Bayesian Modeling of Longitudinal Count Data Using Conway-Maxwell Poisson Distribution

• Activity Number: 188 - Bayesian Application to Biological and Health Sciences
• Type: Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): MORSHED ALAM* and Jane Meza and Yeongjin Gwon
• Companies: University Of Nebraska Medical Center and University of Nebraska Medical Center and University of Nebraska Medical Center
• Keywords: Conway-Maxwell Poisson (CMP); DIC; Hamiltonian MCMC; Random effects

Abstract

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 longitudinally measured from patients within clusters in multisite trials. The Poisson and negative binomial models may not be adequate when data exhibit over and under-dispersion, respectively. We propose a Bayesian Conway-Maxwell Poisson (CMP) regression model to overcome this difficulty as it can capture a wide range of dispersion. Specifically, we develop a regression model with random intercepts and slopes to capture heterogeneity among subjects and dependence over time. We apply an adaptive variant of Hamiltonian MCMC to carry out Bayesian computation and Deviance Information Criterion (DIC) is used for model comparison. Simulation study shows that CMP models outperform among the competing models when data exhibit dispersion. A case study demonstrating the usefulness of the proposed methodology is applied using real clinical trial data.