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A comparison of heterogeneity variance estimators in simulated random‐effects meta‐analyses
Open accessAbstract
Studies combined in a meta‐analysis often have differences in their design and conduct that can lead to heterogeneous results. A random‐effects model accounts for these differences in the underlying study effects, which includes a heterogeneity variance parameter. The DerSimonian‐Laird method is often used to estimate the heterogeneity variance, but simulation studies have found the method can be biased and other methods are available. This paper compares the properties of nine different heterogeneity variance estimators using simulated meta‐analysis data. Simulated scenarios include studies of equal size and of moderate and large differences in size. Results confirm that the DerSimonian‐Laird estimator is negatively biased in scenarios with small studies and in scenarios with a rare binary outcome. Results also show the Paule‐Mandel method has considerable positive bias in meta‐analyses with large differences in study size. We recommend the method of restricted maximum likelihood (REML) to estimate the heterogeneity variance over other methods. However, considering that meta‐analyses of health studies typically contain few studies, the heterogeneity variance estimate should not be used as a reliable gauge for the extent of heterogeneity in a meta‐analysis. The estimated summary effect of the meta‐analysis and its confidence interval derived from the Hartung‐Knapp‐Sidik‐Jonkman method are more robust to changes in the heterogeneity variance estimate and show minimal deviation from the nominal coverage of 95% under most of our simulated scenarios.
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“Meta-analysis was conducted using a random-effect model with restricted maximum likelihood, as the estimator of true heterogeneity, which seems to provide us with less biased estimates than other methods.33”
From Psychological interventions for depression and anxiety: a systematic review and meta-analysis of Iranian chronic pain trials. (2020) · cites this paper as [33]
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“For random-effects models, many methods are available, and their performance has been shown to differ depending on the characteristics of the meta-analysis (such as the number and size of the included studies113 114).”
From PRISMA 2020 explanation and elaboration: updated guidance and exemplars for reporting systematic reviews (2021) · cites this paper as [114]
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“a random-effects model typically cannot adequately estimate heterogeneity with only two effects (Langan et al., 2019)”
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“This method assumes a t-distribution of the pooled effect rather than a normal distribution, which reduces the chance of obtaining false-positive results (Langan et al., 2019).”
From The state of hiring discrimination: A meta-analysis of (almost) all recent correspondence experiments (2023) · cites this paper as Langan et al., 2019
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Lee, E. W.-Y., Cheung, C. W., Wang, L., Wang, F., & Ho, H. C. (2026) · Global Health Research and Policy · doi:10.1016/j.ghrp.2026.05.002
“28 The secondary outcome is obtained from the subgroup analysis subsequently conducted, in which demographic characteristics, location(s) of pain and geographical characteristics were used as proxies for the general socioeconomic status of the surveyed population.”
Boesjes, C. M., de Bruin-Weller, M. S., Zuithoff, N. P. A., el Bouhaddani, S., Haeck, I. M., Kamsteeg, M., Schuttelaar, M. L. A., Treust, L. L., Denholm, N., Akkoç, A., et al. (2026) · Acta Dermato Venereologica · doi:10.2340/actadv.v106.adv-2025-0231
“In all results, the heterogeneity estimates (i.e. CIs of I 2 and tau 2 values) were uncertain with a wide confidence interval, likely related to the low number of studies in this meta analyses (21).”
Ferraz, J. S., & Ribeiro, J. R. I. (2026) · Revista Brasileira de Botânica · doi:10.1007/s40415-026-01155-1
“…fitted a random-effects model (Hedges and Vevea 1998; Borenstein et al. 2009) using the restricted maximum likelihood (REML) estimation (Viechtbauer 2005) and applied Knapp–Hartung adjustments to obtain conservative standard errors (Higgins et al. 2002; Knapp and Hartung 2003; Langan et al. 2019).”
Kranes, M., Münchenberg, P. S., Thomas, C., Schulz, R. S., Campione, A., & Kreutzberg, A. (2026) · Journal of Eating Disorders · doi:10.1186/s40337-026-01660-4
“Following current best-practice recommendations [113, 114], between-study variance was estimated using a restricted maximum likelihood method [115].”
Sokol, R. L., Victor, B. G., Esposti, M. D., Toro, V. M. D., Kernsmith, P. D., Stearns, D. R., Portugal, J., & Heinze, J. E. (2026) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2026.108161
Sotiriadis, A., Tsakiri, I., Papapanou, M., Toulaki, M., Bourou, M. Z., & Siristatidis, C. S. (2026) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd016355
Honda, H., Miwa, T., Warren, D. K., & Takamatsu, A. (2026) · Antimicrobial Stewardship & Healthcare Epidemiology · doi:10.1017/ash.2026.10742
Jan, A., Waheed, B., Hussein, G. A., Pandey, P., Sulthana, H., Kumar, S., & Dagnaw, M. (2026) · Journal of Paediatrics and Child Health · doi:10.1111/jpc.70470
“An I 2 value greater than 50% was considered indicative of substantial heterogeneity [21, 22].”
Zhu, Z. D. J. D., Mao, Y., Fan, Y., Zhu, Z., Xie, L., & Huang, C. (2026) · Frontiers in Medicine · doi:10.3389/fmed.2026.1848571
“…protocol specified the DerSimonian-Laird (DL) estimator; however, based on recent methodological recommendations, we adopted REML as the primary estimator because it provides more accurate estimates of between-study variance under conditions of high heterogeneity or a small number of studies (32).”
Statistical Methods for Assessing Non-Replicable, Outlying, and Influential Studies
Yang, Y., & Nakagawa, S. (2026) · Mathematics · doi:10.3390/math14193436
“We further clarify that Xiao et al. (2024) incorrectly claim that the restricted maximum likelihood (REML) estimator has the best performance in most settings.”
InfluentialAlaycı, B., & Gerçek, Ö. Z. (2026) · BMC Endocrine Disorders · doi:10.21203/rs.3.rs-9973131/v1
Abdurakhmanova, E. G., Bolatbek, A., Zholshybek, N., Mustafa, Z., Almazan, J. U., & Bolla, S. R. (2026) · BMJ Open · doi:10.1136/bmjopen-2026-117491
A Meta‐Analysis of Self–Other Differences in Prejudice
Narciso, S., Mendonça, C., & Mata, A. (2026) · European Journal of Social Psychology · doi:10.1002/ejsp.70094
Taira, N., Nishiwaki, H., Yamaji, N., Takami, R., Noma, H., Ota, E., Levack, W., Hasegawa, T., & Transplant, S. B. C. K. A. (2026) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd016365
Xiao, Y., Xie, P., Li, D., Zhao, T., & Nie, J. (2026) · Psychiatry Research · doi:10.1016/j.psychres.2026.117318
Anemia burden in tuberculosis patients across Southeast Asia: a systematic review and meta-analysis
Shrivastav, V. N., Akurathi, H. K., Kalariya, H., & Savaj, D. (2026) · BMC Pulmonary Medicine · doi:10.1186/s12890-026-04404-x
“…estimating between-study variance (τ²) as it provides more accurate confidence intervals for prevalence meta-analyses, particularly in the presence of high heterogeneity, and has been shown to outperform traditional methods like DerSimonian-Laird in simulation studies (Langan et al., 2019) [37].”
Deng, Y.-H., Liu, Q., & Luo, X.-Q. (2026) · Journal of Human Hypertension · doi:10.1038/s41371-026-01180-3
Kim, S., Oda, H., Oyama, R., Makishi, R., Bade, S., Bade, S., Ally, I., Iijima, Y., Gibo, Y., Minami, K., et al. (2026) · BJPsych Open · doi:10.1192/bjo.2026.12044
“18 Wald-type confidence intervals will be used by default for pooled estimates.”
Montero, J. A. (2026) · European Journal of Clinical Pharmacology · doi:10.1007/s00228-026-04136-1
Metadata
- Authors
- Langan, D., Higgins, J. P. T., Jackson, D., Bowden, J., Veroniki, A. A., Kontopantelis, E., Viechtbauer, W., & Simmonds, M.
- Affiliations
- University of Manchester (GB)
- University of Bristol (GB)
- AstraZeneca (United Kingdom) (GB)
- St. Michael's Hospital (CA)
- Maastricht University (NL)
- University of York (GB)
- Corresponding author
- Langan, Dean
- ORCID
- Venue
- Research Synthesis Methods
- Publisher
- Wiley
- Published
- 2018-09-06
- Volume
- 10
- Issue
- 1
- Pages
- 83-98
- ISSN
- 1759-2879 (ISSN-L)
- 1759-2887
- OpenAlex
- W2885675882
- Semantic Scholar
- 264ababb39dc4b8737425a30c9fb75c5d8eb2bf4
- Cited by
- 1,074
- References
- 51
- Citations by year
- 2026: 214 · 2025: 173 · 2024: 198 · 2023: 144 · 2022: 140 · 2021: 113 · 2020: 60 · 2019: 28 · 2018: 2
- FWCI
- 38.65
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Research Synthesis Methods (publishedVersion)
- PubMed (publishedVersion)
- Research Publications (Maastricht University) (publishedVersion, other-oa)
- Research Explorer (The University of Manchester) (publishedVersion, other-oa)
- White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (submittedVersion)
- Bristol Research (University of Bristol) (submittedVersion, other-oa)
- UCL Discovery (University College London) (submittedVersion)
- Research Publications (Maastricht University) (submittedVersion, other-oa)
- Funders
- National Institute for Health and Care Research (NF-SI-0617-10145)
- Medical Research Council (MC_UU_00011/2, MR/K006665/1)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- random-effects meta-analysis, estimation bias, binary outcomes, confidence interval coverage
- MeSH terms
- Systematic Reviews as Topic, Algorithms, Analysis of Variance, Computer Simulation, Data Interpretation, Statistical, Humans, Probability, Research Design, Software, Meta-Analysis as Topic, Reproducibility of Results, Models, Statistical, Selection Bias, Likelihood Functions, Odds Ratio
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