Abstract
Meta-analysis aggregates information across related studies to provide more reliable statistical inference and has been a vital tool for assessing the safety and efficacy of many high-profile pharmaceutical products. A key challenge in conducting a meta-analysis is that the number of related studies is typically small. Applying classical methods that are asymptotic in the number of studies can compromise the validity of inference, particularly when heterogeneity across studies is present. Moreover, serious adverse events are often rare and can result in one or more studies with no events in at least one study arm. Practitioners remove studies in which no events have occurred in one or both arms or apply arbitrary continuity corrections (e.g., adding one event to arms with zero events) to stabilize or define effect estimates in such settings, which can further invalidate subsequent inference. To address these significant practical issues, we introduce an exact inference method for random effects meta-analysis of a treatment effect in the two-sample setting with rare events, which we coin "XRRmeta". In contrast to existing methods, XRRmeta provides valid inference for meta-analysis in the presence of between-study heterogeneity and when the event rates, number of studies, and/or the within-study sample sizes are small. Extensive numerical studies indicate that XRRmeta does not yield overly conservative inference. We apply our proposed method to two real-data examples using our open-source R package.