Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up

TL;DR

This paper introduces new nonparametric estimators for conditional cure models in heavy-tailed distributions with insufficient follow-up, utilizing extreme value theory to address gaps in current survival analysis methods.

Contribution

It proposes novel extrapolation-based estimators for cure rate and survival functions under challenging data conditions, with proven asymptotic properties and practical validation.

Findings

Estimators are asymptotically normal.

Simulation studies show good small-sample performance.

Application to colon cancer data demonstrates practical utility.

Abstract

When analyzing time-to-event data, it often happens that some subjects do not experience the event of interest. Survival models that take this feature into account (called `cure models') have been developed in the presence of covariates. However, the current literature on nonparametric cure models with covariates cannot be applied when the follow-up is insufficient, i.e., when the right endpoint of the support of the censoring time is strictly smaller than that of the survival time of the susceptible subjects. In this paper we attempt to fill this gap in the literature by proposing new estimators of the conditional cure rate and the conditional survival function using extrapolation techniques coming from extreme value theory. We establish the asymptotic normality of the proposed estimators, and show how the estimators work for small samples by means of a simulation study. We also illustrate their practical applicability through the analysis of data on the survival of colon cancer patients.