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.

► Three nonparametric estimators of the conditional survival function are compared.
► All three estimators can handle an interval-censored response variable.
► A rule-of-thumb is provided to help decide which estimator to choose when.
► Generally the generalized Turnbull estimator exhibits better finite sample properties.