Long Term Survival Probabilities and Kaplan-Meier Estimator
Résumé
The Kaplan-Meier nonparametric estimator has become a standard tool for estimating a survival time distribution in a right censoring schema. However, if the censoring rate is high, this estimator do not provide a reliable estimation of the extreme survival probabilities. In this paper we propose to combine the nonparametric Kaplan-Meier estimator and a parametric-based model into one con- struction. The idea is to fit the tail of the survival function with a parametric model while for the remaining to use the Kaplan-Meier estimator. A procedure for the automatic choice of the location of the tail based on a goodness-of-fit test is proposed. This technique allows us to improve the es- timation of the survival probabilities in the mid and long term. We perform numerical simulations which confirm the advantage of the proposed method.
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