Bayesian model-averaged meta-analysis in medicine

We outline a Bayesian model-averaged (BMA) meta-analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness (Formula presented.) and across-study heterogeneity (Formula presented.). We construct four competing models by orthogonally combining two present-absent assumptions, one for the treatment effect and one for across-study heterogeneity. To inform the choice of prior distributions for the model parameters, we used 50% of the Cochrane Database of Systematic Reviews to specify rival prior distributions for (Formula presented.) and (Formula presented.). The relative predictive performance of the competing models and rival prior distributions was assessed using the remaining 50% of the Cochrane Database. On average, (Formula presented.) —the model that assumes the presence of a treatment effect as well as across-study heterogeneity—outpredicted the other models, but not by a large margin. Within (Formula presented.), predictive adequacy was relatively constant across the rival prior distributions. We propose specific empirical prior distributions, both for the field in general and for each of 46 specific medical subdisciplines. An example from oral health demonstrates how the proposed prior distributions can be used to conduct a BMA meta-analysis in the open-source software R and JASP. The preregistered analysis plan is available at https://osf.io/zs3df/.

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