Meta‐analysis of 2 × 2 tables is common and useful in research topics including analysis of adverse events and survey research data. Fixed‐effects inference typically centers on measures of association such as the Cochran‐Mantel‐Haenszel statistic or Woolf's estimator, but relies on assuming exact homogeneity across studies, which is often unrealistic. By showing that estimators of several widely‐used methods have meaningful estimands even in the presence of heterogeneity, we derive improved confidence intervals for them under heterogeneity. These improvements over current methods are illustrated by simulation, and we also study which factors affect the coverage levels. We find that our confidence intervals provide coverage closer to the nominal level when heterogeneity is present, in both small and large‐sample settings. The conventional confidence intervals derived under homogeneity are often conservative, though anti‐conservative inferences occur in some scenarios. We also apply the proposed methods to a meta‐analysis of 19 randomized clinical trials on the effect of sclerotherapy in preventing first bleeding for patients with cirrhosis and esophagogastric varices. Our methods provide a more interpretable approach to meta‐analyzing binary data and more accuracy in characterizing the uncertainty of the estimators.

中文翻译：

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对2×2表的固定效果荟萃分析的改进推论。

2×2表的荟萃分析在研究主题（包括不良事件分析和调查研究数据）中是常见且有用的。固定效应推论通常集中在关联的度量上，例如Cochran-Mantel-Haenszel统计量或Woolf估计量，但是依赖于假设研究之间的精确同质性，这通常是不现实的。通过显示即使在存在异构性的情况下，几种广泛使用的方法的估计量也具有有意义的估计值，我们得出了异构性下它们的改进的置信区间。通过仿真可以说明对当前方法的这些改进，并且我们还研究了哪些因素会影响覆盖范围。我们发现，在小样本和大样本设置中，存在异质性时，我们的置信区间都可以提供接近标称水平的覆盖率。尽管在某些情况下会出现反保守的推断，但在同质性下得出的常规置信区间通常是保守的。我们还将拟议的方法应用于19项关于硬化疗法预防肝硬化和食管胃底静脉曲张出血的随机临床试验的荟萃分析。我们的方法为元数据的元分析提供了一种更可解释的方法，并且在表征估计量的不确定性时提供了更高的准确性。