Posterior probabilities of effect sizes and heterogeneity in meta-analysis: An intuitive approach of dealing with publication bias

Publication bias remains to be a great challenge when conducting a meta-analysis. It may result in overestimated effect sizes, increased frequency of false positives, and over- or underestimation of the effect size heterogeneity parameter. A new method is introduced, Bayesian Meta-Analytic Snapshot (BMAS), which evaluates both effect size and its heterogeneity and corrects for potential publication bias. It evaluates the probability of the true effect size being zero, small, medium or large, and the probability of true heterogeneity being zero, small, medium or large. This approach, which provides an intuitive evaluation of uncertainty in the evaluation of effect size and heterogeneity, is illustrated with a real-data example, a simulation study, and a Shiny web application of BMAS.