A Chi-Squared Goodness of Fit Test for Recurrent Event Data

Goodness of fit of the distribution function governing the time to occurrence of a recurrent event is considered. We develop a chi-squared type of test (henceforward called R test) based on a nonparametric maximum likelihood estimator (NPMLE) of the inter-event time distribution for recurrent events. The test compares a parametric null to the NPMLE over k partitions of a calendar time over the monitoring period. We investigate small sample and asymptotic properties of four variants of the test as well as power analysis against a sequence of Pitman’s alternatives. The conclusion that transpires from the finite sample simulation study is that significant level is achieved when the right-censoring random variable is not ignored and k ≥ 6. We consider and discuss simulation results for Exponential, Weibull and Lognormal lifetime models. We apply the R test to a real-life recurrent event data.