Smooth Inference for Survival Functions with Arbitrarily Censored Data

We propose a new procedure for estimating the survival function of a time-to-event random variable under arbitrary patterns of censoring. Under mild smoothness assumptions, this procedure allows a unified approach to handling different kinds of censoring, while in many cases increasing efficiency. Our approach uses a seminonparametric (SNP) density to represent the density of failure times. The SNP has a flexible "parametric" representation that admits a convenient expression for the likelihood and allows it to capture arbitrary shapes through choice of a tuning parameter, which may be carried out based on standard selection criteria such as AIC and BIC.We present simulation studies to validate our proposed methods. Using right-censored and interval-censored data from popular parametric models, we compare survival function estimators based on our SNP density approach to that of the corresponding nonparametric estimator. We also develop a test statistic where each survival curve is estimated via our SNP density approach, and demonstrate that it has reliable operating characteristics and can result in increased power relative to nonparametric tests. The new methods are applied to a number of data sets from biomedical studies.