Bayesian Analysis of Doubly Inflated Poisson Regression for Correlated Count Data: Application to DMFT Data

Outcome variables in clinical studies sometimes include count data with inflation in two points (usually zero and k (k>0)). Doubly inflated models can be adopted for modeling these types of data. In statistical modeling, the association among subjects due to longitudinal or cluster study designs is considered by random effects models. In this article, we proposed a doubly inflated random effects model using the Bayesian approach for correlated count data with inflation in two values, and compared this model with Bayesian zero-inflated Poisson and Bayesian Poisson models. The parameters' estimates by these models were obtained by Markov Chain Monte Carlo method using OpenBUGS software. Bayesian models were compared using the deviance information criterion. To this end, we utilized the total number of decayed, missed, and filled teeth of 12-year-old children and also conducted a simulation study. Results of real data and the simulation study revealed that the proposed model is fitted better than previous models.