Funnel plots for detecting bias in meta-analysis: guidelines on choice of axis

Abstract

Asymmetry in funnel plots may indicate publication bias in meta-analysis, but the shape of the plot in the absence of bias depends on the choice of axes. We evaluated standard error, precision (inverse of standard error), variance, inverse of variance, sample size and log sample size (vertical axis) and log odds ratio, log risk ratio and risk difference (horizontal axis). Standard error is likely to be the best choice for the vertical axis: the expected shape in the absence of bias corresponds to a symmetrical funnel, straight lines to indicate 95% confidence intervals can be included and the plot emphasises smaller studies which are more prone to bias. Precision or inverse of variance is useful when comparing meta-analyses of small trials with subsequent large trials. The use of sample size or log sample size is problematic because the expected shape of the plot in the absence of bias is unpredictable. We found similar evidence for asymmetry and between trial variation in a sample of 78 published meta-analyses whether odds ratios or risk ratios were used on the horizontal axis. Different conclusions were reached for risk differences and this was related to increased between-trial variation. We conclude that funnel plots of meta-analyses should generally use standard error as the measure of study size and ratio measures of treatment effect.