Funnel plots in meta–analysis
Jonathan A. C. Sterne
Department of Social Medicine, University of Bristol
Canynge Hall, Whiteladies Road, Bristol BS8 2PR UK
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Roger M. Harbord
Department of Social Medicine, University of Bristol
Canynge Hall, Whiteladies Road, Bristol BS8 2PR UK
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Abstract. Funnel plots are a visual tool for investigating publication and other bias
in meta-analysis. They are simple scatterplots of the treatment effects
estimated from individual studies (horizontal axis) against a measure of
study size (vertical axis). The name “funnel plot” is based on
the precision in the estimation of the underlying treatment effect
increasing as the sample size of component studies increases. Therefore, in
the absence of bias, results from small studies will scatter widely at the
bottom of the graph, with the spread narrowing among larger studies.
Publication bias (the association of publication probability with the
statistical significance of study results) may lead to asymmetrical funnel
plots. It is, however, important to realize that publication bias is only
one of a number of possible causes of funnel-plot asymmetry—funnel
plots should be seen as a generic means of examining small study effects
(the tendency for the smaller studies in a meta-analysis to show larger
treatment effects) rather than a tool to diagnose specific types of bias.
This article introduces the metafunnel command, which produces funnel
plots in Stata. In accordance with published recommendations, standard error
is used as the measure of study size. Treatment effects expressed as ratio
measures (for example risk ratios or odds ratios) may be plotted on a log
scale.
View all articles by these authors:
Jonathan A. C. Sterne, Roger M. Harbord
View all articles with these keywords:
metafunnel, funnel plots, meta-analysis, publication bias, small-study effects
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