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Open Access Research article

The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method

Joanna IntHout1*, John PA Ioannidis234 and George F Borm1

Author Affiliations

1 Department for Health Evidence (HEV), Radboud University Medical Center, Huispost 133, P.O. box 9101, Nijmegen, HB 6500, The Netherlands

2 Stanford Prevention Research Center, Department of Medicine, Stanford University School of Humanities and Sciences, Stanford, CA 94305, USA

3 Department of Health Research and Policy, Stanford University School of Medicine, Stanford, CA 94305, USA

4 Department of Statistics, Stanford University School of Humanities and Sciences, Stanford, CA 94305, USA

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BMC Medical Research Methodology 2014, 14:25  doi:10.1186/1471-2288-14-25

Published: 18 February 2014



The DerSimonian and Laird approach (DL) is widely used for random effects meta-analysis, but this often results in inappropriate type I error rates. The method described by Hartung, Knapp, Sidik and Jonkman (HKSJ) is known to perform better when trials of similar size are combined. However evidence in realistic situations, where one trial might be much larger than the other trials, is lacking. We aimed to evaluate the relative performance of the DL and HKSJ methods when studies of different sizes are combined and to develop a simple method to convert DL results to HKSJ results.


We evaluated the performance of the HKSJ versus DL approach in simulated meta-analyses of 2–20 trials with varying sample sizes and between-study heterogeneity, and allowing trials to have various sizes, e.g. 25% of the trials being 10-times larger than the smaller trials. We also compared the number of “positive” (statistically significant at p < 0.05) findings using empirical data of recent meta-analyses with > = 3 studies of interventions from the Cochrane Database of Systematic Reviews.


The simulations showed that the HKSJ method consistently resulted in more adequate error rates than the DL method. When the significance level was 5%, the HKSJ error rates at most doubled, whereas for DL they could be over 30%. DL, and, far less so, HKSJ had more inflated error rates when the combined studies had unequal sizes and between-study heterogeneity. The empirical data from 689 meta-analyses showed that 25.1% of the significant findings for the DL method were non-significant with the HKSJ method. DL results can be easily converted into HKSJ results.


Our simulations showed that the HKSJ method consistently results in more adequate error rates than the DL method, especially when the number of studies is small, and can easily be applied routinely in meta-analyses. Even with the HKSJ method, extra caution is needed when there are = <5 studies of very unequal sizes.

Meta-analysis; Clinical trial; Trial size; Heterogeneity; Type I error; Random effects; Cochrane Database of Systematic Reviews