Regression models for mixed Poisson and continuous longitudinal data.

In this article we develop flexible regression models in two respects to evaluate the influence of the covariate variables on the mixed Poisson and continuous responses and to evaluate how the correlation between Poisson response and continuous response changes over time. A scenario for dealing with regression models of mixed continuous and Poisson responses when the heterogeneous variance and correlation changing over time exist is proposed. Our general approach is first to jointly build marginal model and to check whether the variance and correlation change over time via likelihood ratio test. If the variance and correlation change over time, we will do a suitable data transformation to properly evaluate the influence of the covariates on the mixed responses. The proposed methods are applied to the interstitial cystitis data base (ICDB) cohort study, and we find that the positive correlations significantly change over time, which suggests heterogeneous variances should not be ignored in modelling and inference.