Robust Bayesian meta-analysis: Model-averaging across complementary publication bias adjustment methods

Abstract

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.

Keywords: Bayesian model-averaging; PET-PEESE; meta-analysis; publication bias; selection models.

FIGURE 1

The model‐averaged weight function with 95% CI for Bem. Results are model‐averaged across the whole model ensemble, including models assuming no publication bias (ω = 1)

FIGURE 2

The relationship between the standard errors and model‐averaged effect size estimate with 95% CI for Bem. Results are model‐averaged across the entire model ensemble. Models assuming no publication bias have both PET and PEESE coefficients set to 0. Black diamonds correspond to the individual study estimates and standard errors

FIGURE 3

Effect size estimates with 95% CIs from a random‐effects meta‐analysis, three RoBMA models, and the RRR for the 15 experiments included in Kvarven et al. Estimates are reported on the Cohen's d scale [Colour figure can be viewed at wileyonlinelibrary.com]