Nonparametric estimation of the gap time distribution 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 be events of entirely different natures. This paper provides a simple nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow-up time is subject to right censoring. The estimator is consistent and, upon proper normalisation, converges weakly to a zero-mean Gaussian process with an easily estimated covariance function. Numerical studies demonstrate that both the distribution function estimator and its covariance function estimator perform well for practical sample sizes. An application to a colon cancer study is presented.