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

## TL;DR

This paper introduces p-uniform*, an improved method to correct for publication bias in meta-analyses, which helps provide more accurate effect size estimates.

## Contribution

The novel contribution is p-uniform*, which improves upon existing methods by offering a more efficient estimator and better handling of between-study variance.

## Key findings

- p-uniform* outperformed p-uniform and random-effects models in the presence of publication bias.
- p-uniform* and 3PSM provided accurate estimates of average effect size and between-study variance with ten or more studies.
- The authors demonstrated the impact of publication bias using real meta-analysis data and provided R code and a web application for p-uniform*.

## 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*.