Bayesian Evidence Synthesis: Safely and Efficiently Combining Statistical Evidence in Meta-Analyses

Bayesian evidence synthesis refers to the process of combining statistical evidence between hypotheses from multiple studies. The evidence is quantified by the Bayes factor. Depending on the underlying model assumptions and research question, different methods can be used for a Bayesian evidence synthesis. The current paper gives an overview of possible models that can be used for this purpose which includes a common effect model, a random effects model, two hybrid effects models, and a fixed effects model. Furthermore, the respective synthesized Bayes factors under each modeling framework are given depending on the implied hypotheses that are tested. We also provide recommendations for prior distributions in Bayesian evidence synthesis for the popular effect size measures, including standardized mean difference, log odds ratio, and Pearson correlation. Additionally, the concept of safe evidence synthesis is described which is particularlyuseful in cumulative/sequential meta-analyses. With this overview and the recommendations for prior specification, researchers can make the best choice to synthesize the evidence from multiple studies. Empirical applications on statistical learning of people with a language impairmentand the incidence of seroma when exercising after breast cancer are used for illustrative purposes. Certain (new) synthesis methods are now also available in the R package BFpack.