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

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Journal of Statistical Theory and Applications, Vol: 11, Issue: 2, Page: 97-119

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Adekpedjou, Akim; Zamba, K. D.
Gowas Publishers
Recurrent Events; Gaussian Process; Pitman's Alternatives; Goodness of Fit; Recurrent Events; Gaussian Process; Pitman's Alternatives; Goodness of Fit; Mathematics; Statistics and Probability
article description
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.