EFFICIENCY LOST BY ANALYZING COUNTS RATHER THAN EVENT TIMES IN POISSON AND OVERDISPERSED POISSON REGRESSION-MODELS

Inference for point processes is most efficient if the event times for each individual are available. Sometimes, the study design is such th at only aggregated data are collected, consisting of the number of eve nts or recurrences for each individual over the observation period. Th is article discusses the loss in efficiency of an analysis of the aggr egated counts versus an analysis of the actual event times. One partic ular case is exemplified--that in which the purpose of the experiment or trial is to compare the effects of treatments--and the loss in effi ciency in the estimator of the treatment effect is computed. The speci fic point process considered here is the nonhomogeneous Poisson proces s, with a proportional intensity model for the treatment effects. Rand om-effects models are also considered, with estimation via a quasi-lik elihood approach. The quasi-likelihood analysis proposed here is an ex tension of such techniques for the homogeneous Poisson process. The re sulting estimating equations for the parameters in the random-effects models are simple and intuitive. The results show that for many usual situations, treatment effects are very efficiently estimated using agg regated data, but the underlying intensity function is not.