described above may include regression, multivariate regression, and the like. The exclusion value may be a p-value or a T-value, etc. The above mathematical techniques may also provide weighting coefficients, constants, and other values associated with the selected items.
In step 156, one or more exclusion tests are applied to the exclusion values to identify one or more terms that are excluded from the remaining functions. At least one item is excluded from the test. In step 157, one or more mathematical techniques are repeated to identify a second exclusion value for the remaining term. In step 158, if the second exclusion value does not identify remaining terms to be excluded from the remaining functions under one or more exclusion tests, then these remaining terms are included in the remaining functions. In step 159, if the second exclusion value identifies a remaining term to be excluded from the residual function under one or more exclusion tests, then one or more of the mathematical techniques of step 157 may be repeated to identify a third exclusion value for the remaining term. These residual terms may be included in the residual function as in step 158, or the process may be iteratively repeated as in step 159 until an exclusion test fails to identify one or more terms to be excluded.
The p-value may be used as an exclusion value for an exclusion test to select terms that are likely to be excluded from the residual function. If a term is eliminated from the residual function, the p-value represents the probability that the term will have an effect on the correlation between the residual function and the residual error. Thus, an exclusion test may eliminate terms having a p-value above an exclusion value threshold. For example, when the exclusion test uses a p-value as the exclusion value, an exclusion p-value of about 0.01 to about 0.10 is preferable, and an exclusion p-value of about 0.03 to about 0.07 is more preferable. The smaller the p-value selected as the exclusion threshold, the more terms are excluded from the residual function.
When the unwanted terms have been excluded under a first exclusion test (such as with a p-value), a second exclusion test (such as with a T-value) can be used to exclude additional terms. For example, if the p-value of the remaining terms after the multiple p-value exclusion test is 0 or close to 0, such that further exclusion under the p-value exclusion test fails, then the T-values of the remaining terms may be used to exclude terms at a T-value threshold. In addition to using exclusion tests based on p-and T-values, other exclusion tests may be used to identify possible terms to exclude from the remaining functions.
Removing terms from the residual function that are not required and do not substantially affect the correlation between the residual function and the residual error enables a desired correlation to be determined between the residual function and the residual error. Preferably, the iterative process for selecting and eliminating the items that most undesirably deviate from the exclusion trial is repeated until the remaining items satisfy the trial. Thus, the desired improvement in measurement performance can be achieved by a compensation method having a simplified function while providing a shorter analysis time. Furthermore, by removing unwanted terms from the residual function, the accuracy of subsequent analysis using different biosensor systems and conditions can be improved.
Table 1 below lists terms (predicted values), weighting coefficients, p-values, and T-values obtained from multivariate regression of data obtained from glucose output signals (currents) from multiple clinical studies using test sensors from multiple test sensor batches. About 100 to 134 glucose concentrations were determined (about 2 measurements per sensor batch were made for each blood sample). The samples were analyzed using a gated amperometric input signal, wherein selected intermediate output signals were recorded from pulses. Temp represents temperature, GrawIs the determined uncompensated analyte concentration in the sample. The ratio parameter R3/2 represents the relationship between the final current generated by the analyte in response to the third and second pulses of the gated current pulse sequence comprising six pulses. Similarly, for example, R32G represents a group derived from R3/2 and GrawAnd TR32 represents the results from temperature and R3/2.
MINITAB (version 14) software was used and multivariate regression of a linear combination of multivariate options was selected to perform the multivariate regression described above. Other statistical software packages or regression options may be used to determine the weighting coefficients for the terms. With respect to table 1 below, a p-value exclusion threshold of 0.05 was used to exclude all entries with p-values above 0.05. The first multivariate regression identified that the terms TR43 and TR53 should be removed from the remaining functions. This regression was repeated to obtain the values in table 1.
TABLE 1
The final compensation function for analysis can then be determined generally as follows:
final compensation function = main function + WC residual function, wherein the main function is combined with the residual function determined and optionally modified with weighting coefficients.
Conventional compensation methods/algorithms from controlled environment test data have the disadvantage that: it is not possible to compensate the self-test data from the user without degrading the measurement performance with respect to the HCP test data. Traditionally, the average percent bias of the self-test data was 3% to 4% higher than the controlled environment test data and the HCP test data. Thus, while self-test errors can be at least partially compensated for analysis under self-test cases by introducing an average percent bias compensation of-3% to-4%, if the compensation is applied to a controlled environment or HCP test case, the determined analyte concentration would be about 3% to 4% on average, which is too low.
Fig. 2A, 2B and 2C show the progression of the residual function derived from the glucose concentration measured with the biosensor system by a plurality of users. The user performs self-test by adopting the following measuring device: the measuring device applies a gated amperometric input signal having 5 excitations to the detection sensors, and the detection sensors are from two different manufacturing batches.
Fig. 2A is a graph of the correlation between the master function (the master function represented by CB1 in the figure) and the total error present in the measured glucose concentration. Fig. 2A shows that the correlation slope is about 4% higher than the desired value of 1.00 and the correlation intercept is about 3% higher than the desired value of 0. The overall correlation coefficient is 52.8% with respect to the main function value in predicting the total error. Fig. 2B is a graph showing the correlation between the residual error in the glucose concentration measured after the residual function (residual function represented by CB1-1 in the figure) was obtained as described above and the value of the residual function. FIG. 2C is a graph of the correlation between the total error present in the measured glucose concentration and the sum of the main function value and the residual function value (denoted as CB1+ CB 1-1). The residual function provides the following improvement: so that the correlation slope and correlation intercept are closer to their expected values of 1 and 0. The combination of the master function and the residual function provided approximately a 0.2 improvement in the correlation coefficient for the data, and a reduction of the Syx value (standard deviation of the total error) from 0.0524 to 0.0392, a 25% improvement ([ 0.0524-0.0392]/0.0524 x 100).
Fig. 2A shows that the main compensation describes about 53% of the total error. Fig. 2B shows that the residual compensation describes about 44% of the remaining 47% error, or about 20% of the total error. Fig. 2C shows that the main compensation and the residual compensation together describe about 74% of the error. Thus, a significant improvement in the measurement performance of the biosensor system in the self-test analysis is observed, since the residual function improves the ability of the compensation method to describe the total error. Thus, the compensation method comprising the main function and the at least one residual function describes at least 60% and preferably at least 70% of the total error from at least 40, preferably from at least 80, more preferably from at least 100 user analyses.
Table 2 below provides error compensation results from two self-test cases. Clinical trial 1 included approximately 52 participating subjects who were self-tested twice using two batches (a and B) of test sensors and who were also tested twice by the HCP, providing a total of approximately 400 analyses. Clinical trial 2 also included approximately 52 subjects who were self-tested twice using two batches (a and B) of test sensors and who were also tested twice by the HCP to provide an additional approximately 400 analyses. The data set from clinical trial 1 is used together with the predetermined master function to determine the residual function from the experimental data (hence as "training data"), while the data from clinical trial 2 provides the results from the compensated analysis. The following abbreviations are used in the tables.
Un-comp: the initial glucose sample concentration estimation is based on a transfer function that utilizes the correlation between the output current and the glucose concentration, and thus does not have any compensation for physical conditions, environmental conditions, operating conditions, or manufacturing variation errors.
CB 1: the whole blood samples have glucose concentrations of 75, 150, 300 or 400mg/dL, hematocrit levels of 20%, 40% or 70%, and target analysis temperatures of 15 ℃, 22 ℃ or 30 ℃, respectively, as a primary function derived from data obtained from whole blood samples under controlled conditions. The primary error compensation is designed to capture the primary effects of temperature and hematocrit.
CB 1-1: residual function derived from the self-test data set of clinical trial 1.
CB 1-2: residual functions were taken from the HCP data set and the self-test data set of clinical trial 1.
The following results are reported in table 2 below:
(1) CB1 column: compensation is only performed through a main function CB 1;
(2) CB1-1 column: compensation is carried out through a CB1+ CB1-1 residual function;
(3) CB1-2 column: compensation is performed by CB1+ CB1-2 residual function.
TABLE 2
For the test data set from clinical trial 2, the master function reduced the percent bias standard deviation from the test sensor from lot a under the HCP test case from 7.52 to 3.64, which was approximately 4 SD units, and provided 97.1% measurement performance within the ± 10% percent bias limit. The residual function (CB 1-1) further reduces the percentage bias standard deviation to 3.252, thereby allowing the performance of the assay to reach 100% within the + -10% limit. For the test sensors from lot a under the self-test case, the master function reduced the percent bias standard deviation from 10.67 to 6.236. The residual function further reduced the percent bias standard deviation from 6.236 with the master function only to 5.958, and the average percent bias from 4.284 to 2.222. The residual function (CB 1-1) improved the measurement performance of the biosensor system from 84.3% of the analysis within the ± 10% percentage bias limit to 96.1%, and thus improved by approximately 14% relative to the main function alone ([ 96.1-84.3]/84.3 x 100). Thus, a compensation method comprising a main function and at least one residual function results in at least 85%, preferably at least 90%, and more preferably at least 95% of the analyte concentration determined from at least 40, preferably from at least 80, and more preferably from at least 100 user self-test analyses within a ± 10% percent bias limit.
Figures 3A-3D show data from an HCP test case clinical trial comprising approximately 134 data points (67 whole blood samples, 2 measurements each) when error compensation using the master function and the residual function was applied. Fig. 3A is an uncompensated dose-response correlation curve between the output signal current from a whole blood sample and the reference glucose concentration for each sample as determined by the YSI reference instrument. The data exhibited relatively large deviations from the reference concentration, which could be attributed to hematocrit as a cause of physical error and to a cause of error in operating conditions resulting from HCP testing. Fig. 3B shows a correlation curve after compensating the data in fig. 3A using error compensation including a main function and a residual function. Fig. 3C plots the percent bias of blood samples collected from the HCP test cases before and after compensation in fig. 3A and 3B, with 99.3% of the compensated data population within ± 10%. FIG. 3D shows the hematocrit sensitivity of the data from FIG. 3A before and after compensation, where the percentage biased hematocrit dependence is substantially removed after compensation.
Table 3 below summarizes the measured performance of the biosensor system before (Un-comp) and after (comp) compensation in the following respect for HCP determined analyte concentrations and self-test determined analyte concentrations: the mean percent bias, percent bias Standard Deviation (SD) and percent within the ± 5%, ± 8% and ± 10% percent bias limits of the reference analyte concentration were determined for the analyte concentrations. These data show that: the SD values after compensation of the main function and the residual function are reduced by more than 50% relative to the uncompensated analyte measurement.
TABLE 3
The combined use of the main function and the residual function resulted in approximately 99% of the analyses being within the ± 10% percent bias limit, greater than 95% of the analyses being within the ± 8% percent bias limit, and greater than 80% of the analyses being within the ± 5% percent bias limit. These results show an improvement of about 40% (100% [99.3-70.9 ]/70.9) at a ± 10% percent bias limit relative to the uncompensated analysis. Thus, for at least 40, preferably for at least 80, more preferably for at least 100 user self-test analyses, a compensation method comprising a master function and at least one residual function may result in a determined analyte concentration of greater than 95% within a ± 8% percent bias limit, and a determined analyte concentration of greater than 60%, preferably greater than 70%, more preferably greater than 80% within a 5% percent bias limit.
Fig. 4A to 4D show results obtained when error compensation including a main function and a residual function is applied to a capillary blood sample and a capillary blood sample spiked with venous blood to adjust the hematocrit content of the sample. The native hematocrit level of the capillary blood sample is in the range of about 30% to about 53%, while the hematocrit level of the blended venous blood sample is adjusted to be in the range of about 20% to about 65%. Capillary blood samples spiked with venous blood were also adjusted to contain from 40mg/dL to 490mg/dL of glucose as the analyte. Thus, the blended sample is adjusted to hematocrit levels and glucose levels above and below those typically observed in patients.
Fig. 4A is a plot of the response correlation between the output signal current from the capillary sample and the venous sample and the reference glucose concentration for each sample determined by the YSI reference instrument. The data exhibited a relatively large deviation from the reference concentration due to the wide range of hematocrit as a cause of the physical error. Fig. 4B shows a correlation curve for a capillary sample and a vein sample after compensating the data in fig. 4A using the same error compensation including the main function and the residual function. The figure confirms that: the performance when using compensation to detect capillary blood samples and venous blood samples is substantially the same.
Figure 4C shows the percent bias in the determined analyte concentrations for the pre-compensation and post-compensation venous blood adjusted samples, with 98.7% of the post-compensation data population within the range of ± 10% percent bias limit. Since only about 50% of the uncompensated data population falls within the range of the ± 10% percent bias limit, this shows a decrease in hematocrit sensitivity and thus an improvement of about 97% (100 x 98.7-50/50) of measurement performance. FIG. 4D shows the hematocrit sensitivity before and after compensation for the blended vein samples, wherein the percentage biased hematocrit dependency is substantially removed by the compensation to provide a substantially straight line. Before compensation, the correlation curve with a slope of about-1.2 shows: for every 1% change in hematocrit sample content relative to the reference sample content, there will be a percentage bias increase of about 1% in the measured analyte concentration. Thus, when the whole blood sample comprises about 30% to about 55% hematocrit, preferably about 20% to about 70% hematocrit, the compensation method including the primary function and the at least one residual function can reduce the slope of the correlation curve representing the sensitivity of hematocrit of the whole blood sample to ± 0.4 or less, preferably to ± 0.2 or less, and more preferably to ± 0.1 or less.
The ability of a biosensor to detect a sensor that reproducibly produces the same output signal in response to the same input signal and sample analyte concentration varies from batch to batch. Although it is preferred to equip the measuring device with a single calibration curve of the transfer function, this limits the manufacturing variations that may exist between different batches of detection sensors. An error compensation method comprising a main function and at least one residual function allows to obtain a better measurement performance for a plurality of test-sensor batches using the same error compensation method. In addition, the error compensation method comprising the main function and the at least one residual function may allow for greater manufacturing variability from lot to lot of the detection sensor while providing the required measurement performance for the biosensor system.
Fig. 5A to 5D show results provided by the main function and results provided by a combination of the main function and the remaining functions when glucose concentration measurement of a whole blood sample is performed using about 10000 detection sensors. Fig. 5A shows the standard deviation of the percent bias values for each test sensor lot before and after compensation for a total of 87 test cases. In FIG. 5A, each number on the X-axis represents a subset of the different batches of detection sensors, each subset including between about 100 and about 130 detection sensors. Approximately 7 different batches of test sensors were used to determine the glucose concentration of venous blood in the controlled environment test case. Approximately 40 different batches of test sensors were used to determine the glucose concentration in the HCP test case. Approximately 40 different batches of test sensors were used to determine the glucose concentration in the case of the user-self test. The Y-axis represents the percent biased standard deviation for multiple concentration measurements performed with each batch of detection sensors.
For the HCP test cases, uncompensated analysis indicated: the average percent bias standard deviation was about 7.9 for about 40 different batches of test sensors. This value is reduced to about 3.97 after compensation with the master function. Adding the residual function to the main compensation provides an average percent bias standard deviation of about 3.59. For the user self-test case, the uncompensated analysis shows: the average percent bias standard deviation was about 8.26 for about 40 different batches of test sensors. After compensation with the master function the value is reduced to about 4.46. Adding the residual function to the main compensation provides an average percent bias standard deviation of about 3.91. The improvement in measurement performance obtained by adding the residual function to the master function is most pronounced as the average percent bias is reduced from 4.17 to 0.20 (about 96% (100 x [4.17-0.20 ]/4.17)) for the user self-test cases. Table 4 below summarizes the results of these measured properties.
TABLE 4
Wherein HCP-Avg represents the arithmetic mean from the HCP test cases at each index of measured performance, and HCP-SD represents the standard deviation of the mean percent bias value of the mean; Self-Avg represents the arithmetic mean of the test cases from the user's Self-test at each index of the measured performance, and Self-SD represents the standard deviation of the mean percent bias values of the mean; and Self-HCP represents the difference between the mean values from the HCP test cases and the mean values from the Self-test cases.
Thus, the measurement performance results of table 4 confirm that: the compensation method comprising the master function and the at least one residual function may provide an average percent bias standard deviation of less than 5, preferably less than 4, for less than 5000 analyses, preferably less than 10000 analyses, under HCP test cases and user self-test cases. The compensation method comprising the principal function and at least one residual function may also provide an average percent bias standard deviation of less than 5, preferably less than 4, for glucose analysis with detection sensors from less than 45 detection sensor batches, preferably from less than 87 detection sensor batches, under HCP test cases and user self-test cases.
The remaining functions provided an improvement of approximately 9% ([ 3.94-3.56]/3.94 x 100) in the mean percent bias standard deviation for the HCP test cases relative to the case when only the master function was used. The residual function also provided an improvement of approximately 13% ([ 4.47-3.88]/4.47 x 100) in the mean percent bias standard deviation for the self-test cases relative to the case when only the master function was used. For the HCP test cases, the remaining functions also provided an improvement in the mean percent bias standard deviation of approximately 23% ([ 2.08-1.59]/2.08 × 100) relative to the case when only the master function was used. Thus, when an error compensation method comprising a master function and at least one residual function is used to determine the glucose concentration of a whole blood sample, an improved accuracy for substantially non-manufacturing variation errors is observed for a plurality of test-sensor batches.
The measured performance results of table 4 also confirm: a compensation method comprising a main function and at least one residual function can increase the number of approximately 10000 analyses that fall within the ± 10% percent bias limit. The effect is more remarkable for the following user self-testing test cases: in these cases of customer self-test, an improvement of about 10% ([ 98-88.8]/88.8 x 100) was observed when the residual function was combined with the master function to compensate the analysis results of about 4200 customer self-test analyses. Thus, a compensation method comprising a master function and at least one residual function enables more than 90%, preferably more than 95% of the analyte concentrations determined with less than 5000 detection sensors, preferably less than 10000 detection sensors, to fall within the ± 10% percent bias limit in the HCP test case and the user self-test case. The compensation method comprising the master function and the at least one residual function can also enable that more than 90%, preferably more than 95% of the analyte concentrations determined with detection sensors from a test sensor lot below 45, preferably a test sensor lot below 87 fall within the ± 10% percentage bias limit in the HCP test case and the user-self test case. Thus, when an error compensation method comprising a main function and at least one residual function is used to determine the glucose concentration of a whole blood sample, an improved accuracy is observed for a plurality of test-sensor batches.
FIG. 5B shows the correlation of the average percent bias for multiple individual test sensor batches with the output current-reference glucose concentration regression slope for each batch. Although these results are from the HCP test cases, it is believed that these results reflect manufacturing differences between sensor batches. Fig. 5B confirms that: the average percent bias between batches resulting from manufacturing differences between different test sensor batches was from-4% to +7.5% (a range of approximately 11.5%). The compensation method, which includes a combination of the main function and the residual function, reduces the range of percentage mean bias originating from manufacturing differences between different detection sensor batches to a range from-4% to +2%, i.e., approximately 6%. Thus, for a mean percentage bias of determined analyte concentrations due to measurement differences between different detection sensor batches, a compensation method comprising a master function and at least one residual function can reduce the mean percentage bias dispersion by more than about 47% ([ 11.5-6]/11.5 x 100). This average percent-bias dispersion can be obtained when the analysis performed by the biosensor system includes a single transfer function, such as a single value of slope and intercept for calibration.
Fig. 5B also confirms that: error compensation, including the main function and the residual function, can improve the measurement performance of the biosensor system beyond the test performance lost in conventional biosensor systems until only manufacturing differences between sensor batches are detected. Thus, the error compensation comprising the main function and the at least one residual function allows for greater manufacturing variability from lot to lot of measurement sensors while providing the desired measurement performance for the biosensor system.
Fig. 5C shows the correlation of the average percent bias of multiple test sensor batches from HCP test cases and consumer self-test cases after compensation with the master function and the residual function. Compared to fig. 5B, the increase in self-test cases decreases the measurement performance because the analysis error from the self-test is added to the determined analyte concentration in addition to having the manufacturing variation error. This effect can be seen from the fact that: the mean percent bias between batches increased from the previous range of-4% to +7.5% of FIG. 5B to the range of-6% to +12% observed in FIG. 5C. Therefore, the dispersion of about 11.5% due to the manufacturing variation error of fig. 5B is increased to about 18% for the combined error due to the manufacturing variation and the user self-determination. A compensation method comprising a combination of a main function and at least one residual function reduces the average percentage bias originating from manufacturing variations and user self-tests to a dispersion from-4% to +4%, i.e. about 8%. Thus, a compensation method comprising a main function and at least one residual function can reduce the average percent biased dispersion of an analysis performed using a plurality of test sensors from a plurality of test sensor lots to within about ± 12%, preferably to within about ± 8%, and more preferably to within about ± 4% under user-self test conditions. This average percent-bias dispersion can be obtained when the analysis performed by the biosensor system includes a single transfer function, such as a single value of slope and intercept for calibration.
Figure 5D shows the percentage of analyte determinations with percentage bias limits within ± 10% for each test sensor lot under HCP test cases and self-test cases. The percentage bias from uncompensated analysis of batches swings very much (between about 40% to about 90%), especially for self-test cases. In contrast, only about 3 of the about 87 batches of test sensors were under 95% within the ± 10% percent bias limit when each analysis was compensated with the master function and at least one of the remaining functions.
For assays that contain errors due to manufacturing variations due to variations in the activity of the reagent during storage, a compensation method that includes a main function and at least one residual function may also improve the measurement performance of such assays. Bottles containing about 50 test sensors taken from each of the seven test sensor batches were left to stand at about 50 ℃ for about two and four weeks. Bottles containing about 50 test sensors taken from each of the seven test sensor batches were left to stand at about-20 ℃ for storage for about two and four weeks for compensation purposes. Two weeks of accelerated aging at about 50 ℃ represents about 24 months of retail shelf storage, while four weeks of accelerated aging at about 50 ℃ represents about 36 months of retail shelf storage.
Subsequently, whole blood samples containing approximately 58mg/dL, 172mg/dL, 342mg/dL, or 512mg/dL glucose at 42% hematocrit level were analyzed in a controlled laboratory environment using a 50 ℃ stored accelerated aging test sensor and a-20 ℃ stored comparative test sensor. Then, additional accelerated aging detection sensors and comparison detection sensors are used to generate a residual function to describe the operating condition error.
The biosensor system is then used to determine the glucose concentration value of the sample without the main or residual compensation and with the main and residual compensation. The percentage bias difference between the accelerated aging detection sensor and the comparative detection sensor over the two-week period is shown in table 5 below, and the percentage bias difference between the accelerated aging detection sensor and the comparative detection sensor over the four-week period is shown in table 6 below.
TABLE 5
TABLE 6
The results obtained from the biosensor systems in tables 5 and 6 confirm that: for at least seven different batches of test sensors from storage for up to 4 weeks (which translates to approximately 36 months of retail shelf storage prior to use), the compensation method comprising the primary function and at least one residual function may allow for an average percent bias difference of ± 5% or less between a-20 ℃ stored test sensor and a 50 ℃ stored test sensor.
Biosensor systems having the ability to generate additional output values in addition to the output value from the analyte or from a mediator that is responsive to the analyte may also benefit from the aforementioned error compensation methods. Systems of this type typically compensate for interferers and other causes using additional output value(s) by: the additional output value(s) is (are) subtracted from the analyte responsive output signal in some manner. The error parameter may be derived directly or indirectly from the analyzed output signal and/or obtained independently of the output signal. Thus, terms may be formed using additional output values in addition to the output value from the analyte or the output value from a mediator that is responsive to the analyte, such as disclosed in PCT international publication WO2009/108239 entitled "Slope-Based Compensation," filed on 6.12.2008. Two types of terms may be used to form the main function and the residual function.
Fig. 6A shows a gated pulse sequence in which the input signal applied to the working electrode and the counter electrode comprises a plurality of pulses, and in which a second input signal is applied to the additional electrode to generate a secondary output signal. The input signal applied to the additional electrode is applied after the end of the input signal for analysis applied between the working electrode and the counter electrode, but may be applied at another time. The input signal for analysis comprises six excitation pulses. The input signal applied to the additional electrode comprises a seventh higher voltage pulse. The solid line depicts the substantially constant input potential and the superimposed dots represent the time at which the current measurement is taken. The input signal is applied to a plurality of detection sensors that are used to determine the glucose concentration of whole blood from a plurality of internal clinical studies.
The excitation of the analytic input signal of fig. 6A includes pulse widths of about 0.2 seconds, about 0.4 seconds, and about 0.5 seconds. Pulse widths from about 0.1 second to about 0.5 second are preferred, although other pulse widths may be used. Pulse widths greater than 2 seconds are preferably not used. The analytical stimuli are separated by approximately 0.5 seconds and approximately 1 second of relaxation (relaxation) and are provided by open circuits. Relaxation widths of about 0.3 seconds to about 1.5 seconds are preferred, although other relaxation widths may be used. The relaxation width immediately before the excitation comprising the current measurement for determining the analyte concentration is preferably less than 1.5 seconds. Preferably, relaxation widths of greater than 5 seconds are not used. In addition to being open-circuited, relaxation can be provided by other methods that do not apply a potential that significantly causes the electrochemical redox reaction of the analyte and/or mediator. Preferably, the application of the input signal for analysis and the measurement of the associated output current from the sample are completed in less than seven seconds.
The secondary output signal in the form of a current from the additional electrode can be considered as an error parameter describing the hematocrit content of the whole blood sample. The hematocrit content of the sample may be considered an error parameter because performing the analysis at a different hematocrit content than that at which the reference correlation was determined may cause an error in the concentration value. The hematocrit content of a sample can be determined from any source, such as electrodes and computational estimates.
The error compensation method comprising a transfer function in combination with a main compensation and a residual compensation is applied as follows:
Gcomp=i5/[Scal*(1+P+WC*R)]，
wherein G iscompIs the compensated analyte (glucose) concentration, i, of the sample5Is the last current value, S, from the fifth excitation pulse as shown in FIG. 6AcalIs the slope from the reference correlation equation, P is the master function, WC is the weighting coefficient, and R is the first residual function. Multiple regressions and term exclusions were performed to determine the values of the residual functions shown in table 7 below.
TABLE 7
Compensating for correlation slope S using a complex exponential function as the primary functioncal. The first residual function is used to compensate for errors that have not been compensated by the main function. The main function and the first residual function with respective appropriate weighting coefficients are determined as follows:
master function =17.5252-0.012154 + i7-Hct'-0.0258*'R3/2'-15.057*'R5/4'-20.04*'R6/5'+16.318*'R6/4'-5.1e-7*'i7-Hct*Graw'+0.0029343*'R43*Graw'+0.01512*'R54*Graw'-0.0191066*'R65*Graw'-1.55e-6*'T*i7-Hct'+0.030154*'T*R54'-0.006368*'T*R53'-9.476e-4*'i7-Hct*R43'+0.011803*'i7-Hct*R54'+8.112e-4*'i7-Hct*R53'+0.013868*'i7-Hct*R65'-0.01303*'i7-Hct*R64'-9.1e-6*'i7-Hct*R54*Graw'+1.02e-5*'i7-Hct*R65*Graw'；
First residual function =4.4084+5.683 × R4/3'-5.1348 × R5/4' -4.2282 × R5/3'-7.971 × R6/5' +7.40 × R6/4'+1.08 e-5' i7-Hct*Graw'-0.0015806*'R32*Graw'-0.018626*′R43*Graw'-0.044513*'R54*Graw'+0.01978*'R53*Graw'+0.04634*'R65*Graw'+0.001481*'T*R32'+0.03006*'T*R54'-0.03737*'T*R64'-0.001453*'i7-Hct*R43'+7.836e-4*'i7-Hct*R53'+6.61e-4*'i7-Hct*R65'+1.75e-5*'i7-Hct*R54*Graw'-2.89e-5*'i7-Hct*R65*Graw'；
Wherein i7-HctIs the current from the hematocrit sensing electrode at the seventh second, T is the measurement device temperature, and R3/2, R4/3, R5/4, R6/5, R5/3, and R6/4 are inter-pulse ratio indices (inter-pulse ratio index) having the general form: the last current of a pulse later in time divided by the last current of an earlier pulseAnd (4) streaming. Additional information can be found in PCT international publication WO 2010/077660 regarding the exponential function and the intermediate signal value ratio.
Figure 6B is a correlation curve between the total error of the data from multiple internal clinical studies and the main function value, which provides a correlation coefficient of 92.9%. Fig. 6C shows a correlation curve between the total error of the same data and the combined value of the main function and the first residual function. By adding the first residual function value, the overall correlation coefficient increased from 92.9% to 95.8%. The improvement in measurement performance can also be seen from the reduction of the SD value from 0.04836 to 0.03707 by adding a first residual function.
Residual function compensation may also be used when the detection sensor is filled twice with samples (such as when the first fill is insufficient and additional samples are added in a short time). When an underfill condition is detected, the start of the analysis may be delayed until the detection sensor is refilled. The error associated with this two-time filling process is first compensated by the main function. The remaining two-time filling error can then be compensated by the residual function.
In the case of a 4-electrode sensor, a sample sequentially passes through a first electrode (a) in front of a second electrode (B), a second electrode (B) in front of a third electrode (C), and a third electrode (C) in front of a fourth electrode (D) in the process of entering a detection sensor, and the time required for the sample to reach between the electrodes (B) and (C) and the time required for the sample to reach between the electrodes (C) and (D) may be expressed as BC and CD, respectively.
The BC time is typically associated with a small underfill volume (about 0.3 μ L relative to a full fill volume of 0.5 μ L), while the CD time is typically associated with a large underfill volume (about 0.5 μ L).
Both of which are substantially mutually exclusive and independent of each other and may each have a different residual function after the same main function. A general compensation function can be expressed as follows:
BCerror = primary function + WCBCResidual functionBC
CD error = primary function + WCCDResidual functionCD
Thus, according to general equation GcompBC=i5/[Scal*(1+P+WC*RBC)]Or GcompCD=i5/[Scal*(1+P+WC*RCD)]A main function, a first residual functionBCAnd a first residual functionCDIs determined as follows:
the master function =32.705-0.025411 × '7' -31.686 × ' R5/4' -33.37 × ' R6/5' +31.386 × ' R6/4' +3e-7 × ' G ' -3.9021e-4 ' R32 ± +0.0029771 ' R43 × ' G ' -0.0029786 ' R54 × +8.09e-6 ' T7 ' -0.015815 × ' T ' R43' +0.14909 × ' T R54' -0.18932 × ' T65 ' + 65 ';
first residual functionBC(vii) =16.995+0.001944 + 7'+90.03 + R5/4' -17.69 + R5/3'-127.72 + R6/5' +37.924 + R6/4'-5.77 e-6' AE 7'-0.0035248 + R43 + G0.004296' R64 'G' +0.9513 'T' R9 '-4.508' T 'R54' +3.5624 'T' R65 '-0.0019169' 7 + R43 '-0.1322' AE 'R54' + 54 'AE 54' -54 'AC 54'; and
first residual functionCD=3.1062+0.011148*'7'+20.345*'R3/2'-143.8*'R4/3'+125.96*'R5/4'+0.032094*'R54*G'-0.008077*'R53*G'-0.024023*'R65*G'+7.43e-5*'T*7'-0.8642*'T*R32'+6.1618*'T*R43'-5.5315*'T*R54'-0.012701*'7*R54'-0.014974*'7*R65'+0.014655*'7*R64'+2.872e-5*'AC*7'-0.052885*'AC*R43'。
In this way, the error compensation method may comprise a single master function that is used in combination with different first residual functions to provide compensation for more than two modes of the biosensor system. Fig. 6D shows the percent bias as a function of time remaining using BC, and fig. 6E shows the percent bias as a function of time remaining using CD. For both the BC first residual and the CD first residual, the master function compensates for environmental and physical sample characteristic error causes including temperature and hematocrit. The operating condition errors associated with the underfill and the refill process, the form of the operating condition error, are compensated by a first residual function corresponding to each underfill case.
TABLE 8
Table 8 above provides additional data describing the compensation results from test sensors that were underfilled at a volume of about 0.3 μ L and a volume of about 0.5 μ L and then completely filled after the initial underfill condition. Therefore, although completely filled by the second filling, the BC detection sensor is originally filled with about 0.3 μ L of whole blood, and the CD detection sensor is originally filled with 0.5 μ L of whole blood. While only about 30% of the uncompensated readings fall within the percent bias limit of 10%, the combination of the main compensation and the remaining compensation results in over 90% of the data falling within the desired ± 10% limit. Thus, when the detection sensor is initially underfilled and then completely filled by the user, a compensation method comprising a main function and at least one residual function may result in more than 90% of the determined analyte concentration falling within the percentage bias limit of ± 10%.
Fig. 7A depicts a schematic of a biosensor system 700 for determining an analyte concentration in a biological fluid sample. The biosensor system 700 includes a measurement device 702 and a detection sensor 704, which may be implemented in any analytical instrument including a desktop device, or a portable or handheld device, etc. The measuring device 702 and the detection sensor 704 may be adapted to implement an electrochemical sensor system, an optical sensor system, a combination thereof, or the like. The biosensor system 700 determines an analyte concentration of a sample according to an error compensation method comprising at least one transfer function, at least one primary compensation, at least one residual compensation, and an output signal. The error compensation method may improve the measurement performance of the biosensor system 700 in determining the analyte concentration of a sample. The biosensor system 700 may be used to determine analyte concentrations including those of glucose, uric acid, lactate, cholesterol, and bilirubin, among others. Although a particular configuration is shown, the biosensor system 700 may have other configurations including additional components.
The detection sensor 704 has a substrate 706, the substrate 706 forming a reservoir 708 and a channel 710 with an opening 712. The reservoir 708 and channel 710 may be covered by a cover with a vent. Reservoir 708 defines a partially enclosed volume. Reservoir 708 may contain components that aid in retaining a liquid sample, such as a water-swellable polymer or a porous polymer matrix. Reagents may be deposited in reservoir 708 and/or channel 710. The reagent may include one or more enzymes, binders, mediators, and the like. The reagent may include a chemical indicator for an optical system. The detection sensor 704 may have other configurations.
In an optical sensor system, the sample interface 714 has an optical port or optical aperture for viewing the sample. The optical port may be covered by a substantially transparent material. The sample interface 714 may have optical ports on opposite sides of the reservoir 708.
In the electrochemical system, the sample interface 714 has a conductor connected to the working electrode 732 and the counter electrode 734, and an output signal for analysis can be measured from these conductors. The sample interface 714 may also include conductors to which one or more additional electrodes 736 may be connected from which secondary output signals may be measured. The electrodes may lie substantially in the same plane or in more than one plane. The electrodes may be disposed on the surface of the substrate 706 that forms the reservoir 708. Each electrode may extend or protrude into the reservoir 708. The dielectric layer may partially cover the conductors and/or electrodes. The sample interface 714 may have additional electrodes and conductors.
The measurement device 702 includes circuitry 716 coupled to a sensor interface 718 and a display 720. The circuit 716 includes a processor 722 coupled to a signal generator 724, an optional temperature sensor 726, and a storage medium 728.
The signal generator 724 provides an electrical input signal to the sensor interface 718 in response to the processor 722. In an optical system, the electrical input signal may be used to manipulate or control the detector and light source in sensor interface 718. In an electrochemical system, sensor interface 718 may communicate the electrical input signal to sample interface 714 to apply the electrical input signal to the biological fluid sample. The electrical input signal may be a potential or a current, and may be constant, varying, or a combination thereof (e.g., when an AC signal with a DC signal offset is applied). The electrical input signal may be applied as a single pulse or in multiple pulses, sequences or periods. The signal generator 724 may also act as a generator recorder to also record the output signal from the sensor interface.
An optional temperature sensor 726 measures the temperature of the sample in the reservoir of the detection sensor 704. The temperature of the sample may be measured, calculated from the output signal, or may be assumed to be equal or similar to the measured ambient temperature or the temperature of the device implementing the biosensor system. The temperature may be measured using a thermistor, thermometer, or other temperature sensing device. Other techniques may be used to determine the sample temperature.
The storage medium 728 may be a magnetic, optical, or semiconductor memory, or other storage device, etc. The storage medium 728 may be a fixed storage device or a removable storage device such as a remotely accessed memory card.
The processor 722 performs analyte analysis and data processing using computer readable software code and data stored in the storage medium 728. Processor 722 may initiate an analyte analysis in response to the presence of detection sensor 704 at sensor interface 718 and a sample being applied to detection sensor 704, or in response to a user input, etc. Processor 722 instructs signal generator 724 to supply an electrical input signal to sensor interface 718. Processor 722 receives the sample temperature from temperature sensor 726. Processor 722 receives output signals from sensor interface 718. The output signal is generated in response to a reaction of an analyte in the sample. The output signal may be generated using an optical system, an electrochemical system, or the like. Processor 722 determines the analyte concentration from the output signal using a compensation method comprising a main function and at least one residual function as previously described. The results of the analyte analysis may be output to the display 720 and may be stored in the storage medium 728.
The correlation equation between analyte concentration and output signal can be described graphically, mathematically, or a combination thereof. The correlation equation may include one or more exponential functions. The correlation equation may be described by a Program Number (PNA) table or another look-up table stored in the storage medium 728. The constants and weighting coefficients may also be stored on the storage medium 728. The instructions for performing the analyte analysis may be provided by computer readable software code stored in the storage medium 728. The code may be object code or any other code that describes or manipulates the functionality described herein. One or more data processes including determining decay rates, K constants, ratios, functions, and the like may be performed on the data from the analyte analysis in processor 722.
In an electrochemical system, sensor interface 718 has contacts that connect to or are in electrical communication with conductors in sample interface 714 of detection sensor 704. Sensor interface 718 transmits electrical input signals from signal generator 724 via these contacts to connectors in sample interface 714. Sensor interface 718 also transmits output signals from the sample to processor 722 and/or signal generator 724 via these contacts.
In light absorbing optics and photogenerated optics, the sensor interface 718 includes a detector that collects and measures light. The detector receives light from the liquid sensor via an optical port in the sample interface 714. In light-absorbing optics, sensor interface 718 also includes a light source such as a laser or light emitting diode. The incident light beam may have a wavelength selected for absorption by the reaction products. Sensor interface 718 directs an incident beam from a light source via an optical port in sample interface 714. The detector may be positioned at an angle, such as 45 deg., to the optical port to receive light reflected from the sample. The detector may be positioned adjacent to an optical port at the other side of the sample from the light source to receive light transmitted through the sample. The detector may be positioned at other locations capable of receiving reflected and/or transmitted light.
The display 720 may be an analog or digital type display. The display 720 may include an LCD, LED, OLED, vacuum fluorescent display, or other display suitable for displaying numerical readings. Other displays may also be used. The display 720 is in electrical communication with the processor 722. The display 720 may be separate from the measurement device 702, such as when the display 720 is in wireless communication with the processor 722. Alternatively, the display 720 may be removable from the measurement device 702, such as when the measurement device 702 is in electrical communication with a remote computing device, a medication metering pump, and the like.
In use, a liquid sample for analysis is delivered to the reservoir 708 by introducing liquid into the opening 712. The liquid sample flows through the channel 710, filling the reservoir 708 and simultaneously venting the previously contained air. The liquid sample chemically reacts with reagents deposited in the channel 710 and/or reservoir 708.
The detection sensor 704 is positioned adjacent to the measurement device 702. The proximity location includes a location that enables sample interface 714 to be in electrical and/or optical communication with sensor interface 718. Electrical communication includes the transmission of input and/or output signals between contacts in sensor interface 718 and conductors in sample interface 714. Optical communication includes the transmission of light between an optical port in sample interface 714 and a detector in sensor interface 718. Optical communication also includes the transmission of light between an optical port in sample interface 714 and a light source in sensor interface 718.
Processor 722 receives the sample temperature from temperature sensor 726. Processor 722 instructs signal generator 724 to provide input signals to sensor interface 718. In the optical regime, sensor interface 718 manipulates the detector and light source in response to the input signal. In an electrochemical system, sensor interface 718 provides the input signal to the sample via sample interface 714. Processor 722 receives an output signal generated in response to a redox reaction of an analyte in a sample as previously described.
Processor 722 determines an analyte concentration of the sample. The measurement device adjusts the correlation between the analyte concentration and the output signal by compensation comprising a main function and at least one residual function. Processor 722 may also implement other compensation and functions.
While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that other embodiments and implementations are possible within the scope of the invention.