We fit a mixed effects logistic regression model to longitudinal adverse event (AE) severity data (four-point ordered categorical response) to describe the dose-AE severity response for an investigational drug. The distribution of the predicted interindividual random effects (Bayes predictions) was extremely bimodal. This extreme bimodality indicated that biased parameter estimates and poor predictive performance were likely. The distribution's primary mode was composed of patients that did not experience an AE. Moreover, the Bayes predictions of these non-AE patients were nearly degenerative, i.e., the predictions were nearly identical. To resolve this extreme bimodality we propose using a two-part mixture modeling approach. The first part models the incidence of AE's, and the second part models the severity grade given the patient had an AE. Unconditional probability predictions are calculated by mixing the incidence and severity model probability predictions. We also report results of simulation studies, which assess the predictive and statistical (bias and precision) performance of our approach.