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In survival analysis it often happens that some subjects under study do notexperience the event of interest; they are considered to be `cured'. Thepopulation is thus a mixture of two subpopulations: the one of cured subjects,and the one of `susceptible' subjects. When covariates are present, a so-calledmixture cure model can be used to model the conditional survival function ofthe population. It depends on two components: the probability of being curedand the conditional survival function of the susceptible subjects. In thispaper we propose a novel approach to estimate a mixture cure model when thedata are subject to random right censoring. We work with a parametric model forthe cure proportion (like e.g. a logistic model), while the conditionalsurvival function of the uncured subjects is unspecified. The approach is basedon an inversion which allows to write the survival function as a function ofthe distribution of the observable random variables. This leads to a verygeneral class of models, which allows a flexible and rich modeling of theconditional survival function. We show the identifiability of the proposedmodel, as well as the weak consistency and the asymptotic normality of themodel parameters. We also consider in more detail the case where kernelestimators are used for the nonparametric part of the model. The new estimatorsare compared with the estimators from a Cox mixture cure model via finitesample simulations. Finally, we apply the new model and estimation procedure ontwo medical data sets.

A General Approach for Cure Models in Survival Analysis