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Biometrika 1999 86(1):59-70; doi:10.1093/biomet/86.1.59
© 1999 by Biometrika Trust
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Nonparametric estimation of the gap time distribution for serial events with censored data

DY LinA1, W SunA2 and Z YingA3

A1 Department of Biostatistics, Box 357232, University of Washington, Seattle, Washington 98195, USA danyu@biostat.washington.edu A2 Schering-Plough Research Institute, 2015 Galloping Hill Road, Kenilworth, NJ 07033, USA wei.sun@spcorp.com A3 Department of Statistics, Hill Center, Busch Campus, Rutgers University, Piscataway, NJ 08855, USA zyging@stat.rutgers.edu

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.

Keywords:Bivariate distribution; Correlated failure times; Dependent censoring; Kaplan-Meier estimator; Multiple events; Multivariate failure time; Recurrent events.


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