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Direct Parametric Inference for the Cumulative Incidence Function in Competing Risks

Description

Thecmpp package provides parametric (Direct) modeling methods for analyzing cumulative incidence functions (CIFs)in the context of competing risks. It includes Gompertz-based models, regression techniques, and parametric (Direct) approachessuch as the Generalized odds rate (GOR), Proportional Odds Model (POM), and Proportional Hazards Model (PHM).The package enables users to estimate and compare CIFs using maximum likelihood estimation, perform regression analysis,and visualize CIFs with confidence intervals. It also supports covariate adjustment and bootstrap variance estimation.

Details

Thecmpp package offers functions for modeling cumulative incidence functions (CIFs) Directlyusing the Gompertz distribution and generalized regression models.

Key features include:

• Direct parametric modeling for cumulative incidence functions.

• Maximum likelihood estimation of parameters.

• Regression analysis with covariates, including treatment effects.

• Visualization of CIFs with confidence intervals.

• Covariate-adjusted CIF estimation.

• Bootstrap variance estimation for model parameters.

Commonly used functions include:

• Initialize: Initializes the data for the Cmpp model.

• LogLike1: Computes the negative log-likelihood for the model without covariate effect.

• compute_grad: Computes the gradient of the log-likelihood.

• compute_hessian: Computes the Hessian matrix of the log-likelihood.

• estimate_parameters_GOR: Estimates parameters using the Generalized odds rate (GOR).

• estimate_parameters_POM: Estimates parameters using the Proportional Odds Model (POM).

• estimate_parameters_PHM: Estimates parameters using the Proportional Hazards Model (PHM).

• CIF_res1: Computes CIF results for competing risks without covariates.

• CIF_Figs: Plots CIFs with confidence intervals (without covariate effect).

• Cmpp_CIF: Computes and plots CIFs for competing risks using GOR, POM, and PHM.

• FineGray_Model: Fits a Fine-Gray regression model for competing risks data andvisualize CIF by Fine-Gray model result usingcmprsk::cuminc andcmprsk::crr.

• bootstrap_variance: Estimates variance of parameters using the bootstrap method.

• GetData: Retrieves initialized data from the Cmpp model.

• Cleanup: Cleans up memory by deleting the Cmpp instance.

Author(s)

Habib Ezzatabadipourhabibezati@outlook.com

References

• Jeong, J.-H., & Fine, J. (2006). Direct parametric inference for the cumulative incidence function.Applied Statistics, 55(2), 187-200.
  

• Jeong, J.-H., & Fine, J. (2007). Parametric regression on cumulative incidence function.Biostatistics, 8(2), 184-196.

See Also

Initialize,LogLike1,compute_grad,compute_hessian,estimate_parameters_GOR,estimate_parameters_POM,estimate_parameters_PHM,CIF_res1,CIF_Figs,Cmpp_CIF,FineGray_Model,bootstrap_variance,GetData,Cleanup

Examples

## Example: Initialize the Cmpp model and compute CIFslibrary(cmpp)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1timee <- rexp(100, rate = 1/10)Initialize(features, timee, delta1, delta2, h = 1e-5)# Initialize the Cmpp model# Estimate parameters using the Generalized odds rate (GOR)initial_params <- rep(0.001, 2 * (ncol(features) + 3))result <- estimate_parameters_GOR(initial_params)print(result)# Compute CIFs for competing risks (without covariate effect | Not Regression model)cif_results <- CIF_res1()print(cif_results)# Plot CIFs with confidence intervalsplot <- CIF_Figs(rep(0.01, 4), timee)print(plot)# Compute and plot adjusted CIFsresult_cif <- Cmpp_CIF(featureID = c(1, 2),featureValue = c(0.5, 1.2),RiskNames = c("Event1", "Event2"),TypeMethod = "GOR",predTime = seq(0, 10, by = 0.5))print(result_cif$Plot$Plot_InputModel) # Plot for the specified modelprint(result_cif$CIF$CIFAdjusted) # Adjusted CIF values# Fit a Fine-Gray model for competing risksresult_fg <- FineGray_Model(CovarNames = c("Covar1", "Covar2", 'Covar3'),Failcode = 1,RiskNames = c("Event1", "Event2"))print(result_fg$Results)  # Summary of the Fine-Gray modelprint(result_fg$Plot) # Plot of the CIFs# Clean up memoryCleanup()

Plot Cumulative Incidence Functions (CIF) with Confidence Intervals

Description

This function plots the cumulative incidence functions (CIF) for two competing risks based on the estimated parameters and their variances. It includes confidence intervals for the CIFs.

Usage

CIF_Figs(initial_params, TimeFailure, OrderType = c(2, 1), RiskNames = NULL)

Arguments

Details

This function performs the following steps:

• Estimates the model parameters using theestimate_parameters function.

• Computes the Hessian matrix using thecompute_hessian function.

• Ensures that the diagonal elements of the covariance matrix are positive.

• Computes the cumulative incidence functions (CIF) for two competing risks.

• Plots the CIFs along with their confidence intervals.

Value

A ggplot object showing the CIFs and their confidence intervals.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)initial_params <- c(0.001, 0.001, 0.001, 0.001)result <- CIF_res1(initial_params)print(result)initial_params <- c(0.01, 0.01, 0.01, 0.01)TimeFailure <- seq(0, 10, by = 0.1)plot <- CIF_Figs(initial_params, TimeFailure)print(plot)

Compute Cumulative Incidence Function (CIF) Results

Description

This function estimates the parameters of the model, computes the Hessian matrix, and calculates the variances and p-values for the parameters. It ensures that the diagonal elements of the covariance matrix are positive.

Usage

CIF_res1(initial_params = rep(0.001, 4))

Arguments

Details

This function performs the following steps:

• Estimates the model parameters using theestimate_parameters function.

• Computes the Hessian matrix using thecompute_hessian function.

• Ensures that the diagonal elements of the covariance matrix are positive.

• Calculates the variances and p-values for the parameters.

Value

A data frame containing:

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)initial_params <- c(0.001, 0.001, 0.001, 0.001)result <- CIF_res1(initial_params)print(result)

Clean up memory by deleting the pointer to the Cmpp instance

Description

This function is used to clean up and delete the instance of the Cmpp class inthe C++ code. It ensures proper memory management and prevents memory leaks bydeleting the pointer to theCmpp object when it is no longer needed.It is important to call this function after you are done with theCmpp objectto ensure that no memory is leaked.

Usage

Cleanup()

Details

TheCleanup function must be called after using theCmpp object to clean upthe allocated memory in C++. Failure to call this function may result in memoryleaks, as the memory allocated for theCmpp object is not automatically freed.

Value

No return value. Called for side effects.

Examples

# Assuming you have previously initialized the Cmpp object with `Initialize()`Cleanup()

Compute and Plot Cumulative Incidence Functions (CIF) for Competing Risks

Description

This function computes and plots the cumulative incidence functions (CIF) for competing risks using three parametric models:Generalized odds rate (GOR), Proportional Odds Model (POM), and Proportional Hazards Model (PHM).It allows for adjusted CIFs based on specific covariate values and provides visualizations for all models.

Usage

Cmpp_CIF(  featureID = NULL,  featureValue = NULL,  RiskNames = NULL,  TypeMethod = "GOR",  predTime = NULL)

Arguments

Details

This function performs the following steps:

• Estimates the model parameters for GOR, POM, and PHM using theestimate_parameters_GOR,estimate_parameters_POM, andestimate_parameters_PHM functions.

• Computes the CIFs for the specified time points and covariate values.

• Generates plots for the CIFs, including adjusted CIFs based on specific covariate values.

• Provides separate plots for each model and a combined plot for all models.

IffeatureID andfeatureValue are provided, the function adjusts the CIFs based on the specified covariate values.IfRiskNames is not provided, the default names "Risk1" and "Risk2" are used. TheTypeMethod parameter determineswhich model's CIF plot is returned in the output.

Value

A list containing:

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)result <- Cmpp_CIF(  featureID = c(1, 2),  featureValue = c(0.5, 1.2),  RiskNames = c("Event1", "Event2"),  TypeMethod = "GOR",  predTime = seq(0, 10, by = 0.5))print(result$Plot$Plot_InputModel)  # Plot for the specified modelprint(result$Plot$PlotAdjusted_AllModels)  # Adjusted CIFs for all modelsprint(result$CIF$CIFAdjusted)  # Adjusted CIF values

Compute the CDF of the Parametric Generalized odds rate (GOR)

Description

This function computes the cumulative distribution function (CDF) of the parametric model (GOR Approach).

Arguments

Value

A numeric value representing the CDF.

Examples

library(cmpp)set.seed(321)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/2)Initialize(features, x, delta1, delta2, h = 1e-3)params <- rep(0.001, (ncol(features) + 3))y <- 0.07z <- features[1, ](cdf_value <- F_cdf_rcpp(params, z, y))

Compute the CDF of the Parametric Proportional Odds Model (POM)

Description

This function computes the cumulative distribution function (CDF) of the parametric model (POM Approach).

Arguments

Value

A numeric value representing the CDF.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/2)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, (ncol(features) + 2))x <- 2cdf_value <- F_cdf_rcpp2(params, features[1, ], x)print(cdf_value)

Compute the CDF of the Parametric Proportional Hazards Model (PHM)

Description

This function computes the cumulative distribution function (CDF) of the parametric model (PHM Approach).

Arguments

Value

A numeric value representing the CDF.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, (ncol(features) + 2))x <- 5cdf_value <- F_cdf_rcpp3(params, features[1, ], x)print(cdf_value)

Fine-Gray Model for Competing Risks Data

Description

This function fits a Fine-Gray model for competing risks data using thecmprsk package.It estimates the subdistribution hazard model parameters, computes cumulative incidence functions (CIFs),and provides a summary of the results along with a plot of the CIFs.

Usage

FineGray_Model(CovarNames = NULL, Failcode = 1, RiskNames = NULL)

Arguments

Details

This function retrieves the data initialized in the Cmpp model using theGetData function.It uses thecrr function from thecmprsk package to fit the Fine-Gray model for competing risks.The function also computes cumulative incidence functions (CIFs) using thecuminc function andgenerates a plot of the CIFs for the competing risks.

Value

A list containing:

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)result <- FineGray_Model(  CovarNames = c("Covar1", "Covar2", "Covar3"),  Failcode = 1,  RiskNames = c("Event1", "Event2"))print(result$Results)  # Summary of the Fine-Gray model#print(result$Plot)     # Plot of the CIFsprint(result$CIF_Results)  # CIF data

Retrieve Initialized Data from the Cmpp Model

Description

This function retrieves the data initialized in the Cmpp model, including the feature matrix, failure times,and competing risks indicators (delta1 anddelta2).

Details

This function requires the Cmpp model to be initialized using theInitialize function. It retrieves thedata stored in the Cmpp object, which includes the feature matrix, failure times, and the binary indicators forcompeting risks. If the Cmpp object is not initialized, the function will throw an error.

Value

A list containing:

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)data <- GetData()print(data$features)  # Feature matrixprint(data$timee)      # Failure timesprint(data$delta1)    # Indicator for the first competing eventprint(data$delta2)    # Indicator for the second competing event

Get Dimensions of the Cmpp Object

Description

This function returns the number of samples and features stored in the Cmpp object.It is primarily used to retrieve the dimensions of the data within the class.

Usage

GetDim()

Details

TheGetDim function allows users to access the internal dimensions of theCmpp class instance, such as the number of samples (Nsamp) and the number of features(Nfeature). This is useful when working with large datasets, especially forchecking the size of the data without needing to manually access the underlyingEigen::MatrixXdorEigen::VectorXd objects directly.

Value

A list containing:

Examples

# Initialize Cmpp objectlibrary(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)# Get dimensionsdims <- GetDim()dims$Nsamp    # Number of samplesdims$Nfeature # Number of features

Initialize Data for the Cmpp Model

Description

This function initializes the data used in the Cmpp model by storing the feature matrix, failure times,and the competing risks indicators in the model environment. These are required for subsequent computations.

Usage

Initialize(features, x, delta1, delta2, h)

Arguments

Details

This function does not return any value but sets up internal data structures required for model computation.Ensure thatfeatures,x,delta1, anddelta2 have matching lengths or dimensions.

Value

This function returnsNULL. The initialized data is stored in the package environment.

Examples

library(cmpp)features <- matrix(rnorm(100), ncol = 5)x <- rnorm(20)delta1 <- sample(0:1, 20, replace = TRUE)delta2 <- 1 - delta1Initialize(features, x, delta1, delta2, h = 1e-5)

Compute the Log-Likelihood for the Model

Description

Computes the negative log-likelihood of the Cmpp model given parameters and the initialized data.The log-likelihood considers Gompertz distributions for competing risks.

Usage

LogLike1(param)

Arguments

Details

This function requires the data to be initialized usingInitialize before being called.The log-likelihood is based on survival probabilities derived from the Gompertz distributions.

Value

A single numeric value representing the negative log-likelihood.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)param <- c(0.01, 0.01, 0.01, 0.01)LogLike1(param)

Estimate Variance of Parameters Using Bootstrap Method

Description

This function estimates the variance of model parameters using the bootstrap method.It repeatedly samples the data with replacement, estimates the parameters for each sample,and computes the variance of the estimated parameters.

Usage

bootstrap_variance(features, x, delta1, delta2, initial_params, n_bootstrap, optimMethod)

Arguments

Details

This function performs bootstrap sampling to estimate the variance of the model parameters.It requires the data to be initialized usingInitialize before being called.

Value

A list containing:

• variances: A numeric vector representing the variance of the estimated parameters.

• bootstrap_estimates: A matrix of parameter estimates for each bootstrap sample.

Examples

library(cmpp)features <- matrix(rnorm(100), ncol = 5)x <- rnorm(20)delta1 <- sample(0:1, 20, replace = TRUE)delta2 <- 1 - delta1initial_params <- c(0.01, 0.01, 0.01, 0.01)n_bootstrap <- 100results <- bootstrap_variance(features, x, delta1, delta2, initial_params, n_bootstrap, optimMethod = "BFGS")print(results$variances)print(results$bootstrap_estimates)

Compute the CDF of the Gompertz Distribution

Description

Calculates the cumulative distribution function (CDF) of the Gompertz distributionfor given input values and parameters.

Usage

cdf_gomp(x, alpha, beta)

Arguments

Details

The Gompertz distribution is commonly used in survival analysis and reliability studies.Ensure thatalpha andbeta are positive for meaningful results.

Value

A numeric vector of the CDF values for each input inx.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)x <- c(1, 2, 3)alpha <- 0.5beta <- 0.1lapply(x, cdf_gomp, alpha = alpha, beta = beta) |> unlist()

Compute the Numerical Gradient of the Log-Likelihood

Description

Calculates the gradient of the negative log-likelihood using finite differences.The function uses a small step size (h) defined during initialization.

Usage

compute_grad(param)

Arguments

Details

This function approximates the gradient using central finite differences.Ensure thath is appropriately set to avoid numerical instability.

Value

A numeric vector of the same length asparam, representing the gradient at the specified parameters.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)param <- c(0.5, 0.1, 0.6, 0.2)compute_grad(param)

Compute the Hessian Matrix of the Log-Likelihood

Description

Calculates the Hessian matrix of the negative log-likelihood function using finite differences.This function is useful for understanding the curvature of the log-likelihood surface and for optimization purposes.

Usage

compute_hessian(param)

Arguments

Details

This function approximates the Hessian matrix using central finite differences.Ensure that the step sizeh is appropriately set during initialization to avoid numerical instability.The function requires the data to be initialized usingInitialize before being called.

Value

A numeric matrix representing the Hessian matrix at the specified parameters.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)# Estimate model parameters using default initial values and the BFGS methodresult <- estimate_parameters()print(result)param <- c(0.5, 0.1, 0.6, 0.2)hessian <- compute_hessian(param)print(hessian)

Compute the Gradient of the Log-Likelihood Function Generalized odds rate (GOR)

Description

This function computes the gradient of the log-likelihood function for the parametric model (GOR Approach).

Arguments

Value

A numeric vector representing the gradient of the log-likelihood.

Examples

library(cmpp)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)set.seed(1984)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/3)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 3))gradient <- compute_log_f_gradient_rcpp(params)print(gradient)

Compute the Gradient of the Log-Likelihood Function Proportional Odds Model (POM)

Description

This function computes the gradient of the log-likelihood function for the parametric model (POM Approach).

Arguments

Value

A numeric vector representing the gradient of the log-likelihood.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/5)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 2))gradient <- compute_log_f_gradient_rcpp2(params)print(gradient)

Compute the Gradient of the Log-Likelihood Function Proportional Hazards Model (PHM)

Description

This function computes the gradient of the log-likelihood function for the parametric model (PHM Approach).

Arguments

Value

A numeric vector representing the gradient of the log-likelihood.

Examples

library(cmpp)set.seed(1984)  features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 2))gradient <- compute_log_f_gradient_rcpp3(params)print(gradient)

Compute the Hessian Matrix of the Log-Likelihood Function Generalized odds rate (GOR)

Description

This function computes the Hessian matrix of the log-likelihood function for the parametric model (GOR Approach).

Arguments

Value

A numeric matrix representing the Hessian matrix of the log-likelihood.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/7)Initialize(features, x, delta1, delta2, h = 1e-4)params <- rep(0.001, 2 * (ncol(features) + 3))hessian <- compute_log_f_hessian_rcpp(params)print(hessian)

Estimate Model Parameters Using Optimization

Description

This function estimates the parameters of a model by minimizing the negativelog-likelihood function using the specified optimization method. It utilizestheoptim() function in R, with the provided initial parameter values andgradient computation. The optimization method can be specified, with "BFGS" beingthe default.

Usage

estimate_parameters(initial_params = rep(0.01, 4), optimMethod = 'BFGS')

Arguments

Details

Theestimate_parameters function performs parameter estimation by minimizingthe negative log-likelihood function using the chosen optimization method. The functionrequires an initial guess for the parameters (a numeric vector) and will optimize thelog-likelihood function. The optimization also takes into account the gradient of thelog-likelihood function, which is computed using thecompute_grad function. The resultof the optimization is an object of classoptim containing the estimated parameters andother details of the optimization process.

The optimization method can be specified via theoptimMethod argument. The default methodis "BFGS", but any method supported by R'soptim() function (such as "Nelder-Mead", "CG", etc.)can be used.

Value

Anoptim object containing the optimization results, including the estimatedparameters, value of the objective function at the optimum, and other optimization details.

See Also

stats::optim for more details on optimization methods and usage.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)# Estimate model parameters using default initial values and the BFGS methodresult <- estimate_parameters()print(result)

Estimate Parameters for the Generalized odds rate (GOR)

Description

This function estimates the parameters of the Generalized odds rate (GOR) using maximum likelihood estimation.It computes the Hessian matrix, calculates standard errors, and derives p-values for the estimated parameters.The function ensures that the diagonal elements of the covariance matrix are positive for valid variance estimates.

Usage

estimate_parameters_GOR(initial_params, FeaturesNames = NULL)

Arguments

Details

This function performs the following steps:

• Estimates the model parameters using theoptim function with the BFGS method.

• Computes the gradient of the log-likelihood using thecompute_log_f_gradient_rcpp function.

• Computes the Hessian matrix numerically using thehessian function from thenumDeriv package.

• Ensures that the diagonal elements of the covariance matrix are positive to avoid invalid variance estimates.

• Calculates standard errors and p-values for the estimated parameters.

The Generalized odds rate (GOR) is a parametric model for cumulative incidence functions in competing risks analysis.It uses Gompertz distributions to model the failure times for competing events.

Value

A data frame containing:

See Also

stats::optim,compute_log_f_gradient_rcpp,log_f_rcpp,compute_log_f_hessian_rcpp.

Examples

library(cmpp)# Example dataset.seed(371)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/4)# Initialize the Cmpp modelInitialize(features, x, delta1, delta2, h = 1e-5)# Define initial parameter valuesinitial_params <- rep(0.001, 2 * (ncol(features) + 3))# Estimate parameters using the GORresult <- estimate_parameters_GOR(initial_params)print(result)

Estimate Parameters for the Proportional Hazards Model (PHM)

Description

This function estimates the parameters of the Proportional Hazards Model (PHM) using maximum likelihood estimation.It computes the Hessian matrix, calculates standard errors, and derives p-values for the estimated parameters.The function ensures that the diagonal elements of the covariance matrix are positive for valid variance estimates.

Usage

estimate_parameters_PHM(initial_params, FeaturesNames = NULL)

Arguments

Details

This function performs the following steps:

• Estimates the model parameters using theoptim function with the BFGS method.

• Computes the gradient of the log-likelihood using thecompute_log_f_gradient_rcpp3 function.

• Computes the Hessian matrix numerically using thehessian function from thenumDeriv package.

• Ensures that the diagonal elements of the covariance matrix are positive to avoid invalid variance estimates.

• Calculates standard errors and p-values for the estimated parameters.

The Proportional Hazards Model (PHM) is a parametric model for cumulative incidence functions in competing risks analysis.It uses Gompertz distributions to model the failure times for competing events.

Value

A data frame containing:

See Also

stats::optim,compute_log_f_gradient_rcpp3,log_f_rcpp3.

Examples

library(cmpp)set.seed(1984)# Example datafeatures <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)# Initialize the Cmpp modelInitialize(features, x, delta1, delta2, h = 1e-5)# Define initial parameter valuesinitial_params <- rep(0.001, 2 * (ncol(features) + 2))# Estimate parameters using the PHMresult <- estimate_parameters_PHM(initial_params)print(result)

Estimate Parameters for the Proportional Odds Model (POM)

Description

This function estimates the parameters of the Proportional Odds Model (POM) using maximum likelihood estimation.It computes the Hessian matrix, calculates standard errors, and derives p-values for the estimated parameters.The function ensures that the diagonal elements of the covariance matrix are positive for valid variance estimates.

Usage

estimate_parameters_POM(initial_params, FeaturesNames = NULL)

Arguments

Details

This function performs the following steps:

• Estimates the model parameters using theoptim function with the BFGS method.

• Computes the gradient of the log-likelihood using thecompute_log_f_gradient_rcpp2 function.

• Computes the Hessian matrix numerically using thehessian function from thenumDeriv package.

• Ensures that the diagonal elements of the covariance matrix are positive to avoid invalid variance estimates.

• Calculates standard errors and p-values for the estimated parameters.

The Proportional Odds Model (POM) is a parametric model for cumulative incidence functions in competing risks analysis.It uses Gompertz distributions to model the failure times for competing events.

Value

A data frame containing:

See Also

stats::optim,compute_log_f_gradient_rcpp2,log_f_rcpp2.

Examples

library(cmpp)set.seed(1984)# Example datafeatures <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)# Initialize the Cmpp modelInitialize(features, x, delta1, delta2, h = 1e-5)# Define initial parameter valuesinitial_params <- rep(0.001, 2 * (ncol(features) + 2))# Estimate parameters using the POMresult <- estimate_parameters_POM(initial_params)print(result)

Compute the PDF of the Parametric Generalized odds rate (GOR)

Description

This function computes the probability density function (PDF) of the parametric model (GOR Approach).

Arguments

Value

A numeric value representing the PDF.

Examples

library(cmpp)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, (ncol(features) + 3))pdf_value <- f_pdf_rcpp(params, features[1, ], x[3])print(pdf_value)

Compute the PDF of the Parametric Proportional Odds Model (POM)

Description

This function computes the probability density function (PDF) of the parametric model (POM Approach).

Arguments

Value

A numeric value representing the PDF.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/9)Initialize(features, x, delta1, delta2, h = 1e-4)params <- rep(0.001, (ncol(features) + 2))pdf_value <- f_pdf_rcpp2(params, features[1, ], x[3])print(pdf_value)

Compute the PDF of the Parametric Proportional Hazards Model (PHM)

Description

This function computes the probability density function (PDF) of the parametric model (PHM Approach).

Arguments

Value

A numeric value representing the PDF.

Examples

library(cmpp)set.seed(21)features <- matrix(rnorm(300, -1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.0001, (ncol(features) + 2))pdf_value <- f_pdf_rcpp3(params, features[4, ], x[4])print(pdf_value)

Fertility History of Rural Women in Shiraz

Description

This dataset includes fertility history information from a cross-sectional studyof 652 women aged 15–49 years in rural areas of Shiraz, Iran.It was used in the article "A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution"to model the cumulative incidence of live births and competing risks (stillborn fetus or abortion).

Usage

fertility_data

Format

A data frame with 652 rows and the following variables:

id

Unique identifier for each case.

time

Time from marriage to event (live birth, competing event, or censoring).

Event

Event indicator:0 = censored,1 = live birth,2 = stillborn fetus or abortion.

age

Age of the woman at the time of the event or censoring.

Education

Education level:1 = Illiterate,2 = Primary/Secondary,3 = Higher Education.

Note

To view the article, follow this link:https://tbiomed.biomedcentral.com/articles/10.1186/1742-4682-8-43

Source

doi:10.1186/1742-4682-8-43https://doi.org/10.1186/1742-4682-8-43

References

Shayan, Z., Ayatollahi, S. M. T., & Zare, N. (2011)."A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution."Theoretical Biology and Medical Modelling, 8:43.doi:10.1186/1742-4682-8-43

Examples

data(fertility_data)head(fertility_data)

Compute the Log-Likelihood Function Generalized odds rate (GOR)

Description

This function computes the log-likelihood function for the parametric model (GOR Approach).

Arguments

Value

A numeric value representing the log-likelihood.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/4)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 3))log_likelihood <- log_f_rcpp(params)print(log_likelihood)

Compute the Log-Likelihood Function Proportional Odds Model (POM)

Description

This function computes the log-likelihood function for the parametric model (POM Approach).

Arguments

Value

A numeric value representing the log-likelihood.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/8)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 2))log_likelihood <- log_f_rcpp2(params)print(log_likelihood)

Compute the Log-Likelihood Function Proportional Hazards Model (PHM)

Description

This function computes the log-likelihood function for the parametric model (PHM Approach).

Arguments

Value

A numeric value representing the log-likelihood.

Examples

library(cmpp)set.seed(1984)features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)delta1 <- sample(c(0, 1), 100, replace = TRUE)delta2 <- 1 - delta1x <- rexp(100, rate = 1/10)Initialize(features, x, delta1, delta2, h = 1e-5)params <- rep(0.001, 2 * (ncol(features) + 2))log_likelihood <- log_f_rcpp3(params)print(log_likelihood)

Create a matrix of given size filled with a constant value

Description

This function creates an⁠n x m⁠ matrix of typeEigen::MatrixXd, where eachelement is set to the specified constant value. This is useful for generatingmatrices with uniform values for testing, initialization, or other purposes incomputational tasks where a matrix filled with a constant is needed.

Usage

makeMat(n, m, value)

Arguments

Details

ThemakeMat function generates a matrix with the given dimensions⁠n x m⁠where all elements are initialized to the same constant value. It is usefulin scenarios where a specific value needs to be assigned to all elements of thematrix, for example in machine learning algorithms, matrix manipulations, or tests.

Value

A numeric matrix of dimensions⁠n x m⁠ filled with the specified value.

Examples

library(cmpp)# Create a 3x3 matrix filled with 5mat <- makeMat(3, 3, 5)print(mat)

Create Dummy Variables

Description

This function creates dummy variables for specified features in a dataset.

Usage

make_Dummy(Data = dat, features = c("sex", "cause_burn"), reff = "first")

Arguments

Value

A list containing two elements:

Examples

dat <- data.frame(sex = c('M', 'F', 'M'), cause_burn = c('A', 'B', 'A'))result <- make_Dummy(Data = dat, features = c('sex', 'cause_burn'), reff = "first")print(result$New_Data)

Compute the PDF of the Gompertz Distribution

Description

Calculates the probability density function (PDF) of the Gompertz distributionfor given input values and parameters.

Usage

pdf_gomp(x, alpha, beta)

Arguments

Details

The PDF provides the relative likelihood of a failure or event occurring at specific time points.Ensure thatalpha andbeta are positive for meaningful results.

Value

A numeric vector of the PDF values for each input inx.

Examples

library(cmpp)data("fertility_data")Nam <- names(fertility_data)fertility_data$Educationdatt <- make_Dummy(fertility_data, features = c("Education"))datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2`datt['Higher_Education'] <- datt$`Education:3`datt$`Education:2` <- datt$`Education:3` <- NULLdatt2 <- make_Dummy(datt, features = 'Event')$New_Datad1 <- datt2$`Event:2`d2 <- datt2$`Event:3`feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |>    data.matrix()timee <- datt2[['time']]Initialize(feat, timee, d1, d2, 1e-10)x <- c(1, 2, 3)alpha <- 0.5beta <- 0.1lapply(x, pdf_gomp, alpha = alpha, beta = beta) |> unlist()