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A re-evaluation of random-effects meta-analysis


  • Julian P. T. Higgins
  • Simon G. Thompson
  • David J. Spiegelhalter


Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to "a priori" judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of 'set shifting' ability in people with eating disorders. Copyright Journal compilation (c) 2009 Royal Statistical Society.

Suggested Citation

  • Julian P. T. Higgins & Simon G. Thompson & David J. Spiegelhalter, 2009. "A re-evaluation of random-effects meta-analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 137-159.
  • Handle: RePEc:bla:jorssa:v:172:y:2009:i:1:p:137-159

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    References listed on IDEAS

    1. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    2. Sander Greenland, 2005. "Multiple-bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306.
    3. Deborah Burr & Hani Doss, 2005. "A Bayesian Semiparametric Model for Random-Effects Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 242-251, March.
    4. Mark G. Vangel & Andrew L. Rukhin, 1999. "Maximum Likelihood Analysis for Heteroscedastic One-Way Random Effects ANOVA in Interlaboratory Studies," Biometrics, The International Biometric Society, vol. 55(1), pages 129-136, March.
    5. Dean A. Follmann & Michael A. Proschan, 1999. "Valid Inference in Random Effects Meta-Analysis," Biometrics, The International Biometric Society, vol. 55(3), pages 732-737, September.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Stephen W. Raudenbush & Anthony S. Bryk, 1985. "Empirical Bayes Meta-Analysis," Journal of Educational and Behavioral Statistics, , vol. 10(2), pages 75-98, June.
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    Cited by:

    1. Yip, Paul S.F. & Yousuf, Saman & Chan, Chee Hon & Yung, Tiffany & Wu, Kevin C.-C., 2015. "The roles of culture and gender in the relationship between divorce and suicide risk: A meta-analysis," Social Science & Medicine, Elsevier, vol. 128(C), pages 87-94.
    2. Takahiro Hasegawa & Brian Claggett & Lu Tian & Scott D. Solomon & Marc A. Pfeffer & Lee-Jen Wei, 0. "The Myth of Making Inferences for an Overall Treatment Efficacy with Data from Multiple Comparative Studies Via Meta-Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-14.
    3. repec:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-016-9507-z is not listed on IDEAS
    4. repec:ags:stataj:180080 is not listed on IDEAS
    5. repec:spr:stabio:v:9:y:2017:i:1:d:10.1007_s12561-016-9179-3 is not listed on IDEAS
    6. Yeojin Chung & Sophia Rabe-Hesketh & Vincent Dorie & Andrew Gelman & Jingchen Liu, 2013. "A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 685-709, October.
    7. repec:eee:csdana:v:113:y:2017:i:c:p:100-110 is not listed on IDEAS
    8. Ian R. White, 2011. "Multivariate random-effects meta-regression: Updates to mvmeta," Stata Journal, StataCorp LP, vol. 11(2), pages 255-270, June.
    9. repec:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0728-0 is not listed on IDEAS
    10. Tomáš Havránek, 2009. "Rose Effect and the Euro: The Magic is Gone," Working Papers IES 2009/20, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Aug 2009.

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