A comparison of Bayesian synthesis approaches for studies comparing two means: A tutorial

Researchers often seek to synthesize results of multiple studies on the same topic to draw statistical or substantive conclusions and to estimate effect sizes that will inform power analyses for future research. The most popular synthesis approach is meta‐analysis. There have been few discussions and applications of other synthesis approaches. This tutorial illustrates and compares multiple Bayesian synthesis approaches (i.e., integrative data analyses, meta‐analyses, data fusion using augmented data‐dependent priors, and data fusion using aggregated data‐dependent priors) and discusses when and how to use these Bayesian synthesis approaches to combine studies that compare two independent group means or two matched group means. For each approach, fixed‐, random‐, and mixed‐effects models with other variants are illustrated with real data. R code is provided to facilitate the implementation of each method and each model. On the basis of these analyses, we summarize the strengths and limitations of each approach and provide recommendations to guide future synthesis efforts.