The DOI matches its Crossref record; 52 of the 52 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“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]
The cited source says what the claim attributes to it.
In the citing paper
“a random-effects model typically cannot adequately estimate heterogeneity with only two effects (Langan et al., 2019)”
From Investigating the replicability of preclinical cancer biology (2021) · cites this paper as Langan et al., 2019
The cited source says what the claim attributes to it.
In the citing paper
“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
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Meta-analysis in clinical trials
DerSimonian, R., & Laird, N. (1986) · Controlled Clinical Trials · doi:10.1016/0197-2456(86)90046-2 · Cited by 39,552
Quantifying heterogeneity in a meta‐analysis
Higgins, J. P. T., & Thompson, S. G. (2002) · Statistics in Medicine · doi:10.1002/sim.1186 · Cited by 36,763
Self-citationConducting Meta-Analyses in R with the metafor Package
Viechtbauer, W. (2010) · Journal of Statistical Software · doi:10.18637/jss.v036.i03 · Cited by 20,464
Self-citationBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009) · doi:10.1002/9780470743386 · Cited by 14,225
Self-citationBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2021) · doi:10.1002/9781119558378 · Cited by 9,799
Self-citationHunter, J., & Schmidt, F. (2004) · doi:10.4135/9781412985031 · Cited by 3,023
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
Harville, D. A. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10480998 · Cited by 2,667
IntHout, J., Ioannidis, J. P., & Borm, G. F. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-25 · Cited by 2,419
Random-effects model for meta-analysis of clinical trials: An update
DerSimonian, R., & Kacker, R. (2007) · Contemporary Clinical Trials · doi:10.1016/j.cct.2006.04.004 · Cited by 2,374
Improved tests for a random effects meta‐regression with a single covariate
Knapp, G., & Hartung, J. (2003) · Statistics in Medicine · doi:10.1002/sim.1482 · Cited by 2,075
Flagged first, then by citations
Cited by
Sorted by citations
Items 501–600 of 1,000
Crespo, M. D. A., Byström, C., Tyraskis, A., Mutanen, A., Stenström, P., Hartman, E., Danielsson, J., Eaton, S. D., Coppi, P. D., Granström, A. L., et al. (2025) · BJS Open · doi:10.1093/bjsopen/zraf107 · Cited by 8
“The restricted maximum likelihood random-effects model with logit transformation was used to minimize bias 21–24 .”
Effects of Artificial Intelligence on Educational Functioning: A Review and Meta-Analysis
Yeo, G., & Lansford, J. E. (2025) · Educational Psychology Review · doi:10.1007/s10648-025-10085-5 · Cited by 16
Hilbert, J., Topfstedt, F., Matuschik, L., Schmitt, L., Panzeri, I., Pospisilik, J. A., & Seifert, G. J. (2026) · European Journal of Epidemiology · doi:10.1007/s10654-025-01359-x · Cited by 7
Sieczkowska, S. M., Mazzolani, B. C., Coimbra, D. R., Longobardi, I., Casale, A. R., da Hora, J. D. F. V. M. P., Roschel, H., & Gualano, B. (2026) · British Journal of Sports Medicine · doi:10.1136/bjsports-2025-110239 · Cited by 9
“Simulation studies 21–23 have demonstrated that the HKSJ method offers improved coverage probabilities compared with the conventional random-effects model.”
Asakawa-Haas, K. D., Spiegel, D., Bossert, L., Garić, A., Schwartz, K., Voracek, M., & Tran, U. S. (2026) · Communications Psychology · doi:10.1038/s44271-026-00414-x · Cited by 9
“Clinical (substantive and methodological) heterogeneity among primary studies was accounted for with a random-effects (RE) meta-analytic modelusingtherestrictedmaximum-likelihood(REML)estimator,asithas themostreasonablepropertiestoestimatetheoveralleffect 38,98,99 .”
Zhu, R., Wang, L., Chen, H., Ren, J., Wang, R., Gong, Y., Guan, Y., Wang, Q., Liu, M., Xu, Z., et al. (2026) · Advances in Nutrition · doi:10.1016/j.advnut.2026.100666 · Cited by 7
“The restricted maximum likelihood method was used to calculate between-study (heterogeneity) variance estimator, because the latter may be negatively biased in scenarios with small studies and in scenarios with a rare dichotomous outcome [23].”
S-ACRISS R: Slovak adaptation of the action crisis scale
Kačmár, P., Wolf, B. M., Bavoľár, J., Schrötter, J., & Lovaš, L. (2022) · Current Psychology · doi:10.1007/s12144-022-02955-w · Cited by 7
An automated process for supporting decisions in clustering-based data analysis
Bernabé-Díaz, J. A., Franco, M., Vivo, J.-M., Quesada-Martínez, M., & Fernández‐Breis, J. T. (2022) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2022.106765 · Cited by 7
Wang, Z., Alzuabi, M. A., Morgan, R. L., Mustafa, R. A., Falck-Ytter, Y. T., Dahm, P., Sultan, S., & Murad, M. H. (2023) · BMJ Evidence-Based Medicine · doi:10.1136/bmjebm-2022-112053 · Cited by 7
Sentenac, M., Twilhaar, E. S., Benhammou, V., Morgan, A. S., Johnson, S. J., Chaimani, A., & Zeitlin, J. A. (2023) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.12957 · Cited by 8
Faggion, C. M., Atieh, M. A., Tsagris, M., Seehra, J., & Pandis, N. (2023) · European Journal Of Oral Sciences · doi:10.1111/eos.12962 · Cited by 7
Nguyen, T. T. B., Hsu, Y.-Y. A., & Sari, Y. P. (2024) · Journal of Nursing Research · doi:10.1097/jnr.0000000000000597 · Cited by 7
Belloni, S., Tiberio, P., Sanctis, R. D., Magon, A., Santoro, A., Zambelli, A., Caruso, R., & Arrigoni, C. (2024) · Critical Reviews in Oncology/Hematology · doi:10.1016/j.critrevonc.2024.104527 · Cited by 8
Yang, Y., Thackray, A. E., Shen, T., Alotaibi, T. F., Alanazi, T. M., Clifford, T., Hartescu, I., King, J. A., Roberts, M. J., Willis, S. A., et al. (2024) · SLEEP · doi:10.1093/sleep/zsae250 · Cited by 7
“The restricted maximum-likelihood estimation method determined the tau-statistic ( τ ) value describing the between-participant, replicate-averaged treatment effect response variability across the distribution of true acute exercise-related effects [51, 52].”
Ezenna, C. G., Krishna, M. M., Joseph, M., Pereira, V., Nadeem, S., Valania, G. E., & Goldsweig, A. M. (2025) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2025.01.016 · Cited by 7
Beck depression inventory-II: A study for meta analytical reliability generalization
Mehmet Taha, E. S. E. R., & Aksu, G. (2021) · Pegem Journal of Education and Instruction · Cited by 7
Siontis, K. C., Balla, A. K., Cha, Y., Pilgrim, T., Sweda, R., Roten, L., Reichlin, T., Friedman, P. A., Windecker, S., & Siontis, G. C. M. (2022) · Heart Rhythm O2 · doi:10.1016/j.hroo.2022.10.007 · Cited by 7
“Rubin et al(21) 18 4 (22) 3 before hospital discharge and 1 at 10 d Akin et al(22) 45 10 (22) Within 7 d post-TAVI Eksik et al(23) 28 1 (4) Before hospital discharge Rivard et al(24) 75 14 (19) Median 2 d (range 0– 30) Shin et al(25) 25 8 (32) Before hospital discharge Eksik et al(26) 55 8 (15) Before hospital dischar…”
BackgroundA Note on Cherry-Picking in Meta-Analyses
Yoneoka, D., & Rieck, B. (2023) · Entropy · doi:10.3390/e25040691 · Cited by 7
Shamim, M. A., Manna, S., Dwivedi, P., Swami, M. K., Sahoo, S., Shukla, R. K. G., Srivastav, S., Thaper, K., Saravanan, A., Anil, A., et al. (2023) · Medicine · doi:10.1097/md.0000000000035937 · Cited by 10
“In the case of a random-effects model, Knapp-Hartung adjustments [84] help con-trol the uncertainty in estimating between-study heterogeneity, reducing false-positivity [81] with less studies.”
BackgroundMethodInfluentialFrancis, M. R., Gidado, S., & Nuorti, J. P. (2024) · The Journal of Infectious Diseases · doi:10.1093/infdis/jiae261 · Cited by 9
“We estimated the pooled SARs and 95% confidence intervals (CIs) with random effects meta-analyses using the inverse variance method and restricted maximum likelihood estimator to account for the heterogeneity between studies [16, 17].”
MethodElectroconvulsive therapy for depression
Munkholm, K., Jørgensen, K. J., & Paludan‐Müller, A. S. (2021) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013843 · Cited by 7
Trkulja, V., & Barić, H. (2021) · Advances in experimental medicine and biology · doi:10.1007/978-981-33-6044-0_20 · Cited by 7
Hand Preference in Stuttering: Meta-Analyses
Παπαδάτου-Παστού, Μ., Papadopoulou, A.-K., Samsouris, C., Mundorf, A., Valtou, M.-M., & Ocklenburg, S. (2023) · Neuropsychology Review · doi:10.1007/s11065-023-09617-z · Cited by 7
“The Hartung-Knapp adjustment (Knapp & Hartung, 2003) was applied to calculate the CI around the pooled effect, as it has been suggested to reduce the chance of false positives, especially when the number of studies is small (IntHout et al., 2014; Langan et al., 2019).”
MethodCarrard, J., Guerini, C., Appenzeller‐Herzog, C., Infanger, D., Königstein, K., Streese, L., Hinrichs, T., Hanssen, H., Gallart‐Ayala, H., Ivanišević, J., et al. (2021) · BMJ Open Sport & Exercise Medicine · doi:10.1136/bmjsem-2020-001008 · Cited by 7
Nisa, C. F., Sasin, E. M., Faller, D. G., Schumpe, B. M., & Bélanger, J. J. (2020) · Nature Communications · doi:10.1038/s41467-020-17614-6 · Cited by 7
Scientific consensus communication about contested science: A preregistered meta-analysisPreprint
van Stekelenburg, A., Schaap, G., Veling, H., Riet, J. V. ‘., & Buijzen, M. (2022) · OSF Preprints (OSF Preprints) · doi:10.31219/osf.io/etsrw · Cited by 8
A meta‐analysis on racial discrimination and alcohol use among Asian Americans
Liu, M. A., Fox, T., Salyers, M. P., Zapolski, T. C. B., & Cyders, M. A. (2024) · Alcoholism Clinical and Experimental Research · doi:10.1111/acer.15475 · Cited by 6
Abdelfattah, O., Sayed, A., ALJWAID, A., Hassan, A. A., Jazar, D. A., Narayanan, A., Link, M. S., & Martinez, M. W. (2025) · Circulation Arrhythmia and Electrophysiology · doi:10.1161/circep.124.013479 · Cited by 6
“12 Heterogeneity was assessed via 2 methods: first, via visual inspection of forest plots.”
Bushi, G., Khatib, M. N., Gaidhane, S., Renuka Jyothi, S., Srivastava, M., Koul, A., Kumar, M., Zahiruddin, Q. S., Rustagi, S., Sah, S. K., et al. (2025) · Brain and Behavior · doi:10.1002/brb3.70048 · Cited by 6
Wang, T., Zhang, Y., Li, F., & Cao, N. (2025) · Computers and Electronics in Agriculture · doi:10.1016/j.compag.2025.110205 · Cited by 6
Mussetto, I., Bernucci, M. C., Kaminska, A. E., Isonne, C., Sciurti, A., Migliara, G., Renzi, E., Massimi, A., Marzuillo, C., Vito, C. D., et al. (2025) · BMC Public Health · doi:10.1186/s12889-025-22697-1 · Cited by 6
“The restricted maximum likelihood method [28] with a Freeman–Tukey transformation [29] was used to calculate the pooled estimated proportions of vaccination intention towards each vaccine separately.”
Effectiveness of the monovalent XBB.1.5 COVID-19 vaccines: A systematic review and meta-analysis
Ma, H., Chen, Y.-Y., Shih, W., Chen, Y., Chen, T., & Fang, C. (2025) · Journal of Microbiology Immunology and Infection · doi:10.1016/j.jmii.2025.07.002 · Cited by 7
Cobourne, M. T., Seehra, J., & Papageorgiou, S. N. (2025) · BDJ · doi:10.1038/s41415-025-8892-z · Cited by 6
“39 Between-study observed heterogeneity/estimated relative inconsistency was assessed using the tau 2 /I 2 metric, respectively, while uncertainty around them was also estimated 40 for meta-analyses with ≥3 studies.”
Long-term clinical efficacy of dentin desensitizing agents: A systematic review and meta-analysis
Corrêa, T. H. R., da Rosa, W. L. D. O., & Lund, R. G. (2025) · Journal of Dentistry · doi:10.1016/j.jdent.2025.106186 · Cited by 6
Ludwig‐Walz, H., Heinisch, S., Siemens, W., Niessner, C., Eberhardt, T., Dannheim, I., Guthold, R., & Bujard, M. (2025) · Journal of sport and health science/Journal of Sport and Health Science · doi:10.1016/j.jshs.2025.101101 · Cited by 12
“39), and similar results were observed when individual measurements were analyzed (sit-and-reach: SMD = (cid:2) 0.05, 95%CI: (cid:2) 0.33 to 0.22; stand-and-reach: SMD = 0.03, 95%CI: (cid:2) 0.13 to 0.18; Supplementary Fig.”
InfluentialSiemens, W., Borenstein, M., Evrenoglou, T., Meerpohl, J. J., & Schwarzer, G. (2025) · BMC Medical Research Methodology · doi:10.1186/s12874-025-02733-9 · Cited by 8
“However, the choice of the τ 2 estimation method had no relevant impact on the PI and the expected proportion of studies when using the restricted maximum likelihood or the Paule-Mandel method (see sensitivity analyses in Supplementary Material) [39].”
Impact of loneliness on health in healthy populations: A meta‐analysis
Zheng, Y., Qualter, P., Rollano, C., Hu, X., Martín, A. A., Nukui, M., Walibhai, W., & Maes, M. (2025) · British Journal of Health Psychology · doi:10.1111/bjhp.70040 · Cited by 6
“We selected REML because it is considered an unbiased estimator and empirical evidence has demonstrated its superior performance compared with other estimators (Hönekopp & Linden, 2022; Langan et al., 2019; Viechtbauer & Cheung, 2010).”
Adverse effects of electroconvulsive therapy
Munkholm, K., Jørgensen, K. J., & Paludan‐Müller, A. S. (2021) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd014995 · Cited by 9
Shah, Y. R., & Turgeon, R. D. (2023) · CJC Open · doi:10.1016/j.cjco.2023.12.002 · Cited by 6
“…a Mantel-Haenszel random-effects model, with a Paule-Mandel estimator and the Hartung-Knapp variance estimate, which provides more-conservative 95% con fi dence intervals (CIs) when heterogeneity is high, compared with the Dersemonian-Laird estimate, 19,20 to calculate effect estimates with 95% CIs.”
Davies, R. W., Lynch, A. E., Kumar, U., & Jakeman, P. M. (2024) · Translational Sports Medicine · doi:10.1155/2024/3184356 · Cited by 6
Occupational psychosocial exposures and chronic low-back pain: a systematic review and meta-analysis
Jahn, A., Andersen, J. H., Seidler, A., Christiansen, D. H., & Dalbøge, A. (2024) · Scandinavian Journal of Work Environment & Health · doi:10.5271/sjweh.4165 · Cited by 10
Cardoso, J. H. C. O., de Lara, I. C. A., Sobreira, L. E. R., Lôbo, A. D. O. M., Silvério, I. I. L., Souza, M. E. C., de Moraes, F. C. A., & Magalhães, M. C. F. (2024) · Clinical Breast Cancer · doi:10.1016/j.clbc.2024.07.011 · Cited by 6
RetractedSchulz, M., Kramer, M. A., Kuß, O., & Mathes, T. (2024) · Research Synthesis Methods · doi:10.1002/jrsm.1748 · Cited by 6
“10,11 15 Despite these simulations, the Peto method is still mentioned in the Cochrane Handbook in the section on meta-analyses of rare events, and there are no specific recommendations for meta-analyses including only a few trials.”
Jo, H.-G., Kim, H., Baek, E., Seo, J., & Lee, D. (2024) · Nutrients · doi:10.3390/nu16162690 · Cited by 6
“However, in the case of t 2 , we adopted the DerSimonian–Laird estimator for continuous outcome data, but we utilized the Paule–Mandel estimator for binary effect size data because it has better properties as an estimate [33].”
MethodGonzalez, J. T., Lolli, L., Veasey, R. C., Rumbold, P. L. S., Betts, J. A., Atkinson, G., & Stevenson, E. (2024) · European Journal of Nutrition · doi:10.1007/s00394-024-03467-y · Cited by 8
“The tau-statistic (τ) value described the between-participant variability across the distribution of true replicate-averaged treatment effects [24, 25].”
BackgroundAhmed, S., Ahmad, E., Fatima, E., Akram, U., Rehman, O. U., Harikrishna, A., Sharif, S., Akmal, N., & Nashwan, A. J. (2024) · European Journal of Obstetrics & Gynecology and Reproductive Biology · doi:10.1016/j.ejogrb.2024.10.012 · Cited by 6
Karwiky, G., Kamarullah, W., Pranata, R., Iqbal, M., Achmad, C., Martha, J. W., & Setiawan, I. (2024) · Heart Rhythm O2 · doi:10.1016/j.hroo.2024.11.006 · Cited by 6
Pouliopoulou, D. V., Billias, N., MacDermid, J. C., Miller, E., O’Brien, K. K., Quinn, K. L., Malvankar‐Mehta, M. S., Pereira, T., Cheung, A. M., Razak, F. A., et al. (2024) · EClinicalMedicine · doi:10.1016/j.eclinm.2024.102993 · Cited by 6
“We used the inverse-variance (IV) random-effects (RE) model with the restricted maximum-likelihood (REML) estimator 32 of the between-study variance to combine re-sults in a two-stage approach.”
Papageorgiou, S. N., Zyli, M., & Papadopoulou, A. K. (2025) · European Journal of Orthodontics · doi:10.1093/ejo/cjaf012 · Cited by 10
“A novel restricted maximum likelihood variance estimator was chosen in all instances [36] and the Knapp & Hartung adjustment [37] was used for meta-analyses with ≥ 3 studies.”
Terra, R. M. O., Favoreto, M. W., Morris, T., Loguércio, A. D., & Reis, A. (2025) · Journal of Dentistry · doi:10.1016/j.jdent.2025.105891 · Cited by 6
Saghazadeh, A., & Rezaei, N. (2022) · International Immunopharmacology · doi:10.1016/j.intimp.2022.109147 · Cited by 7
A meta-analysis of the effect of gamma irradiation on chicken meat quality: Microbiology and colour
Dimov, K. G., & Popova, T. L. (2022) · Food Science and Applied Biotechnology · doi:10.30721/fsab2022.v5.i2.185 · Cited by 6
“The method of restricted maximum likelihood (REML) was applied to estimate heterogeneity variance as recommended by Langan et al. (2019).”
MethodZeng, H. M., Dai, J., Cao, D., Wang, M., Zhao, J., Zeng, Y., Xu, N., Xie, Y., Liu, H., Zeng, H., et al. (2023) · Strahlentherapie und Onkologie · doi:10.1007/s00066-023-02063-z · Cited by 6
“Restricted maximum-likelihood estimator (REML) and the Hartung–Knapp method were also used in the meta-analysis [19].”
MethodTaran, S., Hamad, D. M., von Düring, S., Malhotra, A. K., Veroniki, A. A., McCREDIE, V. A., Singh, J. M., Hansen, B. E., Englesakis, M. F., & Adhikari, N. K. J. (2023) · Journal of Critical Care · doi:10.1016/j.jcrc.2023.154341 · Cited by 7
Self-citationTatas, Z., Koutsiouroumpa, O., Seehra, J., Mavridis, D., & Pandis, N. (2023) · European Journal of Orthodontics · doi:10.1093/ejo/cjad031 · Cited by 6
Korevaar, E., Turner, S., Forbes, A. B., Karahalios, A., Taljaard, M., & McKenzie, J. E. (2023) · Research Synthesis Methods · doi:10.1002/jrsm.1669 · Cited by 5
“33,52 – 54 Rather than assuming normality of b β (cid:4) m , the method assumes the t-distribution (with K-1 degrees of freedom), and includes a small sample standard error adjustment, q, and is calculated as: where and”
BackgroundMethodRothman–Woodroofe symmetry test statistic revisited
Gaigall, D. (2019) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2019.106837 · Cited by 6
Prognostic models for predicting relapse or recurrence of depression
Moriarty, A. S., Meader, N., Gilbody, S. M., Chew-Graham, C. A., Churchill, R. C., Ali, S., Phillips, R. S., Riley, R. D., & McMillan, D. (2019) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013491 · Cited by 5
Ray, D., Muñoz, A., Zhang, M., Li, X., Chatterjee, N., Jacobson, L. P., & Lau, B. M. (2022) · BMC Medical Research Methodology · doi:10.1186/s12874-022-01614-9 · Cited by 6
“Alternative approaches, such as restricted maximum likelihood or non-parametric DerSimonian and Laird methods, may be used to obtain τ̂ 2 when method of moments gives biased estimate, as suggested by recent comparative studies [26, 27].”
MethodGlobal prevalence of falls among older adults with cancer: A systematic review and meta-analysis
Bushi, G., Gaidhane, S., Balaraman, A. K., PadmaPriya, G., Kaur, I., Lal, M., Iqbal, S., Prasad, G. V. S., Pramanik, A., Vishwakarma, T., et al. (2025) · Journal of Geriatric Oncology · doi:10.1016/j.jgo.2025.102202 · Cited by 5
Paravlic, A. H., & Drole, K. (2025) · BMC Sports Science Medicine and Rehabilitation · doi:10.1186/s13102-025-01124-3 · Cited by 7
“Thus, the restricted maximum likelihood with Knap–Hartung standard error adjustment was used for all random effect model analyses [27].”
Guenetxea-Gorostiza, J., Rada, D., Apraiz-Sánchez, I., Mazquiarán-Bergera, L., Urkia-Susín, I., Maíz, E., & Martínez, O. (2025) · Nutrition · doi:10.1016/j.nut.2025.112812 · Cited by 5
Gonçalves, J. P. F., Medrado-Nunes, G. S., Piñeiro, G. T. D. O., Millard, F. A. B., de Oliveira, M. P. R., dos Santos, N. S. S., Oliveira, T., Sandes, P. H. F., Oliveira-Martins, L. P., Silveira-Leal, M. Y., et al. (2025) · Journal of Clinical Neuroscience · doi:10.1016/j.jocn.2025.111307 · Cited by 5
Ahn, S., Cobb, S. J., Butler, R. A., Abdullah, S., Boltz, M. P., Chung, M. L., Roberson, P. N. E., Lee, J., Zhao, X., & Anderson, J. G. (2025) · Western Journal of Nursing Research · doi:10.1177/01939459251341197 · Cited by 5
“23,24 Each study was weighted according to its statistical size and variance within the random-effects model.”
Chene, G., Miquel, L., Agostini, A., Bendifallah, S., Solignac, C., Darné, B. M., Languille, S., Timoh, K. N., & Carbonnel, M. (2025) · Journal of Minimally Invasive Gynecology · doi:10.1016/j.jmig.2025.07.002 · Cited by 5
Pugh, D., Saunders, R., Jones, A., Dunn, B. D., & Buckman, J. E. J. (2025) · Journal of Affective Disorders · doi:10.1016/j.jad.2025.120165 · Cited by 7
Human papillomavirus (HPV) vaccination in women with conisation
Kapp, P., Schmucker, C. M., Siemens, W., Brugger, T., Gorenflo, L., Röbl-Mathieu, M., Grummich, K., Thörel, E., Askar, M., Brotons, M., et al. (2025) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd016121 · Cited by 6
Reddy, R. K., Koeckerling, D., Lip, G. Y. H., Howard, J. P., & Ahmad, Y. (2025) · Journal of the American Heart Association · doi:10.1161/jaha.125.041422 · Cited by 5
Wang, D.-D., Sun, M., Song, X., Liu, K., Chen, X., Li, D.-R., Wang, Y., Sun, M.-H., Yang, R., Feng, Z.-F., et al. (2025) · BMC Medicine · doi:10.1186/s12916-025-04445-9 · Cited by 7
“[27] To account for the uncertainty in the estimation of τ 2 and provide more robust confidence intervals and P -val- ues, especially in meta-analyses with a limited number of studies, we consistently applied the Hartung-Knapp-Sidik-Jonkman (HKSJ) method.”
Pulmonary vasodilators and exercise in Fontan circulation: a systematic review and meta-analysis
Kosmidis, D., Arvanitaki, A., Farmakis, I. T., Liakos, A., Giannopoulos, A., Ziakas, A., & Giannakoulas, G. A. (2023) · Heart · doi:10.1136/heartjnl-2023-323166 · Cited by 5
“28 29 The presence and degree of heterogeneity were estimated with the Cochran’s Q test (a p value of <0.1 indicated significant heterogeneity 30 ) and the I 2 statistic (<30%, 30–60% and >60% shows low, moderate and high heterogeneity, respectively).”
MethodInfluentialSanjaya, H. L., Maharani, B. P., Baskara, A. P., Muhlisin, M., Martien, R., & Zuprizal, Z. (2024) · British Poultry Science · doi:10.1080/00071668.2024.2364331 · Cited by 5
Bushi, G., Khatib, M. N., Singh, M. P., Pattanayak, M., Vishwakarma, T., Ballal, S., Bansal, P., Gaidhane, A. M., Tomar, B. S., Ashraf, A., et al. (2025) · BMC Oral Health · doi:10.1186/s12903-025-05511-7 · Cited by 5
“Where data allowed, sub-group analyses were conducted to explore the impact of demographic, clinical, and psychosocial factors on the outcomes [12, 13].”
Tomczyk, S., & Ewert, C. (2025) · Applied Psychology Health and Well-Being · doi:10.1111/aphw.70006 · Cited by 4
Exact inference for fixed effects meta‐analysis of 2×2$$ 2\times 2 $$ tables
Hansen, S. L., & Rice, K. M. (2023) · Statistics in Medicine · doi:10.1002/sim.9808 · Cited by 5
“F I G U R E 4 Top panel: Excess coverage under heterogeneity of the 95% Blaker intervals using our method for a grid of values with table margins of Mk = Nk = (500,500), Tk = (25, 25).”
BackgroundMethodInfluentialLee, M. A., Hatcher, C., McGuinness, L. A., McBride, N., Battram, T., Wan, W., Fang, S., Wade, K. H., Corbin, L. J., & Timpson, N. J. (2023) · Wellcome Open Research · doi:10.12688/wellcomeopenres.18657.2 · Cited by 5
Tressoldi, P. E., & Storm, L. (2024) · F1000Research · doi:10.12688/f1000research.51746.3 · Cited by 5
Serhan, H. A. A., Gupta, P. C., Khatib, M. N., Padhi, B. K., Gaidhane, S., Zahiruddin, Q. S., Gaidhane, A. M., Kukreti, N., Rustagi, S., & Satapathy, P. (2024) · American Journal of Ophthalmology · doi:10.1016/j.ajo.2024.07.013 · Cited by 5
Prosody and developmental dyslexia: a meta-analysis
Mundy, I. R., & Wood, C. P. (2024) · Reading and Writing · doi:10.1007/s11145-024-10610-y · Cited by 5
“This test is analogous to the Knapp-Har-tung method used within traditional two-level meta-analyses and has been shown to reduce the likelihood of type-1 errors (Langan et al., 2019).”
Efficacy of Amitriptyline in Irritable Bowel Syndrome: A Systematic Review and Meta-analysis
Iqbal, M., Hira, S., Saeed, H., Shahid, S., Butt, S. T., Rashid, K., Ahmad, M. K., Hussain, H. A., Mughal, A., Costa, G. P. A., et al. (2025) · Journal of Neurogastroenterology and Motility · doi:10.5056/jnm24084 · Cited by 7
Combining information across diverse sources: The II‐CC‐FF paradigm
Cunen, C., & Hjort, N. L. (2021) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12530 · Cited by 5
“(2019). We compare this state-of-the-art method with our standard II-CC-FF method, and the II-CC-FF method using the corrected log-likelihood profile in (12). We also include the method for the basic random effect model which comes out of the CD combination framework of Xie et al. (2011). This method is implemented in…”
BackgroundMethodInfluentialBorg, D. N., & O'Brien, J. L. (2021) · Sports Medicine · doi:10.1007/s40279-021-01611-w · Cited by 5
“We chose this estimator because of its conservative performance [19, 20].”
MethodDaraqel, B., Mheissen, S., Li, J., Khan, H., Allan, S., & Zheng, L. (2023) · European Journal of Orthodontics · doi:10.1093/ejo/cjad015 · Cited by 5
Trkulja, V., & Hrabač, P. (2020) · Croatian Medical Journal · doi:10.3325/cmj.2020.61.198 · Cited by 5
Athanasiou, A., Veroniki, A. A., Efthimiou, O., Kalliala, I. E. J., Naci, H., Bowden, S. J., Paraskevaidi, M., Martin‐Hirsch, P. L., Bennett, P. R., Paraskevaidis, E., et al. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-028008 · Cited by 5
Self-citationCombining Results Using Meta‐Analysis
Deeks, J. J., Riley, R. D., & Higgins, J. P. T. (2022) · doi:10.1002/9781119099369.ch9 · Cited by 5
Self-citationMatovu, N., Coleman, H. G., Mesa‐Eguiagaray, I., Τheodoratou, E., & McShane, C. M. (2025) · EClinicalMedicine · doi:10.1016/j.eclinm.2025.103445 · Cited by 5
“23 Pooled mean age at CRC diagnosis was computed separately for studies that directly reported mean age (SD) and in those where the mean was estimated from the median (interquartile range (IQR) or range).”
Evaluating the properties of the fragility index of meta-analyses
Xing, A., Xing, X., Murad, M. H., & Lin, L. (2025) · BMC Medical Research Methodology · doi:10.1186/s12874-025-02648-5 · Cited by 7
“Extra caution is warranted when selecting heterogeneity measures and comparing fragility improvements for MAs with such limited sample sizes [14, 42, 46, 48].”
InfluentialBelloni, S., Virgili, R., Caruso, R., Arrigoni, C., Magon, A., Rocco, G., & Maria, M. D. (2025) · Cancers · doi:10.3390/cancers17193152 · Cited by 5
“Given the high clinical heterogeneity between studies in terms of outcomes and the probability of real variations in the between-study proportion, a random-effect model of the inverse variance was adopted [46], applying the restricted maximum likelihood (REML) method [47].”
Martijn, F. M., Blagden, N., Baguley, T. S., Leroux, E. J., Mackay, J., & Seto, M. C. (2025) · Clinical Psychology Review · doi:10.1016/j.cpr.2025.102690 · Cited by 4
Safia, A., Elhadi, U. A., Merchavy, S., Batheesh, R., & Bathish, N. (2026) · Journal of Cosmetic Dermatology · doi:10.1111/jocd.70655 · Cited by 6
“The characteristics of patients, the techniques of injection, the dosages given, the definitions of “satisfaction,” and the advantages of cosmetics can vary significantly across different cultural settings [29].”
A Meta-Analysis of Music Emotion Recognition Studies
Eerola, T., & Anderson, C. J. (2026) · ACM Computing Surveys · doi:10.1145/3796518 · Cited by 4
“We used Paule–Mandel estimator for between-study heterogeneity [62] and Knapp–Hartung [58] adjustments for confidence intervals.”
Ghazian, N., & Lortie, C. J. (2023) · Ecological Management & Restoration · doi:10.1111/emr.12581 · Cited by 4
Yan, Y., López‐Alcalde, J., Stallings, E., Tejero, E. J., Witt, C. M., & Barth, J. (2024) · PLoS ONE · doi:10.1371/journal.pone.0306772 · Cited by 4
“For the meta-analytic procedure we used the random effects model with Knapp–Hartung adjustment for pooling of studies [37, 38].”
Experimental Induction of Complex Gastroschisis in the Fetal Lamb: Systematic Review
Arai, T., Tianthong, W., Russo, F. M., Basurto, D., Joyeux, L., Coppi, P. D., & Deprest, J. A. (2024) · Prenatal Diagnosis · doi:10.1002/pd.6647 · Cited by 5
“A random‐effects model was used for each outcome, with maximum‐likelihood estimator for tau [2] and the variance‐stabilizing transformation, known as the double‐ arcsine transformation [17].”
Murad, M. H., TOMLINSON, G. A., Brignardello‐Petersen, R., Wang, Z., & Lin, L. (2024) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2024.111653 · Cited by 4
A Reliability Generalization Meta-analysis of the PERMA-Profiler
Çelik, A. K. (2025) · Social Indicators Research · doi:10.1007/s11205-025-03547-4 · Cited by 7
“We used a restricted maximum likelihood to estimate the model because it is an estimation method suitable for using works with small and large samples together and shows low-level bias (Langan et al., 2019).”
Terra, R. M. O., Favoreto, M. W., Morris, T., Loguércio, A. D., & Reis, A. (2025) · Journal of Dentistry · doi:10.1016/j.jdent.2025.105857 · Cited by 4
Muehlemann, E., Liguori, M. G., Pachiou, A., Jung, R. E., & Strauß, F. J. (2025) · Journal of Dentistry · doi:10.1016/j.jdent.2025.105920 · Cited by 4
Meta-Analysis of the Crossed Versus Standard Limb Configuration in Endovascular Aneurysm Repair
Kontopodis, N., Galanakis, N., Ioannou, C. V., Tsetis, D. K., Georgiadis, G. S., & Antoniou, G. A. (2021) · Annals of Vascular Surgery · doi:10.1016/j.avsg.2021.10.037 · Cited by 5
Gogate, A., Ranjan, S., Kumar, A., Bhandari, H., Papademetriou, E., Kim, I., & Potluri, R. C. (2023) · Frontiers in Oncology · doi:10.3389/fonc.2023.1119102 · Cited by 4
“Heterogeneity was estimated using the restricted maximum likelihood (REML) estimator for heterogeneity (33).”
Method
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
