Long-Term Survival Probabilities and Kaplan-Meier Estimator

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Jean-Marie TRICOT*+ and Ion Grama and Jean-Francois Petiot
• Companies: University of South Brittany and University of South Brittany and University of South Brittany
• Keywords: Survival analysis ; Censored data ; Survival probabilities ; Prediction ; Adaptive estimation

Abstract

The nonparametric Kaplan-Meier estimator is a standard tool for estimating a survival time distribution in a right censoring schema. Our goal is to analyze this estimator in the long term, particularly when the censoring rate is high. We combine the Kaplan-Meier estimator and a parametric-based model into one construction which we call semiparametric Kaplan-Meier estimator. Our estimator incorporates a threshold $t$ in such a way that the survival function is estimated by the Kaplan-Meier estimator on $[0,t]$ and by the exponential distribution on $(t,\infty ).$ Our main result is that with an appropriate choice of the threshold $t$ such an estimate is consistent. Rates of convergence are obtained which in particular cases turn to be nearly optimal. A data driven multiple testing procedure for choosing the threshold $t$ is proposed. As byproduct it provides a goodness-of-fit test for the parametric-based part of the model. Our numerical simulations show that the proposed technique improves Kaplan-Meier's in the long as well as in the mid term.