Learn R Programming

cmpp: Parametric Modeling for Competing Risks

Overview

cmpp is an R package designed to facilitate parametric modeling and inference for cumulative incidence functions (CIFs) in competing risks scenarios. The package implements methods discussed in seminal works by Jeong and Fine (2006, 2007), with efficient computation powered by Rcpp for high-performance applications.

Key Features

  • Parametric Modeling:
    • Direct parametric modeling of cumulative incidence functions using Gompertz and Weibull distributions.
    • Support for Generalized odds rates (GOR), Proportional Odds Models (POM), and Proportional Hazards Models (PHM).
  • Regression Models:
    • Proportional hazards and proportional odds models.
    • Flexible generalized odds rate models.
    • Covariate-adjusted CIF estimation.
  • Likelihood-Based Inference:
    • Full maximum likelihood estimation.
    • Delta method for confidence intervals and variance estimation.
  • Goodness-of-Fit Tests:
    • Evaluation of proportional hazards or proportional odds assumptions.
  • Visualization:
    • Plot cumulative incidence functions (CIFs) with confidence intervals.
    • Adjust CIFs based on covariate values.
  • High-Performance Computation:
    • Fast computation using Rcpp and Eigen integration.

Background

Competing risks occur when multiple types of events prevent the observation of a particular event of interest. Traditional survival analysis often misrepresents such data, as it fails to account for competing risks. This package provides parametric methods for cumulative incidence functions (CIFs), offering a more direct and interpretable analysis than traditional cause-specific hazard models.

Implemented Methods

  1. Gompertz-Based Cumulative Incidence Models:

    • Designed for scenarios with improper distributions (plateau in the cumulative incidence curve).
    • Applicable to long-term survival studies, such as breast cancer clinical trials.

  2. Regression Models:

    • Proportional hazards and proportional odds models.
    • Flexible generalized odds rate models.
    • Covariate-adjusted CIF estimation.

  3. Likelihood-Based Inference:

    • Full maximum likelihood estimation.
    • Delta method for confidence intervals and variance estimation.

  4. Visualization:

    • Plot CIFs for competing risks with confidence intervals.
    • Adjust CIFs based on specific covariate values.

Installation

To install the package:

# Install from GitHub
devtools::install_github("stats9/cmpp")

# for windows 
## after download cmpp zip file 
install.packages('cmpp_0.0.1.zip', repos = NULL, type = "win-binary")

# for linux or mac
## after download cmpp tar.gz file
install.packages('cmpp_0.0.1.tar.gz', repos = NULL, type = "source")

Usage

Initialize the Cmpp Model

library(cmpp)
# Example data
features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)
delta1 <- sample(c(0, 1), 100, replace = TRUE)
delta2 <- 1 - delta1
time <- rexp(100, rate = 1/10)

# Initialize the Cmpp model
Initialize(features, time, delta1, delta2, h = 1e-5)

Estimate Parameters

 library(cmpp)
 data("fertility_data")
 Nam <- names(fertility_data)
 fertility_data$Education
 datt <- make_Dummy(fertility_data, features = c("Education"))
 datt <- datt$New_Data 
 datt['Primary_Secondary'] <- datt$`Education:2`
 datt['Higher_Education'] <- datt$`Education:3`
 datt$`Education:2` <- datt$`Education:3` <- NULL
 datt2 <- make_Dummy(datt, features = 'Event')$New_Data
 d1 <- datt2$`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 parameters using the Generalized odds rate (GOR)
initial_params <- rep(0.001, 2 * (ncol(features) + 3))
initial_params2 <- rep(0.001, 2 * (ncol(features) + 2))
result <- estimate_parameters_GOR(initial_params)
print(result)

# Estimate parameters using the Proportional Odds Model (POM)
result_pom <- estimate_parameters_POM(initial_params2)
print(result_pom)

# Estimate parameters using the Proportional Hazards Model (PHM)
result_phm <- estimate_parameters_PHM(initial_params2)
print(result_phm)

Compute Cumulative Incidence Functions (CIFs)

 library(cmpp)
 data("fertility_data")
 Nam <- names(fertility_data)
 fertility_data$Education
 datt <- make_Dummy(fertility_data, features = c("Education"))
 datt <- datt$New_Data 
 datt['Primary_Secondary'] <- datt$`Education:2`
 datt['Higher_Education'] <- datt$`Education:3`
 datt$`Education:2` <- datt$`Education:3` <- NULL
 datt2 <- make_Dummy(datt, features = 'Event')$New_Data
 d1 <- datt2$`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)

# Compute CIFs for competing risks
cif_results <- CIF_res1(rep(0.001, 4))
print(cif_results)

# Plot CIFs with confidence intervals
Res <- CIF_Figs(rep(0.001, 4), timee)
print(Res)

Fine-Gray Model for Competing Risks

 library(cmpp)
 data("fertility_data")
 Nam <- names(fertility_data)
 fertility_data$Education
 datt <- make_Dummy(fertility_data, features = c("Education"))
 datt <- datt$New_Data 
 datt['Primary_Secondary'] <- datt$`Education:2`
 datt['Higher_Education'] <- datt$`Education:3`
 datt$`Education:2` <- datt$`Education:3` <- NULL
 datt2 <- make_Dummy(datt, features = 'Event')$New_Data
 d1 <- datt2$`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)

# Fit a Fine-Gray model
result_fg <- FineGray_Model(
  CovarNames = c("Covar1", "Covar2", "Covar3"),
  Failcode = 1,
  RiskNames = c("Event1", "Event2")
)
print(result_fg$Results)  # Summary of the Fine-Gray model
print(result_fg$Plot)     # Plot of the CIFs

Adjusted CIFs Based on Covariates

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

Bootstrap Variance Estimation

 library(cmpp)
 data("fertility_data")
 Nam <- names(fertility_data)
 fertility_data$Education
 datt <- make_Dummy(fertility_data, features = c("Education"))
 datt <- datt$New_Data 
 datt['Primary_Secondary'] <- datt$`Education:2`
 datt['Higher_Education'] <- datt$`Education:3`
 datt$`Education:2` <- datt$`Education:3` <- NULL
 datt2 <- make_Dummy(datt, features = 'Event')$New_Data
 d1 <- datt2$`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)
datt <- GetData()

# Estimate variance of parameters using bootstrap
results <- bootstrap_variance(datt$features, datt$timee, 
    datt$delta1, datt$delta2, rep(0.001, 4), n_bootstrap = 500)
print(results$variances)
print(results$bootstrap_estimates)

Example Workflow

library(cmpp)

# Load example data
features <- matrix(rnorm(300, 1, 2), nrow = 100, ncol = 3)
delta1 <- sample(c(0, 1), 100, replace = TRUE)
delta2 <- 1 - delta1
time <- rexp(100, rate = 1/10)

# Initialize the Cmpp model
Initialize(features, time, delta1, delta2, h = 1e-5)

# Estimate parameters
initial_params <- rep(0.001, 2 * (ncol(features) + 3))
params <- estimate_parameters_GOR(initial_params)
print(params)

# Compute CIFs
cif_results <- CIF_res1(rep(0.001, 4))
print(cif_results)

# Plot CIFs
Res <- CIF_Figs(rep(0.01, 4), time)
print(Res)

Example Of Data Inside cmpp package

 library(cmpp)
 data("fertility_data")
 Nam <- names(fertility_data)
 fertility_data$Education
 datt <- make_Dummy(fertility_data, features = c("Education"))
 datt <- datt$New_Data 
 datt['Primary_Secondary'] <- datt$`Education:2`
 datt['Higher_Education'] <- datt$`Education:3`
 datt$`Education:2` <- datt$`Education:3` <- NULL
 datt2 <- make_Dummy(datt, features = 'Event')$New_Data
 d1 <- datt2$`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 matrix
 print(data$timee)      # Failure times
 print(data$delta1)    # Indicator for the first competing event
 print(data$delta2)    # Indicator for the second competing event
 result <- Cmpp_CIF(
   featureID = c(1, 2),
   featureValue = c(0.5, 1.2),
   RiskNames = c("Event1", "Event2"),
   TypeMethod = "GOR",
   predTime = seq(0, 10, by = 0.5)
 )
 print(result$Plot$Plot_InputModel)  # Plot for the specified model
 print(result$Plot$PlotAdjusted_AllModels)  # Adjusted CIFs for all models
 print(result$CIF$CIFAdjusted)  # Adjusted CIF values

References

  1. Jeong, J.-H., & Fine, J. (2006). Direct parametric inference for the cumulative incidence function. Applied Statistics, 55(2), 187-200.
  2. Jeong, J.-H., & Fine, J. (2007). Parametric regression on cumulative incidence function. Biostatistics, 8(2), 184-196.

Copy Link

Version

Install

install.packages('cmpp')

Monthly Downloads

523

Version

0.0.1

License

GPL (>= 2)

Maintainer

Habib Ezzatabadipour

Last Published

May 2nd, 2025

Functions in cmpp (0.0.1)

compute_log_f_gradient_rcpp2

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

Compute the CDF of the Gompertz Distribution
compute_grad

Compute the Numerical Gradient of the Log-Likelihood
compute_log_f_gradient_rcpp3

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

Direct Parametric Inference for the Cumulative Incidence Function in Competing Risks
estimate_parameters_POM

Estimate Parameters for the Proportional Odds Model (POM)
f_pdf_rcpp2

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

Create Dummy Variables
f_pdf_rcpp3

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

Fertility History of Rural Women in Shiraz
log_f_rcpp3

Compute the Log-Likelihood Function Proportional Hazards Model (PHM)
log_f_rcpp2

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

Create a matrix of given size filled with a constant value
log_f_rcpp

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

Compute the PDF of the Gompertz Distribution
estimate_parameters_GOR

Estimate Parameters for the Generalized odds rate (GOR)
estimate_parameters_PHM

Estimate Parameters for the Proportional Hazards Model (PHM)
f_pdf_rcpp

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

Estimate Model Parameters Using Optimization
LogLike1

Compute the Log-Likelihood for the Model
compute_log_f_hessian_rcpp

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

Plot Cumulative Incidence Functions (CIF) with Confidence Intervals
F_cdf_rcpp2

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

Clean up memory by deleting the pointer to the Cmpp instance
FineGray_Model

Fine-Gray Model for Competing Risks Data
F_cdf_rcpp

Compute the CDF of the Parametric Generalized odds rate (GOR)
CIF_res1

Compute Cumulative Incidence Function (CIF) Results
F_cdf_rcpp3

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

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

Get Dimensions of the Cmpp Object
GetData

Retrieve Initialized Data from the Cmpp Model
Initialize

Initialize Data for the Cmpp Model
compute_hessian

Compute the Hessian Matrix of the Log-Likelihood
compute_log_f_gradient_rcpp

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

Estimate Variance of Parameters Using Bootstrap Method