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Funnel plots in meta-analysis

Author

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  • Jonathan A.C. Sterne

    (Department of Social Medicine, University of Bristol)

  • Roger M. Harbord

    (Department of Social Medicine, University of Bristol)

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. Copyright 2004 by StataCorp LP.

Suggested Citation

  • Jonathan A.C. Sterne & Roger M. Harbord, 2004. "Funnel plots in meta-analysis," Stata Journal, StataCorp LP, vol. 4(2), pages 127-141, June.
  • Handle: RePEc:tsj:stataj:v:4:y:2004:i:2:p:127-141
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    References listed on IDEAS

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    1. Thomas J. Steichen & Matthias Egger & Jonathan Sterne, 1999. "Tests for publication bias in meta-analysis," Stata Technical Bulletin, StataCorp LP, vol. 8(44).
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    Cited by:

    1. Ugur, Mehmet & Awaworyi, Sefa & Solomon, Edna, 2016. "Technological innovation and employment in derived labour demand models: A hierarchical meta-regression analysis," MPRA Paper 73557, University Library of Munich, Germany.
    2. Michael J. Crowther & Dean Langan & Alex J. Sutton, 2012. "Graphical augmentations to the funnel plot to assess the impact of a new study on an existing meta-analysis," Stata Journal, StataCorp LP, vol. 12(4), pages 605-622, December.
    3. Ugur, Mehmet & Trushin, Eshref & Solomon, Edna & Guidi, Francesco, 2016. "R&D and productivity in OECD firms and industries: A hierarchical meta-regression analysis," Research Policy, Elsevier, vol. 45(10), pages 2069-2086.
    4. Neisser, Carina, 2017. "The elasticity of taxable income: A meta-regression analysis," ZEW Discussion Papers 17-032, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    5. Galindo, Luis Miguel & Samaniego, Joseluis & Ferrer, Jimy & Alatorre, José Eduardo & Reyes, Orlando, 2016. "Cambio climático, políticas públicas y demanda de energía y gasolinas en América Latina: un meta-análisis," Documentos de Proyectos 718, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    6. repec:eee:wdevel:v:96:y:2017:i:c:p:1-18 is not listed on IDEAS
    7. Soon, Jan-Jan & Ahmad, Siti-Aznor, 2015. "Willingly or grudgingly? A meta-analysis on the willingness-to-pay for renewable energy use," Renewable and Sustainable Energy Reviews, Elsevier, vol. 44(C), pages 877-887.
    8. Wamisho, Kassu, 2013. "A Meta Regression Analysis of Soil Organic Carbon Sequestration in Corn Belt States: Implication for Cellulosic Biofuel Production," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149741, Agricultural and Applied Economics Association.
    9. Asim,Salman & Chase,Robert S. & Dar,Amit & Schmillen,Achim Daniel, 2015. "Improving education outcomes in South Asia : findings from a decade of impact evaluations," Policy Research Working Paper Series 7362, The World Bank.
    10. Roger M. Harbord & Ross J. Harris & Jonathan A. C. Sterne, 2009. "Updated tests for small-study effects in meta-analyses," Stata Journal, StataCorp LP, vol. 9(2), pages 197-210, June.
    11. Tom M. Palmer & Jaime L. Peters & Alex J. Sutton & Santiago G. Moreno, 2008. "Contour-enhanced funnel plots for meta-analysis," Stata Journal, StataCorp LP, vol. 8(2), pages 242-254, June.
    12. Smith, William C. & Anderson, Emily & Salinas, Daniel & Horvatek, Renata & Baker, David P., 2015. "A meta-analysis of education effects on chronic disease: The causal dynamics of the Population Education Transition Curve," Social Science & Medicine, Elsevier, vol. 127(C), pages 29-40.

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