On an extension of the promotion time cure model

TL;DR

This paper introduces an extended promotion time cure model that simplifies estimation and variance calculation for censored survival data with cured subjects, demonstrated through simulations and a breast cancer case study.

Contribution

It proposes a new model inspired by the Cox model, enabling straightforward estimation and variance computation for cure rate data.

Findings

Estimation procedure is simpler and computationally efficient.

Asymptotic properties of estimators are established.

Model performs well in simulations and real data application.

Abstract

We consider the problem of estimating the distribution of time-to-event data that are subject to censoring and for which the event of interest might never occur, i.e., some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model \citep{yakovlev1996}, which adapts the Cox model to the presence of cured subjects. Estimating the conditional distribution results in a complicated constrained optimization problem, and inference is difficult as no closed-formula for the variance is available. We propose a new model, inspired by the Cox model, that leads to a simple estimation procedure and that presents a closed formula for the variance. We derive some asymptotic properties of the estimators and we show the practical behaviour of our procedure by means of simulations. We also apply our model and estimation method to a breast cancer data set.