Mixture Models for Mixed Poisson Processes with Baseline Counts in Randomized Controlled Trials

For the analysis of count data from comparative clinical study with patient screening which refers to the baseline observation, Cook and Wei (2003) proposed a conditional Gamma-Poisson model as a natural extension of ANCOVA. However, in some cases this model suffers from its insufficient capacity in expressing the inter-patient heterogeneity. As alternative we propose extended models that include an additional random effect into the conventional Poisson mixture, which can be estimated through conditioning by total sum of count or baseline. The resulting models can offer improved summary of patient heterogeneity, as well as other population parameters. The proposed models are illustrated with seizure count data from a clinical experiment for an anti-epileptic drug.