A Transition Model for Analysis of Zero-Inflated Longitudinal Count Data Using Generalized Poisson Regression Model

Abstract

In most of the longitudinal studies, involving count responses, excess zeros are common in practice. Usually, the current response measurement in a longitudinal sequence is a function of previous outcomes. For example, in a study about acute renal allograft rejection, the number of acute rejection episodes for a patient in current time is a function of this outcome at previous follow-up times. In this paper, we consider a transition model for accounting the dependence of current outcome on the previous outcomes in the presence of excess zeros. We propose the use of the generalized Poisson distribution as a flexible distribution for considering overdispersion (or underdispersion). The maximum likelihood estimates of the parameters are obtained using the EM algorithm. Some simulation studies are performed for illustration of the proposed methods. Also, analysis of a real data set of a kidney allograft rejection study illustrates the application of the proposed model.

Keywords

• count data
• EM algorithm
• generalized Poisson distribution
• longitudinal data
• transition models
• zero-inflated models