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The radial plot in meta‐analysis: approximations and applications

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  • John Copas
  • Claudia Lozada‐Can

Abstract

Summary. Fixed effects meta‐analysis can be thought of as least squares analysis of the radial plot, the plot of standardized treatment effect against precision (reciprocal of the standard deviation) for the studies in a systematic review. For example, the least squares slope through the origin estimates the treatment effect, and a widely used test for publication bias is equivalent to testing the significance of the regression intercept. However, the usual theory assumes that the within‐study variances are known, whereas in practice they are estimated. This leads to extra variability in the points of the radial plot which can lead to a marked distortion in inferences that are derived from these regression calculations. This is illustrated by a clinical trials example from the Cochrane database. We derive approximations to the sampling properties of the radial plot and suggest bias corrections to some of the commonly used methods of meta‐analysis. A simulation study suggests that these bias corrections are effective in controlling levels of significance of tests and coverage of confidence intervals.

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  • John Copas & Claudia Lozada‐Can, 2009. "The radial plot in meta‐analysis: approximations and applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 329-344, July.
    • Handle: RePEc:bla:jorssc:v:58:y:2009:i:3:p:329-344
    DOI: 10.1111/j.1467-9876.2008.00650.x
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    Cited by:

    1. Stanley, T. D. & Doucouliagos, Hristos, 2013. "Better than random: weighted least squares meta-regression analysis," Working Papers eco_2013_2, Deakin University, Department of Economics.
    2. Dan Jackson, 2018. "Discussion on Quantifying publication bias in meta‐analysis," Biometrics, The International Biometric Society, vol. 74(3), pages 795-796, September.
    3. John B. Copas & Dan Jackson & Ian R. White & Richard D. Riley, 2018. "The role of secondary outcomes in multivariate meta‐analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1177-1205, November.

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