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Meta‐analysis of clinical trials is a methodology to summarize information from a collection of trials about an intervention, in order to make informed inferences about that intervention. Random effects allow the target population outcomes to vary among trials. Since meta‐analysis is often an important element in helping shape public health policy, society depends on biostatisticians to help ensure that the methodology is sound. Yet when meta‐analysis involves randomized binomial trials with low event rates, the overwhelming majority of publications use methods currently not intended for such data. This statistical practice issue must be addressed. Proper methods exist, but they are rarely applied. This tutorial is devoted to estimating a well‐defined overall relative risk, via a patient‐weighted random‐effects method. We show what goes wrong with methods based on ‘inverse‐variance’ weights, which are almost universally used. To illustrate similarities and differences, we contrast our methods, inverse‐variance methods, and the published results (usually inverse‐variance) for 18 meta‐analyses from 13  Journal of the American Medical Association  articles. We also consider the 2007 case of rosiglitazone (Avandia), where important public health issues were at stake, involving patient cardiovascular risk. The most widely used method would have reached a different conclusion. © 2016 The Authors.  Statistics in Medicine  published by John Wiley & Sons Ltd.

Low‐event‐rate meta‐analyses of clinical trials: implementing good practices