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

Understanding the relationship between covariates and clinical outcomes is a fundamental goal in biostatistics, particularly in the context of survival analysis and cure models. Traditional methods often lack the flexibility to assess complex dependencies or to evaluate covariate effects in a nonparametric manner. Moreover, there is a growing need for computationally efficient tools that integrate hypothesis testing and model diagnostics within the framework of long-term survival and cure probability estimation.

We present a comprehensive R package that implements both novel and existing methods across three key areas: dependency analysis, nonparametric hypothesis testing in cure models, and goodness-of-fit testing for the cure rate in mixture cure models. For dependency analysis, we include functions based on martingale difference correlation and divergence to assess covariate effects on the conditional mean. To test the significance of covariates on cure probability, we propose a nonparametric framework comprising four approaches, three based on martingale difference correlation and one based on L₂ distance. An extended version of the test also allows for adjustment by a second covariate. For model checking, we introduce the goft() function for analytical goodness-of-fit testing and plotCure() for visual comparison of parametric and nonparametric cure probability estimates under logit, probit, and cloglog link functions.

The proposed methods showed a good performance in both simulated and real-world datasets. Martingale-based dependency measures effectively identified covariates influencing the conditional mean, while the nonparametric tests accurately detected covariate effects on cure probability. The extended test enhanced interpretability in multivariable settings. Goodness-of-fit analyses confirmed that the proposed tools correctly identified appropriate link functions, with visual outputs from plotCure() closely matching analytical results from goft(). Overall, the package enables accurate and efficient inference in the analysis of cure models.