Statistical methods for meta-analyses including information from studies without any events-add nothing to nothing and succeed nevertheless

Abstract

Meta-analyses with rare events, especially those that include studies with no event in one ('single-zero') or even both ('double-zero') treatment arms, are still a statistical challenge. In the case of double-zero studies, researchers in general delete these studies or use continuity corrections to avoid them. A number of arguments against both options has been given, and statistical methods that use the information from double-zero studies without using continuity corrections have been proposed. In this paper, we collect them and compare them by simulation. This simulation study tries to mirror real-life situations as completely as possible by deriving true underlying parameters from empirical data on actually performed meta-analyses. It is shown that for each of the commonly encountered effect estimators valid statistical methods are available that use the information from double-zero studies without using continuity corrections. Interestingly, all of them are truly random effects models, and so also the current standard method for very sparse data as recommended from the Cochrane collaboration, the Yusuf-Peto odds ratio, can be improved on. For actual analysis, we recommend to use beta-binomial regression methods to arrive at summary estimates for the odds ratio, the relative risk, or the risk difference. Methods that ignore information from double-zero studies or use continuity corrections should no longer be used. We illustrate the situation with an example where the original analysis ignores 35 double-zero studies, and a superior analysis discovers a clinically relevant advantage of off-pump surgery in coronary artery bypass grafting.

Keywords: continuity correction; meta-analysis; rare events; safety; sparse data.