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-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.

Keywords:

• Conditional binomial model
• count outcomes
• exact p-value
• null distribution
• simulation study

Acknowledgments

The authors would like to thank the Associate Editor and a reviewer for all suggestions which lead to considerable improvements of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been partially funded under grant HO 1286/16-1 by the German Research Foundation (DFG).