Bootstrapping the Profile Likelihood Ratio Test for the Risk Ratio in Meta-Analysis of Rare Events

Rare event meta-analysis is challenging, as some standard meta-analysis methods do not work well to handle rare event outcomes. Furthermore, statistical inference used to determine whether a particular claim is significant on this issue has attracted little attention in the literature. Therefore, our objective is to construct the test statistic for testing a risk ratio in a meta-analysis of rare events. We introduce the Wald test based on the profile maximum likelihood estimator, the likelihood ratio test, and the bootstrap p-value. The performance of these methods is evaluated using simulations. It turns out that the likelihood ratio test is more powerful than the existing methods, which are the inverse-variance weighted average method, the Mantel–Haenszel method, and the test-related estimation in log-linear model. This paper uses two real data sets from meta-analytic studies in medical research to illustrate the approaches in application.