One-sample and two-sample analysis of heterogeneous person-time data in clinical trials

In this paper, we investigate the performance of different parametric and nonparametric approaches for analyzing overdispersed person-time-event rates in the clinical trial setting. We show that the likelihood-based parametric approach may not maintain the right size for the tested overdispersed person-time-event data. The nonparametric approaches may use an estimator as either the mean of the ratio of number of events over follow-up time within each subjects or the ratio of the mean of the number of events over the mean follow-up time in all the subjects. Among these, the ratio of the means is a consistent estimator and can be studied analytically. Asymptotic properties of all estimators were studied through numerical simulations. This research shows that the nonparametric ratio of the mean estimator is to be recommended in analyzing overdispersed person-time data. When sample size is small, some resampling-based approaches can yield satisfactory results.