Quantifying the risk of error when interpreting funnel plots

Abstract

Funnel plots are widely used to investigate possible publication bias in meta-analyses. There has, however, been little formal assessment of whether a visual inspection of a funnel plot is sufficient to identify publication bias. Visual assessment of bias in a funnel plot is quantified using two new statistics: the Imbalance and the Asymmetry Distance, both intended to replicate how a funnel plot is typically assessed. A simulation study was performed to assess the performance of these two statistics for identifying publication bias. The two statistics both have high type I error and low statistical power, unless the number of studies in the meta-analysis is very large. These results suggest that visual inspection of a funnel plot is unlikely to lead to a valid assessment of publication bias. In most systematic reviews, visual inspection of a funnel plot may give a misleading impression of the presence or absence of publication bias. Formal statistical tests for bias should generally be preferred.