Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values

Regression models are proposed for joint analysis of Poisson and continuous longitudinal data with nonignorable missing values under fully parametric framework. Our primary interest is to evaluate the influence of the covariates on both Poisson and continuous responses. First, we form the full likelihood with complete data using the multivariate Poisson model and conditional multivariate normal distribution and then construct an ECM algorithm to find the maximum likelihood estimates of the model parameters. Then, under the assumption that the missingness mechanisms for the two responses are independent but nonignorable, namely, dependent on both observed and missing data of the two responses, we choose the logit model for the missingness mechanisms and selection model for the full likelihood. Also, we build two implementations of the Monte Carlo EM algorithm for estimating the parameters in the model. Wald test is employed to test the significance of covariates. Finally, we present the results of the Monte Carlo simulation to evaluate the performance of the proposed methodology and an application to the interstitial cystitis data base (ICDB) cohort study. To the best of our knowledge, our model is the first parametric model for joint analysis of Poisson and continuous longitudinal data with nonignorable missing value.