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The Stata Journal
Volume 12 Number 4: pp. 605-622

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Graphical augmentations to the funnel plot to assess the impact of a new study on an existing meta-analysis

Michael J. Crowther
Department of Health Sciences
University of Leicester
Leicester, UK
Dean Langan
Clinical Trials Research Unit (CTRU)
University of Leeds
Leeds, UK
Alex J. Sutton
Department of Health Sciences
University of Leicester
Leicester, UK
Abstract.  Funnel plots are currently advocated to investigate the presence of publication bias (and other possible sources of bias) in meta-analysis. A previously described augmentation to the funnel plot—to aid its interpretation in assessing publication biases—is the addition of statistical contours indicating regions where studies would have to be for a given level of significance, as implemented in the Stata package confunnel by Palmer et al. (2008, Stata Journal 8: 242–254).

In this article, we describe the implementation of a new range of overlay augmentations to the funnel plot, many described in detail recently by Langan et al. (2012, Journal of Clinical Epidemiology 65: 511–519). The purpose of these overlays is to display the potential impact a new study would have on an existing meta-analysis, providing an indication of the robustness of the meta-analysis to the addition of new evidence. Thus these overlays extend the use of the funnel plot beyond assessments of publication biases. Two main graphical displays are described: 1) statistical significance contours, which define regions of the funnel plot where a new study would have to be located to change the statistical significance of the meta-analysis; and 2) heterogeneity contours, which show how a new study would affect the extent of heterogeneity in a given meta-analysis.

We present the extfunnel command, which implements the methods of Langan et al. (2012, Journal of Clinical Epidemiology 65: 511–519), and, furthermore, we extend the graphical displays to illustrate the impact a new study has on lower and upper confidence interval values and the confidence interval width of the pooled meta-analytic result. We also describe overlays for the impact of a future study on user-defined limits of clinical equivalence. We implement inversevariance weighted methods by using both explicit formulas for contour lines and a simulation approach optimized in Mata.
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