In personalized medicine, subgroup analyses play an important role in identifying treatment effects for different subgroups of patients. We study subgroup analysis where the study endpoint follows a Poisson distribution. The Bayesian empirical meta-analytical predictive (eMAP) prior approach is applied to the setup of two arm clinical trial studies. To resolve the computational difficulty, we derive an analytical approximation for the multivariate marginal distribution under the normal mixture prior assumption. The approximation results and the model performance are demonstrated using simulated count data. The simulations are programmed in R, JAGS, and pbdR.