Long Term Survival Probabilities and Kaplan-Meier Estimator

Ion Grama (1) , Jean-Marie Tricot (1) , Jean-François Petiot (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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.

Mots clés: Adaptive estimation; censored data; model selection; prediction; survival analysis; survival probabilities

Domaines: Applications [stat.AP]

Ion Grama, Jean-Marie Tricot, Jean-François Petiot. Long Term Survival Probabilities and Kaplan-Meier Estimator. 2013. ⟨hal-00918822⟩