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. While it is common to use arbitrary continuity corrections or remove zero-event studies to stabilize or define effect estimates in such settings, these practices can 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. XRRmeta is also justified in its treatment of zero-event studies through a conditional inference argument. Importantly, our extensive numerical studies indicate that XRRmeta does not yield overly conservative inference. We apply our proposed method to reanalyze the occurrence of major adverse cardiovascular events among type II diabetics treated with rosiglitazone and in a more recent example examining the utility of face masks in preventing person-to-person transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease 2019 (COVID-19).

翻译：荟萃分析通过整合相关研究的信息提供更可靠的统计推断，已成为评估众多知名药品安全性和有效性的关键工具。进行荟萃分析面临的主要挑战是相关研究数量通常较少。应用基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，可能导致一项或多项研究中至少有一个研究组无事件发生。虽然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，但这些做法可能使后续推断失效。为解决这些重大实践问题，我们提出了一种在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”。与现有方法不同，当事件率、研究数量和/或研究内样本量较小时，XRRmeta置信区间的覆盖率能保证达到或超过名义水平（仅受蒙特卡洛误差影响）。XRRmeta通过条件推断论证合理处理了零事件研究。重要的是，大量数值研究表明XRRmeta不会导致过度保守的推断。我们将所提方法应用于重新分析罗格列酮治疗2型糖尿病患者中主要不良心血管事件的发生情况，以及一项更近期的研究——探讨口罩在预防严重急性呼吸综合征冠状病毒2（SARS-CoV-2）和2019冠状病毒病（COVID-19）人际传播中的效用。