On the exact null-distribution of a test for homogeneity of the risk ratio in meta-analysis of studies with rare events

Abstract

This paper focuses on the test for homogeneity of relative risk in meta-analysisof count outcomes. Meta-analysis of studies with rare events faces particular chal-lenges, since the number of studies are low and the frequency of events may besmall in some or all treatment arms. In such a case, the conventional chi-square testfor homogeneity becomes undefined and we suggest a new chi-square test which isalways defined. However, the chi-square approximation is poor. We therefore intro-duce methodology to obtain its exact distribution which is based on the productbinomial likelihood. The exact p-value is then derived and the performance of themethod is investigated using simulations. The results show that the type I error ofthe proposed method satisfies the nominal significance level in rare events situations.Also, the exact distribution behaves very similar to the simulated distribution. Areal data example of a meta-analysis with an extreme form of rare event studies isused to illustrate the new test.

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ORCID for Dankmar Bohning: orcid.org/0000-0003-0638-7106

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