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Exact inference on the random‐effects model for meta‐analyses with few studies
Author(s) -
Michael Haben,
Thornton Suzanne,
Xie Minge,
Tian Lu
Publication year - 2019
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12998
Subject(s) - inference , random effects model , computer science , frequentist inference , meta analysis , econometrics , statistics , mathematics , artificial intelligence , bayesian inference , medicine , bayesian probability
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.