Résumé 150 :

Cure regression models are a special topic in lifetime analysis. Such models are designed to take into account situations where a proportion of subjects will never experience the event under study. In such a case the lifetime is considered infinite. For instance, medical studies could reveal a proportion of patients for whom the disease under surveillance will never recur, and these patients could be considered as cured. A well studied topic in Labor Economics is the time to get a new job after a permanent layoff. It is commonly accepted that a proportion of the labor force will withdraw and never get a new job. The crucial issue in cure models is to estimate the conditional probability of an infinite lifetime. In most of the applications the analysis is made more difficult by the presence of a finite random right censorship. Several cure regression models have been considered in the literature and most of them consider a logistic regression for the conditional probability of an infinite lifetime. To our best knowledge, no goodness-of-fit procedure has been proposed yet. The difficulty comes from the fact that it is impossible to know whether a censored observation has a finite or infinite lifetime. In this contribution we propose a kernel smoothing based model check procedure that is able to detect general (nonparametric) alternatives. The assumptions on the lifetime of interest and the censorship are very general and the critical values are given by a standard normal distribution.