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.

[1]  A Whitehead,et al.  Borrowing strength from external trials in a meta-analysis. , 1996, Statistics in medicine.

[2]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[3]  S. Thompson,et al.  Quantifying heterogeneity in a meta‐analysis , 2002, Statistics in medicine.

[4]  D J Spiegelhalter,et al.  Bayesian approaches to random-effects meta-analysis: a comparative study. , 1995, Statistics in medicine.

[5]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[6]  D J Spiegelhalter,et al.  Bayesian methods for cluster randomized trials with continuous responses. , 2001, Statistics in medicine.

[7]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[8]  A. Dawid.  The Well-Calibrated Bayesian , 1982 .

[9]  Gerta Rücker,et al.  Bmc Medical Research Methodology Open Access Undue Reliance on I 2 in Assessing Heterogeneity May Mislead , 2022 .

[10]  David J Spiegelhalter,et al.  Prior distributions for the intracluster correlation coefficient, based on multiple previous estimates, and their application in cluster randomized trials , 2005, Clinical trials.

[11]  David R. Jones,et al.  How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS , 2005, Statistics in medicine.

[12]  Alexander J Sutton,et al.  What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. , 2004, Statistics in medicine.

[13]  David J Spiegelhalter,et al.  A re-evaluation of random-effects meta-analysis , 2009, Journal of the Royal Statistical Society. Series A,.

[14]  Stephen Senn,et al.  (www.interscience.wiley.com) DOI: 10.1002/sim.2639 Trying to be precise about vagueness , 2022 .

[15]  Alex J. Sutton,et al.  Bayesian methods in meta-analysis and evidence synthesis , 2001 .

[16]  M. Daniels.  A prior for the variance in hierarchical models , 1999 .

[17]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[18]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .