Correcting for publication bias in a meta-analysis with the p-uniform* method

Publication bias is a major threat to the validity of a meta-analysis, resulting in overestimated effect sizes. We propose a generalization and improvement of the publication bias method p-uniform called p-uniform*. P-uniform* improves upon p-uniform in three ways, as it (i) entails a more efficient estimator, (ii) eliminates the overestimation of effect size caused by 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, two implementations of the three-parameter selection model (3PSM) approach, and the random-effects model. Statistical properties of p-uniform* and 3PSM were comparable and generally outperformed p-uniform and the random-effects model if publication bias was present. We explain that p-uniform* uses a more parsimonious model than 3PSM and demonstrate that both methods 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. We re-analyze the data of two published meta-analyses using p-uniform, p-uniform*, and 3PSM to illustrate the impact of publication bias on the results. We also offer recommendations for applied researchers, and we share R code in an R package as well as an easy-to-use web application for applying p-uniform*.