Bayesian Modeling for Longitudinal Count Data: Applications in Biomedical Research

Biomedical count data such as the number of seizures for epilepsy patients, number of new tumors at each visit or the number vomiting after each chemo-radiation for the cancer patients are common. Often these counts are measured longitudinally from patients or within clusters in multi-site trials. The Poisson and negative binomial models may not be adequate when data exhibit over or under-dispersion, respectively. On the contrary, a variety of dispersion conditions in count data can be captured by Conway-Maxwell Poisson (CMP) model. This doctoral dissertation relegates to developing a statistical methodology to model longitudinal count data distributed as CMP via mixed effect modeling approach. We propose a Bayesian CMP regression model. Specifically, we develop a regression model with random intercept and slope to capture heterogeneity among subjects and dependence over time. In addition, a Bayesian generalized additive mixed effect model based on CMP is proposed by assuming a non-linear shape of the functional relationship between mean of longitudinal response and covariates. Case studies demonstrating the usefulness of the proposed methodology by using real life clinical trial data are also presented. We apply an adaptive variant of Hamiltonian MCMC to carry out Bayesian computation. The Deviance Information Criterion (DIC), along with other Bayesian model assessment criteria such as (LPML), (WAIC), (LOO) are used for model comparisons. Both in simulation studies and real data analysis, we conclude that in terms of model fitting, CMP models outperform the competing models when data exhibit dispersion