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Contemp Clin Trials. 2015 Nov;45(Pt A):130-8. doi: 10.1016/j.cct.2015.05.009. Epub 2015 May 21.

Advances in the meta-analysis of heterogeneous clinical trials I: The inverse variance heterogeneity model.

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Research School of Population Health, Australian National University, Canberra, Australia. Electronic address:
Epigear International, Sunrise Beach, Australia; School of Population Health, University of Queensland, Brisbane, Australia.
School of Agricultural, Computational and Environmental Sciences, University of Southern Queensland, Toowoomba, Australia.
Department of Community Medicine, Kuwait University, Kuwait.
School of Population Health, University of Queensland, Brisbane, Australia.


This article examines an improved alternative to the random effects (RE) model for meta-analysis of heterogeneous studies. It is shown that the known issues of underestimation of the statistical error and spuriously overconfident estimates with the RE model can be resolved by the use of an estimator under the fixed effect model assumption with a quasi-likelihood based variance structure - the IVhet model. Extensive simulations confirm that this estimator retains a correct coverage probability and a lower observed variance than the RE model estimator, regardless of heterogeneity. When the proposed IVhet method is applied to the controversial meta-analysis of intravenous magnesium for the prevention of mortality after myocardial infarction, the pooled OR is 1.01 (95% CI 0.71-1.46) which not only favors the larger studies but also indicates more uncertainty around the point estimate. In comparison, under the RE model the pooled OR is 0.71 (95% CI 0.57-0.89) which, given the simulation results, reflects underestimation of the statistical error. Given the compelling evidence generated, we recommend that the IVhet model replace both the FE and RE models. To facilitate this, it has been implemented into free meta-analysis software called MetaXL which can be downloaded from


Fixed effect; Heterogeneity; Meta-analysis; Quasi-likelihood; Random effects

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