Confidence interval estimation for the Mantel-Haenszel estimator of the risk ratio and risk difference in rare event meta-analysis with emphasis on the bootstrap

This paper takes a deeper look into uncertainty assessment of the Mantel-Haenszel estimator (MHE). In the homogeneity case, all developed confidence intervals for the risk ratio and risk difference behave acceptably, even in therare events situation. For heterogeneity, the non-parametric bootstrap approachprovides confidence intervals for the risk difference with acceptable coverage,depending on the number of studies. For the risk ratio, the situation is morecomplex as typically distributions for the log-relative risk are considered. TheMHE overestimates the expected value of the distribution of the log-relativerisk whatever it may be. However, if we consider as true value the estimand ofMHE, reasonable coverage probabilities can be achieved with the bootstrap. Asource of this problem is that the moments of a non-linearly transformedrelative risk variable are not equal to the non-linearly transformed moments ofthe respective relative risk variable.