Estimating publication bias in meta-analyses of peer-reviewed studies: A meta-meta-analysis across disciplines and journal tiers.

Selective publication and reporting in individual papers compromise the scientific record, but are meta-analyses as compromised as their constituent studies? We systematically sampled 63 meta-analyses (each comprising at least 40 studies) in PLoS One, top medical journals, top psychology journals, and Metalab, an online, open-data database of developmental psychology meta-analyses. We empirically estimated publication bias in each, including only the peer-reviewed studies. Across all meta-analyses, we estimated that "statistically significant" results in the expected direction were only 1.17 times more likely to be published than "nonsignificant" results or those in the unexpected direction (95% CI: [0.93, 1.47]), with a confidence interval substantially overlapping the null. Comparable estimates were 0.83 for meta-analyses in PLoS One, 1.02 for top medical journals, 1.54 for top psychology journals, and 4.70 for Metalab. The severity of publication bias did differ across individual meta-analyses; in a small minority (10%; 95% CI: [2%, 21%]), publication bias appeared to favor "significant" results in the expected direction by more than threefold. We estimated that for 89% of meta-analyses, the amount of publication bias that would be required to attenuate the point estimate to the null exceeded the amount of publication bias estimated to be actually present in the vast majority of meta-analyses from the relevant scientific discipline (exceeding the 95th percentile of publication bias). Study-level measures ("statistical significance" with a point estimate in the expected direction and point estimate size) did not indicate more publication bias in higher-tier versus lower-tier journals, nor in the earliest studies published on a topic versus later studies. Overall, we conclude that the mere act of performing a meta-analysis with a large number of studies (at least 40) and that includes non-headline results may largely mitigate publication bias in meta-analyses, suggesting optimism about the validity of meta-analytic results.