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Res Synth Methods. 2016 Mar;7(1):55-79. doi: 10.1002/jrsm.1164. Epub 2015 Sep 2.

Methods to estimate the between-study variance and its uncertainty in meta-analysis.

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Li Ka Shing Knowledge Institute, St. Michael's Hospital, 209 Victoria Street, East Building, Toronto, Ontario, M5B 1T8, Canada.
MRC Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge, CB2 0SR, UK.
Department of Psychiatry and Psychology, School for Mental Health and Neuroscience, Maastricht University, The Netherlands.
Department of Medical Biometry, Institute for Quality and Efficiency in Health Care (IQWiG), Im Mediapark 8, 50670, Cologne, Germany.
MRC Biostatistics Unit Hub for Trials Methodology Research, Cambridge, UK.
Department of Statistics, TU Dortmund University, 44221, Dortmund, Germany.
Institute for Biometrics and Epidemiology, German Diabetes Center, Leibniz Institute for Diabetes Research at Heinrich Heine University, 40225, Düsseldorf, Germany.
School of Social and Community Medicine, University of Bristol, Bristol, UK.
Centre for Reviews and Dissemination, University of York, York, UK.
Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Ioannina, Greece.


Meta-analyses are typically used to estimate the overall/mean of an outcome of interest. However, inference about between-study variability, which is typically modelled using a between-study variance parameter, is usually an additional aim. The DerSimonian and Laird method, currently widely used by default to estimate the between-study variance, has been long challenged. Our aim is to identify known methods for estimation of the between-study variance and its corresponding uncertainty, and to summarise the simulation and empirical evidence that compares them. We identified 16 estimators for the between-study variance, seven methods to calculate confidence intervals, and several comparative studies. Simulation studies suggest that for both dichotomous and continuous data the estimator proposed by Paule and Mandel and for continuous data the restricted maximum likelihood estimator are better alternatives to estimate the between-study variance. Based on the scenarios and results presented in the published studies, we recommend the Q-profile method and the alternative approach based on a 'generalised Cochran between-study variance statistic' to compute corresponding confidence intervals around the resulting estimates. Our recommendations are based on a qualitative evaluation of the existing literature and expert consensus. Evidence-based recommendations require an extensive simulation study where all methods would be compared under the same scenarios.


bias; confidence interval; coverage probability; heterogeneity; mean squared error

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