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An informed reference prior for between‐study heterogeneity in meta‐analyses of binary outcomes

It is well known that when a Bayesian meta‐analysis includes a small number of studies, inference can be sensitive to the choice of prior for the between‐study variance. Choosing a vague prior does not solve the problem, as inferences can be substantially different depending on the degree of vagueness. Moreover, because the data provide little information on between‐study heterogeneity, posterior inferences for the between‐study variance based on vague priors will tend to be unrealistic. It is thus preferable to adopt a reasonable, informed prior for the between‐study variance. However, relatively little is known about what constitutes a realistic distribution. On the basis of data from the Cochrane Database of Systematic Reviews, this paper describes the distribution of between‐study variance in published meta‐analyses, and proposes some realistic, informed priors for use in meta‐analyses of binary outcomes. It is hoped that these priors will improve the calibration of inferences from Bayesian meta‐analyses. Copyright © 2011 John Wiley & Sons, Ltd.