Publication bias is a ubiquitous threat to the validity of meta-analysis and the accumulation of scientific evidence. In order to estimate and counteract the impact of publication bias, multiple methods have been developed; however, recent simulation studies have shown the methods' performance to depend on the true data generating process, and no method consistently outperforms the others across a wide range of conditions.Unfortunately, when different methods lead to contradicting conclusions, researchers can choose those methods that lead to a desired outcome. To avoid the condition-dependent, all-or-none choice between competing methods and conflicting results, we extend robust Bayesian meta-analysis and model-average across two prominent approaches of adjusting for publication bias: (1) selection models of p-values and (2) models adjusting for small-study effects. The resulting model ensemble weights the estimates and the evidence for the absence/presence of the effect from the competing approaches with the support they receive from the data. Applications, simulations, and comparisons to preregistered, multi-lab replications demonstrate the benefits of Bayesian model-averaging of complementary publication bias adjustment methods.
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.
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