A Zero-Inflated Bivariate Poisson Regression Model and Application to Some Dental Epidemiological Data

Abstract

For the analysis of Data in the form of paired (pre-treatment, post-treatment) counts we propose a zero-inflated bivariate Poisson regression (ZIBPR) model. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model which can be used in a procedure for testing treatment effects. The Procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post- treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then analyze the DMFT index data based on the ZIBPR model and compare with the analysis using the ZIPR model.