A general approach for cure models in survival analysis

Valentin Patilea and Ingrid Van Keilegom
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Ingrid Van Keilegom: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2020042, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: 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 : the one of cured subjects, and the one of ‘susceptible’ subjects. In this paper 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 (like e.g. a logistic model), while the conditional survival function of the uncured subjects is unspecified. The approach is based on an inversion which allows to write the survival function as a function of the distribution of the observable random 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 weak 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 finite sample simulations. Finally, we apply the new model and estimation procedure on two medical data sets.

Keywords: Asymptotic normality; bootstrap; kernel smoothing; logistic regression; mixture cure model; semiparametric model (search for similar items in EconPapers)
Date: 2020-01-01
Note: In: Annals of Statistics, Vol. 48, no. 4, p. 2323-2346 (2020)
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020042

DOI: 10.1214/19-AOS1889

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