A simple nonparametric estimator of the bivariate survival function under univariate censoring

Abstract

In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of the censoring time. The use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve. The estimator is strongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated covariance function. Numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes. Applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied.