BackgroundIn meta-analysis, the presence of funnel plot asymmetry is attributed to publication or other small-study effects, which causes larger effects to be observed in the smaller studies. This issue potentially mean inappropriate conclusions are drawn from a meta-analysis. If meta-analysis is to be used to inform decision-making, a reliable way to adjust pooled estimates for potential funnel plot asymmetry is required.MethodsA comprehensive simulation study is presented to assess the performance of different adjustment methods including the novel application of several regression-based methods (which are commonly applied to detect publication bias rather than adjust for it) and the popular Trim & Fill algorithm. Meta-analyses with binary outcomes, analysed on the log odds ratio scale, were simulated by considering scenarios with and without i) publication bias and; ii) heterogeneity. Publication bias was induced through two underlying mechanisms assuming the probability of publication depends on i) the study effect size; or ii) the p-value.ResultsThe performance of all methods tended to worsen as unexplained heterogeneity increased and the number of studies in the meta-analysis decreased. Applying the methods conditional on an initial test for the presence of funnel plot asymmetry generally provided poorer performance than the unconditional use of the adjustment method. Several of the regression based methods consistently outperformed the Trim & Fill estimators.ConclusionRegression-based adjustments for publication bias and other small study effects are easy to conduct and outperformed more established methods over a wide range of simulation scenarios.

Objective To assess the performance of novel contour enhanced funnel plots and a regression based adjustment method to detect and adjust for publication biases. Design Secondary analysis of a published systematic literature review. Data sources Placebo controlled trials of antidepressants previously submitted to the US Food and Drug Administration (FDA) and matching journal publications. Methods Publication biases were identified using novel contour enhanced funnel plots, a regression based adjustment method, Egger's test, and the trim and fill method. Results were compared with a meta-analysis of the gold standard data submitted to the FDA. Results Severe asymmetry was observed in the contour enhanced funnel plot that appeared to be heavily influenced by the statistical significance of results, suggesting publication biases as the cause of the asymmetry. Applying the regression based adjustment method to the journal data produced a similar pooled effect to that observed by a meta-analysis of the FDA data.

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Between-study heterogeneity and publication bias are common features of a meta-analysis that can be present simultaneously. When both are suspected, consideration must be made of each in the assessment of the other. We consider extended funnel plot tests for detecting publication bias, and selection modelling and trim-and-fill methods to adjust for publication bias in the presence of between-study heterogeneity. These methods are applied to two example data sets. Results indicate that ignoring between-study heterogeneity when assessing publication bias can be misleading, but that methods to test or adjust for publication bias in the presence of heterogeneity may not be powerful when the meta-analysis is not large. It is therefore unrealistic to expect to disentangle the effects of publication bias and heterogeneity reliably in all except the largest meta-analyses. Copyright (c) 2010 Royal Statistical Society.

Funnel plots are commonly used to investigate publication and related biases in meta-analysis. Although asymmetry in the appearance of a funnel plot is often interpreted as being caused by publication bias, in reality the asymmetry could be due to other factors that cause systematic differences in the results of large and small studies, for example, confounding factors such as differential study quality. Funnel plots can be enhanced by adding contours of statistical significance to aid in interpreting the funnel plot. If studies appear to be missing in areas of low statistical significance, then it is possible that the asymmetry is due to publication bias. If studies appear to be missing in areas of high statistical significance, then publication bias is a less likely cause of the funnel asymmetry. It is proposed that this enhancement to funnel plots should be used routinely for meta-analyses where it is possible that results could be suppressed on the basis of their statistical significance.