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Exact inference on the random‐effects model for meta‐analyses with few studies

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  • Haben Michael
  • Suzanne Thornton
  • Minge Xie
  • Lu Tian

Abstract

We describe an exact, unconditional, non‐randomized procedure for producing confidence intervals for the grand mean in a normal‐normal random effects meta‐analysis. The procedure targets meta‐analyses based on too few primary studies, ≤7, say, to allow for the conventional asymptotic estimators, e.g., DerSimonian and Laird (1986), or non‐parametric resampling‐based procedures, e.g., Liu et al. (2017). Meta‐analyses with such few studies are common, with one recent sample of 22,453 heath‐related meta‐analyses finding a median of 3 primary studies per meta‐analysis (Davey et al., 2011). Reliable and efficient inference procedures are therefore needed to address this setting. The coverage level of the resulting CI is guaranteed to be above the nominal level, up to Monte Carlo error, provided the meta‐analysis contains more than 1 study and the model assumptions are met. After employing several techniques to accelerate computation, the new CI can be easily constructed on a personal computer. Simulations suggest that the proposed CI typically is not overly conservative. We illustrate the approach on several contrasting examples of meta‐analyses investigating the effect of calcium intake on bone mineral density.

Suggested Citation

  • Haben Michael & Suzanne Thornton & Minge Xie & Lu Tian, 2019. "Exact inference on the random‐effects model for meta‐analyses with few studies," Biometrics, The International Biometric Society, vol. 75(2), pages 485-493, June.
  • Handle: RePEc:bla:biomet:v:75:y:2019:i:2:p:485-493
    DOI: 10.1111/biom.12998
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    Cited by:

    1. Keisuke Hanada & Tomoyuki Sugimoto, 2023. "Inference using an exact distribution of test statistic for random-effects meta-analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 281-302, April.
    2. Fahad M. Al Amer & Christopher G. Thompson & Lifeng Lin, 2021. "Bayesian Methods for Meta-Analyses of Binary Outcomes: Implementations, Examples, and Impact of Priors," IJERPH, MDPI, vol. 18(7), pages 1-14, March.
    3. Bodnar, Olha & Bodnar, Taras, 2021. "Objective Bayesian meta-analysis based on generalized multivariate random effects model," Working Papers 2021:5, Örebro University, School of Business.

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