Bayesian Conway-Maxwell-Poisson (CMP) regression for longitudinal count data

Longitudinal count data has been widely collected in biomedical research, public health, and clinical trials. These repeated measurements over time on the same subjects need to account for an appropriate dependency. The Poisson regression model is the first choice to model the expected count of interest, however, this may not be an appropriate when data exhibit over-dispersion or under-dispersion. Recently, Conway-Maxwell-Poisson (CMP) distribution is popularly used as the distribution offers a flexibility to capture a wide range of dispersion in the data. In this article, we propose a Bayesian CMP regression model to accommodate over and under-dispersion in modeling longitudinal count data. Specifically, we develop a regression model with random intercept and slope to capture subject heterogeneity and estimate covariate effects to be different across subjects. We implement a Bayesian computation via Hamiltonian MCMC (HMCMC) algorithm for posterior sampling. We then compute Bayesian model assessment measures for model comparison. Simulation studies are conducted to assess the accuracy and effectiveness of our methodology. The usefulness of the proposed methodology is demonstrated by a well-known example of epilepsy data.