Estimation of Survival Curves from Dependent Censorship Models via a Generalized Self-Consistent Property with Nonparametric Bayesian Estimation Application

Abstract

This article presents a family of estimators of the survival function based on right-censored observations which admit the possibility that the censoring variables may not be independent of the true failure variables. This family is obtained by generalizing the self-consistent property (Efron, 1967) of the product limit estimator (Kaplan and Meier, 1958). By assuming a Dirichlet process prior distribution of the observable random vectors, nonparametric Bayesian estimators of the survival curve-which is also a member of this family--are derived under a special loss function. These nonparametric Bayesian estimators generalize results of Susarla and Van Ryzin (1976), who impose a Dirichlet process prior on the failure survival function without considering any prior distribution of the censoring variables. Large sample properties of this family of nonparametric Bayesian estimators are also derived.