Hazard-Based Nonparametric Survivor Function Estimation

Abstract

SummaryA representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables. This leads to a class of nonparametric survivor function estimators that avoid negative mass. The transformation from hazard function to survivor function is weakly continuous and compact differentiable, so that such properties as strong consistency, weak convergence to a Gaussian process and bootstrap applicability for a hazard function estimator are inherited by the corresponding survivor function estimator. The set of point mass assignments for a survivor function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators. Special cases arise from a simple empirical hazard rate estimator, and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips. The latter is shown to equal van der Laan's repaired nonparametric maximum likelihood estimator, for which a Greenwood-like variance estimator is given. Simulation studies are presented to compare the moderate sample performance of various nonparametric survivor function estimators.