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

BackgroundConventional systematic review techniques have limitations when the aim of a review is to construct a critical analysis of a complex body of literature. This article offers a reflexive account of an attempt to conduct an interpretive review of the literature on access to healthcare by vulnerable groups in the UKMethodsThis project involved the development and use of the method of Critical Interpretive Synthesis (CIS). This approach is sensitised to the processes of conventional systematic review methodology and draws on recent advances in methods for interpretive synthesis.ResultsMany analyses of equity of access have rested on measures of utilisation of health services, but these are problematic both methodologically and conceptually. A more useful means of understanding access is offered by the synthetic construct of candidacy. Candidacy describes how people's eligibility for healthcare is determined between themselves and health services. It is a continually negotiated property of individuals, subject to multiple influences arising both from people and their social contexts and from macro-level influences on allocation of resources and configuration of services. Health services are continually constituting and seeking to define the appropriate objects of medical attention and intervention, while at the same time people are engaged in constituting and defining what they understand to be the appropriate objects of medical attention and intervention. Access represents a dynamic interplay between these simultaneous, iterative and mutually reinforcing processes. By attending to how vulnerabilities arise in relation to candidacy, the phenomenon of access can be better understood, and more appropriate recommendations made for policy, practice and future research.DiscussionBy innovating with existing methods for interpretive synthesis, it was possible to produce not only new methods for conducting what we have termed critical interpretive synthesis, but also a new theoretical conceptualisation of access to healthcare. This theoretical account of access is distinct from models already extant in the literature, and is the result of combining diverse constructs and evidence into a coherent whole. Both the method and the model should be evaluated in other contexts.

Because of appropriate type I error rates and reduction in the correlation between the lnOR and its variance, the alternative regression test can be used in place of Egger's regression test when the summary estimates are lnORs.

Many routinely used summary methods provide widely ranging estimates when applied to sparse data with high imbalance between the size of the studies' arms. A sensitivity analysis using several methods and continuity correction factors is advocated for routine practice.

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Objective To assess the effect of publication bias on the results and conclusions of systematic reviews and meta-analyses. Design Analysis of published meta-analyses by trim and fill method. Studies 48 reviews in Cochrane Database of Systematic Reviews that considered a binary endpoint and contained 10 or more individual studies. Main outcome measures Number of reviews with missing studies and effect on conclusions of meta-analyses. Results The trim and fill fixed effects analysis method estimated that 26 (54%) of reviews had missing studies and in 10 the number missing was significant. The corresponding figures with a random effects model were 23 (48%) and eight. In four cases, statistical inferences regarding the effect of the intervention were changed after the overall estimate for publication bias was adjusted for. Conclusions Publication or related biases were common within the sample of meta-analyses assessed. In most cases these biases did not affect the conclusions. Nevertheless, researchers should check routinely whether conclusions of systematic reviews are robust to possible non-random selection mechanisms.

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