Nonparametric tests for the gap time distributions of serial events based on censored data

This article deals with the problem of comparing two populations with respect to the distribution of the gap time between two successive events when each subject can experience a series of events and when the event times are potentially right censored. Several families of nonparametric tests are developed, all of which allow arbitrary distributions and dependence structures for the serial events. The asymptotic and small-sample properties of the proposed tests are investigated. An illustration with data taken from a colon cancer study is provided. The related problem of testing the independence of two successive gap times is also studied.