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The role of secondary outcomes in multivariate meta‐analysis

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  • John B. Copas
  • Dan Jackson
  • Ian R. White
  • Richard D. Riley

Abstract

Univariate meta‐analysis concerns a single outcome of interest measured across a number of independent studies. However, many research studies will have also measured secondary outcomes. Multivariate meta‐analysis allows us to take these secondary outcomes into account and can also include studies where the primary outcome is missing. We define the efficiency E as the variance of the overall estimate from a multivariate meta‐analysis relative to the variance of the overall estimate from a univariate meta‐analysis. The extra information gained from a multivariate meta‐analysis of n studies is then similar to the extra information gained if a univariate meta‐analysis of the primary effect had a further n(1−E)/E studies. The variance contribution of a study's secondary outcomes (its borrowing of strength) can be thought of as a contrast between the variance matrix of the outcomes in that study and the set of variance matrices of all the studies in the meta‐analysis. In the bivariate case this is given a simple graphical interpretation as the borrowing‐of‐strength plot. We discuss how these findings can also be used in the context of random‐effects meta‐analysis. Our discussion is motivated by a published meta‐analysis of 10 antihypertension clinical trials.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:67:y:2018:i:5:p:1177-1205
    DOI: 10.1111/rssc.12274
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    References listed on IDEAS

    as
    1. 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.
    2. Han Chen & Alisa K. Manning & Josée Dupuis, 2012. "A Method of Moments Estimator for Random Effect Multivariate Meta-Analysis," Biometrics, The International Biometric Society, vol. 68(4), pages 1278-1284, December.
    3. Richard D. Riley, 2009. "Multivariate meta‐analysis: the effect of ignoring within‐study correlation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(4), pages 789-811, October.
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    1. Manpreet Blessin & Sophie Lehmann & Angela M. Kunzler & Rolf van Dick & Klaus Lieb, 2022. "Resilience Interventions Conducted in Western and Eastern Countries—A Systematic Review," IJERPH, MDPI, vol. 19(11), pages 1-25, June.

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