Non-parametric cure rate estimation under insufficient follow-up using extremes

TL;DR

This paper introduces a novel non-parametric estimator for the cure rate in survival analysis that accounts for insufficient follow-up by leveraging extreme value theory, improving accuracy over existing methods.

Contribution

It proposes a new cure rate estimator using extreme value extrapolation, addressing the challenge of insufficient follow-up in survival data.

Findings

Estimator is asymptotically normal.

Performs well in small sample simulations.

Applied successfully to breast cancer survival data.

Abstract

An important research topic in survival analysis is related to the modeling and estimation of the cure rate, i.e. the proportion of subjects that will never experience the event of interest. However, most estimation methods proposed so far in the literature do not handle the case of insufficient follow-up, that is when the right end point of the support of the censoring time is strictly less than that of the survival time of the susceptible subjects, and consequently these estimators overestimate the cure rate in that case. We fill this gap by proposing a new estimator of the cure rate that makes use of extrapolation techniques from the area of extreme value theory. We establish the asymptotic normality of the proposed estimator, and show how the estimator works for small samples by means of a simulation study. We also illustrate its practical applicability through the analysis of data on the survival of breast cancer patients.