This study explores the performance of classical methods for detecting publication bias—namely, Egger’s regression test, Funnel Plot test, Begg’s Rank Correlation and Trim and Fill method—in meta-analysis of studies that report multiple effects. Publication bias, outcome reporting bias, and a combination of these were generated. Egger’s regression test and the Funnel Plot test were extended to three-level models, and possible cutoffs for the estimator of the Trim and Fill method were explored. Furthermore, we checked whether the combination of results of several methods yielded a better control of Type I error rates. Results show that no method works well across all conditions and that performance depends mainly on the population effect size value and the total variance.
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