A Monte Carlo Simulation Comparison of Some Nonparametric Survival Functions for Incomplete Data

Music City Center 

This article presents a comparative analysis of a novel piecewise exponential estimator (NPEE) for censored data against three widely recognized estimators: the Kaplan-Meier estimator (KME), the Nelson estimator (NE), and an empirical Bayes type estimator (EBE). The NPEE, characterized by continuity on [0, ∞) and an exponential tail with a hazard rate derived through a novel nonparametric approach, retains the core advantages of the KME while addressing limitations inherent in the other estimators. These shortcomings restrict the broader applicability of the KME, NE, and EBE. To evaluate model performance, a simulation study was conducted using absolute bias and relative efficiency as quality metrics. Comparisons were performed across three levels of censoring, two sample sizes, and various quantiles. Results demonstrate that the NPEE, which is asymptotically equivalent to the KME, outperforms the other estimators for finite sample sizes, providing a robust alternative in survival function estimation.

survival function

censored data

piecewise exponential estimator

Kaplan-Meier estimator

simulation study

nonparametric methods 

Isolated Statisticians