Estimation of the extreme survival probabilities from censored data

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 does 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 construction. 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 estimation of the survival probabilities in the mid and long term. We perform numerical simulations which confirm the advantage of the proposed method.