Choose whether to model adverse events in a logistic model (Berry and Berry, 2004 1 ; Model 1b of Xia, Ma, and Carlin, 2011 2 ) or as a log-linear model adjusting for exposure time (Model 2b of Xia, Ma, and Carlin, 2011 b ).
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.