This paper presents methods for meta-analysis of $2 \times 2$ tables, both with and without allowing heterogeneity in the treatment effects. Meta-analysis is common in medical research, but most existing methods are unsuited for $2 \times 2$ tables with rare events. Usually the tables are modelled as pairs of binomial variables, but we will model them as Poisson pairs. The methods presented here are based on confidence distributions, and offer optimal inference for the treatment effect parameter. We also propose an optimal method for inference on the ratio between treatment effects, and illustrate our methods on a real dataset.

翻译：本文提出了针对2×2列联表的荟萃分析方法，涵盖允许与不允许处理效应异质性的情形。荟萃分析在医学研究中十分常见，但现有方法大多不适用于罕见事件下的2×2列联表。此类列联表通常被建模为成对的二项变量，但本文将采用泊松对模型进行建模。所提出的方法基于置信分布，能够为处理效应参数提供最优推断。我们还提出了一种针对处理效应比值的最优推断方法，并通过真实数据集展示了所提方法的实际应用。