P-uniform

Publication bias is a major threat to the validity of a meta-analysis resulting in overestimated effect sizes. P-uniform is a meta-analysis method that corrects estimates for publication bias but overestimates average effect size if heterogeneity in true effect sizes (i.e., between-study variance) is present. We propose an extension and improvement of p-uniform called p-uniform*. P-uniform* improves upon p-uniform in three important ways, as it (i) entails a more efficient estimator, (ii) eliminates the overestimation of effect size in case of between-study variance in true effect sizes, and (iii) enables estimating and testing for the presence of the between-study variance. We compared the statistical properties of p-uniform* with p-uniform, the selection model approach of Hedges (1992), and the random-effects model. Statistical properties of p-uniform* and the selection model approach were comparable and generally outperformed p-uniform and the random-effects model if publication bias was present. We demonstrate that p-uniform* and the selection model approach estimate average effect size and between-study variance rather well with ten or more studies in the meta-analysis when publication bias is not extreme. P-uniform* generally provides more accurate estimates of the between-study variance in meta-analyses containing many studies (e.g., 60 or more) and if publication bias is present. However, both methods do not perform well if the meta-analysis only includes statistically significant studies. P-uniform performed best in this case but only when between-study variance was zero or small. We offer recommendations for applied researchers, and provide an R package and an easy-to-use web application for applying p-uniform*.