Robust Bayesian meta-analysis: Addressing publication bias with model-averaging

Meta-analysis is an important quantitative tool for cumulative science, but its application is frustrated by publication bias. In order to test and adjust for publication bias, we extend model-averaged Bayesian meta-analysis with selection models. The resulting robust Bayesian meta-analysis (RoBMA) methodology does not require all-or-none decisions about the presence of publication bias, can quantify evidence in favor of the absence of publication bias, and performs well under high heterogeneity. By model-averaging over a set of 12 models, RoBMA is relatively robust to model misspecification and simulations show that it outperforms existing methods. We demonstrate that RoBMA finds evidence for the absence of publication bias in Registered Replication Reports and reliably avoids false positives. We provide an implementation in R so that researchers can easily use the new methodology in practice.