A new and improved confidence interval for the Mantel-Haenszel risk difference

Writing the variance of the Mantel–Haenszel estimator under the null of homogeneity and inverting the corresponding test, we arrive at an improved confidence interval for the common risk difference in stratified 2 × 2 tables. This interval outperforms a variety of other intervals currently recommended in the literature and implemented in software. We also discuss a score‐type confidence interval that allows to incorporate strata/study weights. Both of these intervals work very well under many scenarios common in stratified trials or in a meta‐analysis, including situations with a mixture of both small and large strata sample sizes, unbalanced treatment allocation, or rare events. The new interval has the advantage that it is available in closed form with a simple formula. In addition, it applies to matched pairs data. We illustrate the methodology with various stratified clinical trials and a meta‐analysis. R code to reproduce all analysis is provided in the Appendix. Copyright © 2014 John Wiley & Sons, Ltd.