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

Haben Michael, Suzanne Thornton, Minge Xie, Lu Tian

Research output: Contribution to journalArticle

1 Scopus citations


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, (Formula presented.), 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.

Original languageEnglish (US)
Pages (from-to)485-493
Number of pages9
Issue number2
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Agricultural and Biological Sciences(all)
  • Applied Mathematics
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Statistics and Probability


  • bone mineral density
  • exact inference
  • meta-analysis
  • small-sample

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