Single-index mixture cure model under monotonicity constraints

TL;DR

This paper introduces a monotone single-index mixture cure model for survival data with a cure fraction, offering a flexible alternative to traditional parametric models and demonstrating improved performance under certain conditions.

Contribution

It proposes a novel monotone single-index model for cure probability, along with a profile likelihood estimation method utilizing isotonic regression, enhancing model flexibility and interpretability.

Findings

The estimator is consistent under monotonicity.

Simulation shows improved performance over non-constrained models.

Application to melanoma data demonstrates practical utility.

Abstract

We consider survival data in the presence of a cure fraction, meaning that some subjects will never experience the event of interest. We assume a mixture cure model consisting of two sub-models: one for the probability of being uncured (incidence) and one for the survival of the uncured subjects (latency). Various approaches, ranging from parametric to nonparametric, have been used to model the effect of covariates on the incidence, with the logistic model being the most common one. We propose a monotone single-index model for the incidence and introduce a new estimation method that is based on the profile maximum likelihood approach and techniques from isotonic regression. The monotone single-index structure relaxes the parametric logistic assumption while maintaining interpretability of the regression coefficients. We investigate the consistency of the proposed estimator and show through a simulation study that, when the monotonicity assumption is satisfied, it performs better compared to the non-constrained single-index/Cox mixture cure model. To illustrate its practical use, we use the new method to study melanoma cancer survival data.