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

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Abstract
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*.
Funding Information
  • Netherlands Organization for Scientific Research (406-13-050)
  • Netherlands Organization for Scientific Research (VI.Veni.211G.012)
  • European Research Council (726361 (IMPROVE))

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