Nonparametric estimation of the gap time distributions for serial events with censored data

In many follow-up studies, each subject can potentially experience a series of events, which may be repetitions of essentially the same event or may b e events of entirely different natures. This paper provides a simple nonpar ametric estimator for the multivariate :distribution function of the gap ti mes between successive events when the follow-up time is subject to right c ensoring. The estimator is consistent and, upon proper normalisation, conve rges weakly to a zero-mean Gaussian process with an easily estimated covari ance function. Numerical studies demonstrate that both the distribution fun ction estimator and its covariance function estimator perform well for prac tical sample sizes. An application to a colon cancer study is presented.