ABSTRACT This paper focuses on the test for homogeneity of relative risk in meta-analysis of count outcomes. Meta analysis of studies with rare events faces particular challenges, since the number of studies are low and the frequency of events may be small in some or all treatment arms. In such a case, the conventional chi-square test for homogeneity becomes undefined and we suggest a new chi-square test which is always defined. However, the chi-square approximation is poor. We therefore introduce methodology to obtain its exact distribution based on the product binomial likelihood. The exact p-value is then derived and the performance of the method is investigated using simulations. The results show that the type I error of the proposed method satisfies the nominal significance level in rare events situations. A real data example of a meta-analysis with an extreme form of rare event studies is used to illustrate the new test.

中文翻译：

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关于罕见事件研究荟萃分析中风险比同质性检验的精确零分布

摘要 本文侧重于在计数结果的荟萃分析中检验相对风险的同质性。对罕见事件研究的 Meta 分析面临着特殊的挑战，因为研究数量很少，并且在某些或所有治疗组中事件发生的频率可能很小。在这种情况下，用于同质性的传统卡方检验变得不确定，我们建议使用始终定义的新卡方检验。然而，卡方近似很差。因此，我们引入了基于乘积二项式似然获得其精确分布的方法。然后导出精确的 p 值，并使用模拟研究该方法的性能。结果表明，所提方法的I类误差满足罕见事件情况下的名义显着性水平。