Modeling time-dependent overdispersion in longitudinal count data

Poisson regression is important in the analysis of longitudinal count data. However, the variance of responses is often much greater than the sample mean in practice, contradicting the Poisson model. To solve this overdispersion problem, negative binomial regression model was introduced by earlier researchers by adding another error term to the Poisson model. By default, the parameter of the additional error term, called the overdispersion parameter, is constant during the study period, but we find that it may fail in the research of epilepsy. Thus a formal likelihood ratio test is proposed and the test conforms that a time-dependent overdispersion phenomenon does exist. Then a mixed effect negative binomial model is proposed to take into account the time-dependent overdispersion, producing significantly better regression results compared with most earlier models. The proposed test and regression approach can easily be done by SAS PROC NLMIXED. The extensive simulation studies are conducted to evaluate the performance of the methods proposed.