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Biometrika 2000 87(3):619-632; doi:10.1093/biomet/87.3.619
© 2000 by Biometrika Trust
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Nonparametric estimation of heterogeneity variance for the standardised difference used in meta-analysis

U Malzahn, D Böhning and H HollingZ

Department of Epidemiology, Institute for Social Medicine, Free University of Berlin, Fabeckstr. 60-62, 14195 Berlin, Germany E-mail: malzahn@zedat.fu-berlin.de; boehning@zedat.fu-berlin.de Z Institute of Psychology, University of Münster, Fliednerstraße 21, 48149 Münster, Germany E-mail: holling@psy.uni-muenster.de

The standardised difference has become a frequently used measure of the effect of interest in meta-analysis. Given population heterogeneity, we propose a nonparametric moment estimator for the heterogeneity variance in the corresponding random effects model. The advantages of this approach are threefold. First, it recognises that the specific variances for the individual studies themselves are given in the form of estimates. Secondly, the simple structure of a moment estimator leads to numerical, closed-form expressions. Thirdly, the new estimator appears to behave better than other known estimators. Simulation-free, exact comparisons of the new estimator with the Hedges estimator are provided in terms of bias, variance and mean squared error. Furthermore, by means of a simulation study with unbalanced study sizes we compared the new estimator both with the Hedges estimator and the DerSimonian-Laird estimator.

Key Words: moment estimator; noncentral t-distribution; population heterogeneity; random effects model


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