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August 2020 A general approach for cure models in survival analysis
Valentin Patilea, Ingrid Van Keilegom
Ann. Statist. 48(4): 2323-2346 (August 2020). DOI: 10.1214/19-AOS1889


In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be “cured.” The population is thus a mixture of two subpopulations, one of cured subjects and one of “susceptible” subjects. We propose a novel approach to estimate a mixture cure model when covariates are present and the lifetime is subject to random right censoring. We work with a parametric model for the cure proportion, while the conditional survival function of the uncured subjects is unspecified. The approach is based on an inversion which allows us to write the survival function as a function of the distribution of the observable variables. This leads to a very general class of models which allows a flexible and rich modeling of the conditional survival function. We show the identifiability of the proposed model as well as the consistency and the asymptotic normality of the model parameters. We also consider in more detail the case where kernel estimators are used for the nonparametric part of the model. The new estimators are compared with the estimators from a Cox mixture cure model via simulations. Finally, we apply the new model on a medical data set.


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Valentin Patilea. Ingrid Van Keilegom. "A general approach for cure models in survival analysis." Ann. Statist. 48 (4) 2323 - 2346, August 2020.


Received: 1 December 2018; Revised: 1 May 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134797
Digital Object Identifier: 10.1214/19-AOS1889

Primary: 62N01 , 62N02
Secondary: 62F12 , 62G05

Keywords: asymptotic normality , bootstrap , kernel smoothing , logistic regression , mixture cure model , Semiparametric model

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.48 • No. 4 • August 2020
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