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 often apply arbitrary continuity corrections or remove zero-event studies 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 comparing event rates in two treatment arms under a random effects framework, which we coin "XRRmeta". In contrast to existing methods, the coverage of the confidence interval from XRRmeta is guaranteed to be at or above the nominal level (up to Monte Carlo error) 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 and we apply our proposed method to two real-data examples using our open source R package.

翻译：元分析通过汇总相关研究的信息提供更可靠的统计推断，已成为评估许多知名药物安全性和有效性的重要工具。进行元分析的关键挑战在于相关研究的数量通常较少。应用依赖于研究数量渐近性的经典方法可能会损害推断的有效性，尤其是在研究间存在异质性的情况下。此外，严重不良事件通常罕见，可能导致一个或多个研究组中至少一个臂出现零事件。研究者在此类情况下常采用任意连续性校正或剔除零事件研究来稳定或定义效应估计值，这可能会进一步破坏后续推断的有效性。为应对这些重大实际问题，我们提出了一种随机效应框架下比较两个治疗组事件率的精确推断方法，并将其命名为"XRRmeta"。与现有方法相比，当事件发生率、研究数量及/或研究内样本量较小时，XRRmeta生成的置信区间覆盖概率保证达到或超过名义水平（考虑蒙特卡洛误差）。大量数值研究表明XRRmeta不会产生过度保守的推断，我们通过开源R包将所提方法应用于两个真实数据示例。