Meta-analysis in clinical trials revisited
Open accessAbstract
In this paper, we revisit a 1986 article we published in this Journal, Meta-Analysis in Clinical Trials, where we introduced a random-effects model to summarize the evidence about treatment efficacy from a number of related clinical trials. Because of its simplicity and ease of implementation, our approach has been widely used (with more than 12,000 citations to date) and the "DerSimonian and Laird method" is now often referred to as the 'standard approach' or a 'popular' method for meta-analysis in medical and clinical research. The method is especially useful for providing an overall effect estimate and for characterizing the heterogeneity of effects across a series of studies. Here, we review the background that led to the original 1986 article, briefly describe the random-effects approach for meta-analysis, explore its use in various settings and trends over time and recommend a refinement to the method using a robust variance estimator for testing overall effect. We conclude with a discussion of repurposing the method for Big Data meta-analysis and Genome Wide Association Studies for studying the importance of genetic variants in complex diseases.
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
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.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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 · see citing works
Self-citationQuantifying 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 · see citing works
The combination of estimates from different experiments
Cochran, W. G. (1954) · Biometrics · doi:10.2307/3001666 · Cited by 5,380 · see citing works
Primary, Secondary, and Meta-Analysis of Research
GLASS, G. V. (1976) · Educational Researcher · doi:10.3102/0013189x005010003 · Cited by 4,890 · see citing works
How should meta‐regression analyses be undertaken and interpreted?
Thompson, S. G., & Higgins, J. P. T. (2002) · Statistics in Medicine · doi:10.1002/sim.1187 · Cited by 3,026 · see citing works
IntHout, J., Ioannidis, J. P., & Borm, G. F. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-25 · Cited by 2,419 · see citing works
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 · see citing works
Self-citationInterpersonal expectancy effects: the first 345 studies
Rosenthal, R., & Rubin, D. B. (1978) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00075506 · Cited by 1,143 · see citing works
Getting to Scale with Good Educational Practice
Elmore, R. F. (1996) · Harvard Educational Review · doi:10.17763/haer.66.1.g73266758j348t33 · Cited by 1,071 · see citing works
A random‐effects regression model for meta‐analysis
Berkey, C. S., Hoaglin, D. C., Mosteller, F. C., & Colditz, G. A. (1995) · Statistics in Medicine · doi:10.1002/sim.4780140406 · Cited by 882 · see citing works
A refined method for the meta-analysis of controlled clinical trials with binary outcome
Hartung, J., & Knapp, G. (2001) · Statistics in Medicine · doi:10.1002/sim.1009 · Cited by 775 · see citing works
A common genetic variant is associated with adult and childhood obesity.
Herbert, A., Gerry, N. P., McQueen, M. B., Heid, I. M., Pfeufer, A., Illig, T., Wichmann, H.-E., Meitinger, T., Hunter, D., Hu, F. B., et al. (2006) · Science · doi:10.1126/science.1124779 · Cited by 732 · see citing works
Han, B., & Eskin, E. (2011) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2011.04.014 · Cited by 680 · see citing works
Extending DerSimonian and Laird's methodology to perform multivariate random effects meta‐analyses
Jackson, D., White, I. R., & Thompson, S. G. (2009) · Statistics in Medicine · doi:10.1002/sim.3602 · Cited by 591 · see citing works
Some Statistical Methods for Combining Experimental Results
Laird, N. M., & Mosteller, F. C. (1990) · International Journal of Technology Assessment in Health Care · doi:10.1017/s0266462300008916 · Cited by 568 · see citing works
Self-citationThe Tennessee Study of Class Size in the Early School Grades
Mosteller, F. C. (1995) · The Future of Children · doi:10.2307/1602360 · Cited by 517 · see citing works
Kontopantelis, E., & Reeves, D. (2010) · Statistical Methods in Medical Research · doi:10.1177/0962280210392008 · Cited by 264 · see citing works
Jackson, D., Bowden, J., & Baker, R. (2010) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2009.09.017 · Cited by 226 · see citing works
A Method of Moments Estimator for Random Effect Multivariate Meta‐Analysis
Chen, H., Manning, A. K., & Dupuis, J. (2012) · Biometrics · doi:10.1111/j.1541-0420.2012.01761.x · Cited by 212 · see citing works
Sustained Inquiry in Education: Lessons from Skill Grouping and Class Size
Mosteller, F. C., Light, R. J., & Sachs, J. (1996) · Harvard Educational Review · doi:10.17763/haer.66.4.36m328762x21610x · Cited by 174 · see citing works
Lin, D. Y., & Zeng, D. (2009) · Genetic Epidemiology · doi:10.1002/gepi.20435 · Cited by 151 · see citing works
The Scholastic Aptitude Test: A Critical Appraisal
Slack, W. V. (1980) · Harvard Educational Review · doi:10.17763/haer.50.2.d755627708652757 · Cited by 148 · see citing works
The exact distribution of Cochran's heterogeneity statistic in one‐way random effects meta‐analysis
Biggerstaff, B. J., & Jackson, D. (2008) · Statistics in Medicine · doi:10.1002/sim.3428 · Cited by 130 · see citing works
Kontopantelis, E., & Reeves, D. J. (2012) · Statistical Methods in Medical Research · doi:10.1177/0962280211413451 · Cited by 117 · see citing works
Evaluating the Effect of Coaching on SAT Scores: A Meta-Analysis
DerSimonian, R., & Laird, N. (1983) · Harvard Educational Review · doi:10.17763/haer.53.1.n06j5h5356217648 · Cited by 114 · see citing works
Self-citationJackson, D., White, I. R., & Riley, R. D. (2013) · Biometrical Journal · doi:10.1002/bimj.201200152 · Cited by 112 · see citing works
Jackson, D. (2013) · Research Synthesis Methods · doi:10.1002/jrsm.1081 · Cited by 83 · see citing works
Heid, I. M., Huth, C., Loos, R. J. F., Kronenberg, F., Adámková, V., Anand, S. S., Ardlie, K., Biebermann, H., Bjerregaard, P., Boeing, H., et al. (2009) · PLoS Genetics · doi:10.1371/journal.pgen.1000694 · Cited by 77 · see citing works
Self-citationKulinskaya, E., Döllinger, M., & Bjørkestøl, K. (2011) · Research Synthesis Methods · doi:10.1002/jrsm.54 · Cited by 69 · see citing works
A Note on Variance Estimation in Random Effects Meta-Regression
Sidik, K., & Jonkman, J. N. (2005) · Journal of Biopharmaceutical Statistics · doi:10.1081/bip-200067915 · Cited by 69 · see citing works
Testing for Homogeneity in Meta-Analysis I. The One-Parameter Case: Standardized Mean Difference
Kulinskaya, E., Döllinger, M., & Bjørkestøl, K. (2010) · Biometrics · doi:10.1111/j.1541-0420.2010.01442.x · Cited by 63 · see citing works
Jackson, D., Turner, R., Rhodes, K. M., & Viechtbauer, W. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-103 · Cited by 50 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
NASH limits anti-tumour surveillance in immunotherapy-treated HCC
Pfister, D., Núñez, N. G., Pinyol, R., Govaere, O., Pinter, M., Szydlowska, M., Gupta, R., Qiu, M., Deczkowska, A., Weiner, A., et al. (2021) · Nature · doi:10.1038/s41586-021-03362-0 · Cited by 1,294 · see citing works
Coffee consumption and health: umbrella review of meta-analyses of multiple health outcomes
Poole, R., Kennedy, O. J., Roderick, P., Fallowfield, J. A., Hayes, P. C., & Parkes, J. (2017) · BMJ · doi:10.1136/bmj.j5024 · Cited by 835 · see citing works
Borchard, N., Schirrmann, M., Cayuela, M. L., Kammann, C., Wrage-Mönnig, N., Estavillo, J. M., Fuertes-Mendizábal, T., Sigua, G., Spokas, K., Ippolito, J. A., et al. (2019) · Science of The Total Environment · doi:10.1016/j.scitotenv.2018.10.060 · Cited by 592 · see citing works
Semahegn, A., Torpey, K., Manu, A., Assefa, N., Tesfaye, G., & Ankomah, A. (2020) · Systematic Reviews · doi:10.1186/s13643-020-1274-3 · Cited by 555 · see citing works
Wang, Y., Kala, M. P., & Jafar, T. H. (2020) · PLOS ONE · doi:10.1371/journal.pone.0244630 · Cited by 382 · see citing works
Qin, P., Li, Q., Zhao, Y., Chen, Q., Sun, X., Liu, Y., Li, H., Wang, T., Chen, X., Zhou, Q., et al. (2020) · European Journal of Epidemiology · doi:10.1007/s10654-020-00655-y · Cited by 323 · see citing works
Danopoulos, E., Jenner, L. C., Twiddy, M., & Rotchell, J. M. (2020) · Environmental Health Perspectives · doi:10.1289/ehp7171 · Cited by 302 · see citing works
“The DerSimonian-Laird t 2 estimator was used for all the random-e ff ects models (DerSimonian and Laird 1986, 2015) because this accounts for variations both within and between studies.”
Global etiology of bacterial meningitis: A systematic review and meta-analysis.
Oordt-Speets, A. M., Bolijn, R., van Hoorn, R. C., Bhavsar, A., & Kyaw, M. H. (2018) · PloS One · doi:10.1371/journal.pone.0198772 · Cited by 288 · see citing works
di Giacomo, E., Krausz, M., Colmegna, F., Aspesi, F., & Clerici, M. (2018) · JAMA Pediatrics · doi:10.1001/jamapediatrics.2018.2731 · Cited by 253 · see citing works
Mazeas, A., Duclos, M., Pereira, B., & Chalabaev, A. (2022) · Journal of Medical Internet Research · doi:10.2196/26779 · Cited by 222 · see citing works
Geidl, W., Schlesinger, S., Mino, E., Miranda, L., & Pfeifer, K. (2020) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-020-01007-5 · Cited by 183 · see citing works
Wang, S., Sun, Q., Zhai, L., Bai, Y., Wei, W., & Jia, L. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16030340 · Cited by 164 · see citing works
Systematic Review and Meta-Analysis of Human Skin Diseases Due to Particulate Matter
Ngoc, L., Park, D., Lee, Y., & Lee, Y.-C. (2017) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph14121458 · Cited by 159 · see citing works
Wallach, J. D., Sullivan, P. G., Trepanowski, J. F., Sainani, K. L., Steyerberg, E. W., & Ioannidis, J. P. A. (2017) · JAMA Internal Medicine · doi:10.1001/jamainternmed.2016.9125 · Cited by 148 · see citing works
Michelson, M., & Reuter, K. (2019) · Contemporary Clinical Trials Communications · doi:10.1016/j.conctc.2019.100443 · Cited by 152 · see citing works
Being a cybervictim and a cyberbully – The duality of cyberbullying: A meta-analysis
Lozano-Blasco, R., Cortés-Pascual, A., & Latorre-Martínez, M. P. (2020) · Computers in Human Behavior · doi:10.1016/j.chb.2020.106444 · Cited by 142 · see citing works
Hui, W., Li, T., Liu, W., Zhou, C., & Gao, F. (2019) · PLoS ONE · doi:10.1371/journal.pone.0210016 · Cited by 140 · see citing works
RetractedPjrek, E., Friedrich, M.-E., Cambioli, L., Dold, M., Jäger, F., Komorowski, A., Lanzenberger, R., Kasper, S., & Winkler, D. (2020) · Psychotherapy and Psychosomatics · doi:10.1159/000502891 · Cited by 136 · see citing works
Toh, J. Z. K., Pan, X.-H., Tay, P. W. L., Ng, C. H., Yong, J. N., Xiao, J., Koh, J. H., Tan, E. Y., Tan, E. X. X., Dan, Y. Y., et al. (2022) · Clinical Gastroenterology and Hepatology · doi:10.1016/j.cgh.2021.09.021 · Cited by 130 · see citing works
Trindade, I. A., Guiomar, R., Carvalho, S. A., Duarte, J., Lapa, T., Menezes, P., Nogueira, M. R., Patrão, B., Pinto-Gouveia, J., & Castilho, P. (2021) · The Journal of Pain · doi:10.1016/j.jpain.2021.04.003 · Cited by 117 · see citing works
Robertson, F. C., Lepard, J. R., Mekary, R. A., Davis, M. C., Yunusa, I., Gormley, W. B., Baticulon, R. E., Mahmud, M. R., Misra, B. K., Rattani, A., et al. (2019) · Journal of Neurosurgery · doi:10.3171/2017.10.jns17359 · Cited by 116 · see citing works
Fan, D., Xia, Q., Liu, L., Wu, S., Tian, G., Wang, W., Wu, S., Guo, X., & Liu, Z. (2017) · PLOS ONE · doi:10.1371/journal.pone.0170194 · Cited by 115 · see citing works
Semnani-Azad, Z., Khan, T. A., Blanco Mejia, S., de Souza, R. J., Leiter, L. A., Kendall, C. W. C., Hanley, A. J., & Sievenpiper, J. L. (2020) · JAMA Network Open · doi:10.1001/jamanetworkopen.2020.9993 · Cited by 103 · see citing works
Said Abasse, K., Essien, E. E., Abbas, M., Yu, X., Xie, W., Sun, J., Akter, L., & Cote, A. (2022) · Nutrients · doi:10.3390/nu14030666 · Cited by 98 · see citing works
Wallach, J. D., Sullivan, P. G., Trepanowski, J. F., Steyerberg, E. W., & Ioannidis, J. P. A. (2016) · BMJ · doi:10.1136/bmj.i5826 · Cited by 89 · see citing works
Simpson, R., Simpson, S., Ramparsad, N., Lawrence, M., Booth, J., & Mercer, S. W. (2019) · Journal of Neurology, Neurosurgery & Psychiatry · doi:10.1136/jnnp-2018-320165 · Cited by 86 · see citing works
Polymorphisms and endometriosis: A systematic review and meta-analyses
Méar, L., Herr, M., Fauconnier, A., Pineau, C., & Vialard, F. (2020) · Human Reproduction Update · doi:10.1093/humupd/dmz034 · Cited by 85 · see citing works
Al-Rifai, R. H., Abdo, N. M., Paulo, M. S., Saha, S., & Ahmed, L. A. (2021) · Frontiers in Endocrinology · doi:10.3389/fendo.2021.668447 · Cited by 78 · see citing works
Alexakis, C., Kumar, S., Saxena, S., & Pollok, R. (2017) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.14171 · Cited by 69 · see citing works
Marini, S., Crawford, K., Morotti, A., Lee, M. J., Pezzini, A., Moomaw, C. J., Flaherty, M. L., Montaner, J., Roquer, J., Jimenez-Conde, J., et al. (2019) · JAMA Neurology · doi:10.1001/jamaneurol.2018.4519 · Cited by 68 · see citing works
Wen, Y., Li, J., Long, Q., Yue, C.-C., He, B., & Tang, X.-G. (2020) · International Journal of Surgery · doi:10.1016/j.ijsu.2020.04.063 · Cited by 62 · see citing works
Simpson, R., Simpson, S., Ramparsad, N., Lawrence, M., Booth, J., & Mercer, S. W. (2020) · Multiple Sclerosis and Related Disorders · doi:10.1016/j.msard.2019.101493 · Cited by 45 · see citing works
Glucagon-like peptide-1 receptor agonists as add-on therapy to insulin for type 1 diabetes mellitus
Tan, X., Pan, X., Wu, X., Zheng, S., Chen, Y., Liu, D., & Zhang, X. (2023) · Frontiers in Pharmacology · doi:10.3389/fphar.2023.975880 · Cited by 44 · see citing works
Karalexi, M. A., Georgakis, M. K., Dimitriou, N. G., Vichos, T., Katsimpris, A., Petridou, E. T., & Papadopoulos, F. C. (2020) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2020.104721 · Cited by 41 · see citing works
Yoshiji, S., Minamino, H., Tanaka, D., Yamane, S., Harada, N., & Inagaki, N. (2022) · Diabetes, Obesity and Metabolism · doi:10.1111/dom.14666 · Cited by 40 · see citing works
Sadowski, A., Dunlap, C., Lacombe, A., & Hanes, D. (2021) · Clinical and Translational Gastroenterology · doi:10.14309/ctg.0000000000000275 · Cited by 38 · see citing works
“Owing to the heterogeneity across study methodologies, a random-effects metaanalysis was used to derive pooled standardized mean difference (SMD) with 95% CIs using an inverse variance model (25).”
MethodTeng, I., Tseng, S., Aulia, B., Shih, C., Bai, C., & Chang, J. (2020) · Obesity Reviews · doi:10.1111/obr.13080 · Cited by 35 · see citing works
Azarpazhooh, M. R., Avan, A., Cipriano, L. E., Munoz, D. G., Erfanian, M., Amiri, A., Stranges, S., & Hachinski, V. (2020) · Ageing Research Reviews · doi:10.1016/j.arr.2019.101002 · Cited by 32 · see citing works
Patients’ adherence to smartphone apps in the management of bipolar disorder: a systematic review
Patoz, M.-C., Hidalgo-Mazzei, D., Pereira, B., Blanc, O., de Chazeron, I., Murru, A., Verdolini, N., Pacchiarotti, I., Vieta, E., Llorca, P.-M., et al. (2021) · International Journal of Bipolar Disorders · doi:10.1186/s40345-021-00224-6 · Cited by 30 · see citing works
Liu, X., Qiu, Y., Yu, E. D., Xiang, S., Meng, R., Niu, K. F., & Zhu, H. (2020) · American Journal of Reproductive Immunology · doi:10.1111/aji.13219 · Cited by 29 · see citing works
Wilkinson, J., Heal, C., Antoniou, G. A., Flemyng, E., Ahnström, L., Alteri, A., Avenell, A., Barker, T. H., Borg, D. N., Brown, N. J. L., et al. (2025) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2025.111824 · Cited by 28 · see citing works
Li, Y., Jin, N., Zhan, Q., Huang, Y., Sun, A., Yin, F., Li, Z., Hu, J., & Liu, Z. (2025) · Frontiers in Endocrinology · doi:10.3389/fendo.2025.1495306 · Cited by 22 · see citing works
“Given the high heterogeneity among the included studies due to variations in study design, ML models, predictive factors, and parameters, we used the Der Simonian and Laird random-effects model to pool the AUCs in the meta-analysis (37).”
He, W., Li, S., Wang, B., Mu, K., Shao, X., Yao, Q., Li, L., Li, Q., & Zhang, J.-A. (2019) · Journal of Hypertension · doi:10.1097/hjh.0000000000001826 · Cited by 21 · see citing works
Soltani, S., Abdollahi, S., Aune, D., & Jayedi, A. (2021) · Scientific Reports · doi:10.1038/s41598-021-81671-0 · Cited by 22 · see citing works
Liu, Y., Li, Y., Xu, H., Zhao, X., Zhu, Y., Zhao, B., Yao, Q., Duan, H., Guo, C., & Li, Y. (2023) · Environmental Research · doi:10.1016/j.envres.2023.115373 · Cited by 21 · see citing works
Lin, H., Tam, K., & Kuan, Y. (2023) · European Journal of Neurology · doi:10.1111/ene.15839 · Cited by 19 · see citing works
Muneer, S., Santhosh, M., Parangusan, H., & Bhadra, J. (2026) · International Journal of Technology and Design Education · doi:10.1007/s10798-025-10005-2 · Cited by 14 · see citing works
Khalil, I., Rahman, M. T., & Hossain, I. (2025) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2025.04.013 · Cited by 8 · see citing works
Ruffolo, A. F., Salvatore, S., Torella, M., Frigerio, M., Soligo, M., Rubod, C., Lallemant, M., Cosson, M., Serati, M., & Braga, A. (2025) · Maturitas · doi:10.1016/j.maturitas.2025.108755 · Cited by 2 · see citing works
- Authors
- DerSimonian, R., & Laird, N.
- Affiliations
- National Institutes of Health (US)
- Harvard University (US)
- Corresponding author
- DerSimonian, Rebecca
- ORCID
- Laird, Nan
- Venue
- Contemporary Clinical Trials
- Publisher
- Elsevier BV
- Published
- 2015-11
- Volume
- 45
- Issue
- Pt A
- Pages
- 139-145
- ISSN
- 1551-7144 (ISSN-L)
- PMC
- PMC4639420
- OpenAlex
- W2161701454
- Cited by
- 2,677
- References
- 32
- Citations by year
- 2026: 247 · 2025: 316 · 2024: 289 · 2023: 293 · 2022: 328 · 2021: 371 · 2020: 319 · 2019: 181 · 2018: 150 · 2017: 132 · 2016: 44 · 2015: 3 · 2013: 1 · 2012: 3
- FWCI
- 98.91
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Contemporary Clinical Trials (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health (Z99 AI999999)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- meta-analysis, random effects models, treatment efficacy, treatment effect heterogeneity, robust variance estimation, genome-wide association study, genetic variants, complex diseases
- MeSH terms
- Clinical Trials as Topic, Humans, Research Design, Meta-Analysis as Topic, Models, Statistical, Genome-Wide Association Study
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