This thesis first addresses the statistical issues that are associated with the use of meta-analysis in the presence of rare events. Limitations of commonly used effect measures, such as the log odds ratio and log relative risk, are described. Then, the benefits of using the arcsine difference as the effect measure in meta-analysis are investigated, and the various effect measures are compared in a simulation study. Finally, real data on the adverse events from long-acting beta-agonists in asthma patients is considered. Using this data, the results of a meta-analysis with the arcsine difference effect measure are compared to previously published results using the log odds ratio.