Funnel plots, and tests for funnel plot asymmetry, have been widely used to examine bias in the results of meta-analyses. Funnel plot asymmetry should not be equated with publication bias, because it has a number of other possible causes. This article describes how to interpret funnel plot asymmetry, recommends appropriate tests, and explains the implications for choice of meta-analysis model This article recommends how to examine and interpret funnel plot asymmetry (also known as small study effects 2 ) in meta-analyses of randomised controlled trials. The recommendations are based on a detailed MEDLINE review of literature published up to 2007 and discussions among methodologists, who extended and adapted guidance previously summarised in the Cochrane Handbook for Systematic Reviews of Interventions. 7 What is a funnel plot?A funnel plot is a scatter plot of the effect estimates from individual studies against some measure of each study's size or precision. The standard error of the effect estimate is often chosen as the measure of study size and plotted on the vertical axis 8 with a reversed scale that places the larger, most powerful studies towards the top. The effect estimates from smaller studies should scatter more widely at the bottom, with the spread narrowing among larger studies. 9 In the absence of bias and between study heterogeneity, the scatter will be due to sampling variation alone and the plot will resemble a symmetrical inverted funnel (fig 1). A triangle centred on a fixed effect summary estimate and extending 1.96 standard errors either side willCorrespondence to: J A C Sterne jonathan.sterne@bristol.ac.ukTechnical appendix (see

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Among patients with degenerative grade I spondylolisthesis, the addition of lumbar spinal fusion to laminectomy was associated with slightly greater but clinically meaningful improvement in overall physical health-related quality of life than laminectomy alone. (Funded by the Jean and David Wallace Foundation and others; SLIP ClinicalTrials.gov number, NCT00109213.).

It is known that the existence of publication bias can influence the conclusions of a meta-analysis. Some methods have been developed to deal with publication bias, but issues remain. One particular method called 'trim and fill' is designed to adjust for publication bias. The method, which is intuitively appealing and comprehensible by non-statisticians, is based on a simple and popular graphical tool called the funnel plot. We present a simulation study designed to evaluate the behaviour of this method. Our results indicate that when the studies are heterogeneous (that is, when they estimate different effects), trim and fill may inappropriately adjust for publication bias where none exists. We found that trim and fill may spuriously adjust for non-existent bias if (i) the variability among studies causes some precisely estimated studies to have effects far from the global mean or (ii) an inverse relationship between treatment efficacy and sample size is introduced by the studies' a priori power calculations. The results suggest that the funnel plot itself is inappropriate for heterogeneous meta-analyses. Selection modelling is an alternative method warranting further study. It performed better than trim and fill in our simulations, although its frequency of convergence varied, depending on the simulation parameters.

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