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With availability of each individual event times, inference for point processes is most efficient. However there are times when the study de-sign is such that only count data are collected, consisting of the number of events or recurrences for each individual over the entire follow-up times. This thesis discusses the loss in efficiency of an analysis of such count data versus an analysis of the actual-event times. One particu-lar case is exemplified, that in which the purpose of the experiment or trial is to compare the effects of treatments, and the loss in efficiency in the estimator of the treatment effect is computed.The specific point process considered here is the non-homogeneous poison process, with a proportional intensity model for the treatment effects. Random effects models are also considered with estimation via a quasi-likelihood approach. The quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poison process. The resulting 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 efficiently estimated using aggregate data; however when only end of follow-up counts are collected, the underlying intensity function is not. Multiple follow-up count data is shown to recover much of the information lost by end of follow-up counts.The efficiency of the quasi likelihood estimators is shown to be high relative to specific likelihood alternatives. Tests and diagnostic procedures for checking model assumptions are presented.The quasi likelihood estimators developed here require the assumption of a para-metric form for the intensity function. This thesis also develops a non-parametric approach to the estimation of the intensity function. Combined with quasi likelihood estimators for covariates, this provides a simple method for the analysis of recurrent event data, requiring less stringent assumptions than traditional methods. We examine the small sample behavior of these procedures with simulation studies. The stud-ies show that for the situations we consider, the methods work well and display adequate small sample characteristics. Analyses of illustrative examples demonstrate the application of the procedures.