UMMS Affiliation

Department of Population and Quantitative Health Sciences

Publication Date


Document Type



Statistics and Probability


Methods for random-effects meta-analysis require an estimate of the between-study variance, tau(2) . The performance of estimators of tau(2) (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study-level effects and also the performance of related estimators of the overall effect. However, as we show, the performance of the methods varies widely among effect measures. For the effect measures mean difference (MD) and standardized MD (SMD), we use improved effect-measure-specific approximations to the expected value of Q for both MD and SMD to introduce two new methods of point estimation of tau(2) for MD (Welch-type and corrected DerSimonian-Laird) and one WT interval method. We also introduce one point estimator and one interval estimator for tau(2) in SMD. Extensive simulations compare our methods with four point estimators of tau(2) (the popular methods of DerSimonian-Laird, restricted maximum likelihood, and Mandel and Paule, and the less-familiar method of Jackson) and four interval estimators for tau(2) (profile likelihood, Q-profile, Biggerstaff and Jackson, and Jackson). We also study related point and interval estimators of the overall effect, including an estimator whose weights use only study-level sample sizes. We provide measure-specific recommendations from our comprehensive simulation study and discuss an example.


between-study variance, mean difference, meta-analysis, random-effects model, standardized mean difference

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© 2019 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution, and reproduction in any medium, provided the original work is properly cited.

DOI of Published Version



Stat Med. 2020 Jan 30;39(2):171-191. doi: 10.1002/sim.8422. Epub 2019 Nov 11. Link to article on publisher's site

Journal/Book/Conference Title

Statistics in medicine

PubMed ID


Related Resources

Link to Article in PubMed

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.