Estimation of the extreme survival probabilities from censored data

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 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 t 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- t 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.

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. Estimation of the extreme survival probabilities from censored data. BULETINUL ACADEMIEI DE S TIINT E A REPUBLICII MOLDOVA. MATEMATICA, 2014, 74 (1), pp.33-62. ⟨hal-01015579⟩