On the performance of some non-parametric estimators of the conditional survival function with interval-censored data

Simple nonparametric estimators of the conditional distribution of a response variable given a continuous covariate are often useful in survival analysis. Since a few nonparametric estimation options are available, a comparison of the performance of these options may be of value to determine which approach to use in a given application. In this note, we compare various nonparametric estimators of the conditional survival function when the response is subject to interval- and right-censoring. The estimators considered are a generalization of Turnbull's estimator proposed by Dehghan and Duchesne (2011) and two nonparametric estimators for complete or right-censored data used in conjunction with imputation methods, namely the Nadaraya-Watson and generalized Kaplan-Meier estimators. We study the finite sample integrated mean squared error properties of all these estimators by simulation and compare them to a semi-parametric estimator. We propose a rule-of-thumb based on simple sample summary statistics to choose the most appropriate among these estimators in practice.