Choose whether to model adverse events in a logistic model (Berry and Berry, 20041; Model 1b of Xia, Ma, and Carlin, 20112) or as a log-linear model adjusting for exposure time (Model 2b of Xia, Ma, and Carlin, 2011b).
Xia, H.A., Ma, H., and Carlin, B.P. (2011). Bayesian Hierarchical Modeling for Detecting Safety Signals in Clinical Trials. Journal of Biopharmaceutical Statistics 21, 1006-1029.