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Correction for bias in meta-analysis of little-replicated studies.

ABSTRACT: Meta-analyses conventionally weight study estimates on the inverse of their error variance, in order to maximize precision. Unbiased variability in the estimates of these study-level error variances increases with the inverse of study-level replication. Here, we demonstrate how this variability accumulates asymmetrically across studies in precision-weighted meta-analysis, to cause undervaluation of the meta-level effect size or its error variance (the meta-effect and meta-variance).Small samples, typical of the ecological literature, induce big sampling errors in variance estimation, which substantially bias precision-weighted meta-analysis. Simulations revealed that biases differed little between random- and fixed-effects tests. Meta-estimation of a one-sample mean from 20 studies, with sample sizes of 3-20 observations, undervalued the meta-variance by c. 20%. Meta-analysis of two-sample designs from 20 studies, with sample sizes of 3-10 observations, undervalued the meta-variance by 15%-20% for the log response ratio (lnR); it undervalued the meta-effect by c. 10% for the standardized mean difference (SMD).For all estimators, biases were eliminated or reduced by a simple adjustment to the weighting on study precision. The study-specific component of error variance prone to sampling error and not parametrically attributable to study-specific replication was replaced by its cross-study mean, on the assumptions of random sampling from the same population variance for all studies, and sufficient studies for averaging. Weighting each study by the inverse of this mean-adjusted error variance universally improved accuracy in estimation of both the meta-effect and its significance, regardless of number of studies. For comparison, weighting only on sample size gave the same improvement in accuracy, but could not sensibly estimate significance.For the one-sample mean and two-sample lnR, adjusted weighting also improved estimation of between-study variance by DerSimonian-Laird and REML methods. For random-effects meta-analysis of SMD from little-replicated studies, the most accurate meta-estimates obtained from adjusted weights following conventionally weighted estimation of between-study variance.We recommend adoption of weighting by inverse adjusted-variance for meta-analyses of well- and little-replicated studies, because it improves accuracy and significance of meta-estimates, and it can extend the scope of the meta-analysis to include some studies without variance estimates.

SUBMITTER: Doncaster CP

PROVIDER: S-EPMC5993351 | biostudies-literature | 2018 Mar

REPOSITORIES: biostudies-literature

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Correction for bias in meta-analysis of little-replicated studies.

Doncaster C Patrick CP Spake Rebecca R

Methods in ecology and evolution 20171121 3

Meta-analyses conventionally weight study estimates on the inverse of their error variance, in order to maximize precision. Unbiased variability in the estimates of these study-level error variances increases with the inverse of study-level replication. Here, we demonstrate how this variability accumulates asymmetrically across studies in precision-weighted meta-analysis, to cause undervaluation of the meta-level effect size or its error variance (the meta-effect and meta-variance).Small samples ...[more]

PMID: 29938012

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Project description: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.

Dataset Information

Correction for bias in meta-analysis of little-replicated studies.

Publications

Correction for bias in meta-analysis of little-replicated studies.

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