The safety evaluation of pharmaceutical products involves pre-clinical animal studies, pre-licensure randomized clinical trials and post-approval safety surveillance. Sequential design and analysis are of particular interest because they allow early termination of the trial or quick detection that the product exceeds a prescribed bound on the adverse event rate. After a review of recent developments in this area, we propose a new class of sequential generalized likelihood ratio tests for evaluating adverse event rates in two-armed pre-licensure clinical trials and single- armed post-approval surveillance. The proposed approach is illustrated using data from the Rotavirus Efficacy and Safety Trial (REST). Simulation studies of the performance of the proposed approach and other methods are also given.