Marginalized models for longitudinal count data

In this paper, we propose two marginalized models for longitudinal count data. The first marginalized model has a Markovian structure to account for the serial correlation of longitudinal outcomes. We also propose another marginalized model with a Markovian structure for serial correlation as well as random effects for both overdispersion and long-term dependence. In these models, along with it being possible to permit likelihood-based estimation, inference is valid under ignorability which distinguishes them from generalized estimating equation (GEE) approaches. Fisher-scoring and Quasi-Newton algorithms are developed for estimation purposes. Monte Carlo studies show that the proposed models perform well in the sense of reducing the bias of marginal mean parameters compared to the misspecification of the dependence model in these models. The models are used to draw inferences from a previously analyzed trial on epileptic seizures. (C) 2019 Elsevier B.V. All rights reserved.