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MDCcure: An R package for martingale difference correlation and hypothesis testing in mixture cure models.

Blanca E Monroy-Castillo¹, M Amalia Jácome², Ricardo Cao¹

¹MODES Research group, CITIC (Center for Information and Communications Technology Research), Department of Mathematics, Faculty of Informatics, Universidade da Coruña, 15071 Campus de Elviña s/n, A Coruña, Spain.

Computer Methods and Programs in Biomedicine

|October 28, 2025

Summary

This summary is machine-generated.

This study introduces an R package for advanced cure model analysis, offering new nonparametric methods for covariate effects and model diagnostics. The package provides efficient tools for biostatisticians to improve survival analysis and cure probability estimation.

Keywords:

Cure probability Fast optimization Goodness of fit test Martingale difference correlation Nonparametric test

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Area of Science:

Biostatistics
Survival Analysis
Computational Statistics

Background:

Assessing covariate-clinical outcome relationships is crucial in biostatistics, especially for survival and cure models.
Traditional methods struggle with complex dependencies and nonparametric evaluation of covariate effects.
There's a need for efficient computational tools for hypothesis testing and diagnostics in cure models.

Purpose of the Study:

To present a comprehensive R package for advanced biostatistical analysis of cure models.
To implement novel and existing methods for dependency analysis, nonparametric hypothesis testing, and goodness-of-fit testing.
To enhance the estimation of long-term survival and cure probabilities.

Main Methods:

Developed an R package with functions for martingale difference correlation and divergence to analyze covariate effects on conditional means.
Proposed a nonparametric framework with four approaches (three martingale-based, one L2 distance-based) for testing covariate significance on cure probability.
Included goodness-of-fit testing (goft()) and visual comparison tools (plotCure()) for cure rate models.

Main Results:

The R package demonstrated strong performance in simulations and real-world data analysis.
Martingale-based measures effectively identified covariates impacting conditional means.
Nonparametric tests accurately detected covariate effects on cure probability, with enhanced interpretability in multivariable settings.

Conclusions:

The R package provides accurate and efficient inference tools for cure model analysis.
The implemented methods improve the assessment of covariate relationships and model fit.
This facilitates better understanding and estimation of long-term survival and cure probabilities.