A Comparison od a New Piecewise Exponential Estimator with Existing Nonparametric Estimators of a Survival Function: A Simulation Study

• Activity Number: 627
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ganesh Malla*+
• Keywords: Survival function ; Piecewise exponential estimator ; Kaplan-Meier estimator ; Empirical Bayes type estimator ; Censoring

Abstract

This paper discusses a new piecewise exponential estimator (NPEE) of a survival function (SF) for censored data, which is continuous on [0, 1). For comparison purposes, we consider the Kaplan-Meier estimator (KME) and the empirical Bayes type estimator (EBE) derived by Rai et al.(1980). The EBE estimate beyond the last observation is determined solely by the prior. The NPEE retains the spirit of the KME and provides an exponential tail with a hazard rate deter mined by a novel nonparametric consideration. The NPEE has been compared with the KME and EBE for small sample sizes by simulation. The simulation comparisons are by the measures of bias and three norms, (L1; L2; and L-norm); for three levels of censoring, (15%; 50%; 75%), and two sample sizes (10 and 30). Generally speaking, the NPEE, which is asymptotically equivalent to the KME (Malla and Mukerjee (2010)), seems to be better than the KME, especially when we have heavy censoring and/or small sample sizes, and is at least as good as the EBE.