Box 2. Examples of Plots and Statistical Tests to Assess the Risk of Publication Bias

Is there possible evidence of publication bias?

Forest plots.

Funnel plots.

Doi plot [54].

What is the degree of funnel plot (a)symmetry?

Egger’s weighted regression [43].

Begg’s and Mazumdar’s rank correlation test [55].

Macaskill’s funnel plot regression [31].

Peters’ regression test [56].

Debray’s regression using estimates of asymptotic precision as study weights [46].

Luis Furuya-Kanamori index [54].

Meta-regression residuals and inverse sample size [33].

Imbalance and asymmetry distance [51].

Is the summary effect size at least partly due to publication bias?

Rosenthal’s and Orwin’s Fail-safe N [37].

How much might publication bias influence the summary effect size?

Duval and Tweedie’s Trim-and-Fill method [39].

Copas’ selection model [3].

Precision-Effect Test and Precision-Effect Estimate with Standard Errors [22].

Rücker’s Limit Meta-Analysis Method [57].

Is the p-value distribution affecting the meta-analysis a true effect and how large is this effect?

p-curve [58–60].

p-uniform method [61, 62].

Are p-values affecting the probability of selection of study for publication and how can it affect the meta-analysis true effect?

Three-parameter selection model [61, 62].

Fixed Weights Selection Model [61–63].

Is there evidence bias from selective (non)inclusion of results?

Potential bias index [64, 65]

Risk Of Bias due to Missing Evidence tool [2]

How much might both small-study effects and selection for statistical significance influence the summary effect size?

Robust Bayesian Meta-Analysis [38].