Meta-analysis of proportions using generalized linear mixed models.
Open accessAbstract
Epidemiologic research often involves meta-analyses of proportions. Conventional two-step methods first transform each study’s proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been recommended in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.
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Cites
Fitting Linear Mixed-Effects Models Using <b>lme4</b>
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015) · Journal of Statistical Software · doi:10.18637/jss.v067.i01 · Cited by 86,835 · see citing works
Conducting Meta-Analyses in <i>R</i> with the <b>metafor</b> Package
Viechtbauer, W. (2010) · Journal of Statistical Software · doi:10.18637/jss.v036.i03 · Cited by 20,464 · see citing works
Models for Longitudinal Data: A Generalized Estimating Equation Approach
Zeger, S. L., Liang, K., & Albert, P. S. (1988) · Biometrics · doi:10.2307/2531734 · Cited by 4,505 · see citing works
Transformations Related to the Angular and the Square Root
Freeman, M. F., & Tukey, J. W. (1950) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729756 · Cited by 2,634 · see citing works
Rotenstein, L. S., Ramos, M. A., Torre, M., Segal, J. B., Peluso, M. J., Guille, C., Sen, S., & Mata, D. A. (2016) · JAMA · doi:10.1001/jama.2016.17324 · Cited by 2,479 · see citing works
The arcsine is asinine: the analysis of proportions in ecology.
Warton, D., & Hui, F. K. C. (2011) · Ecology · doi:10.1890/10-0340.1 · Cited by 2,306 · see citing works
Barendregt, J. J., Doi, S. A., Lee, Y. Y., Norman, R. E., & Vos, T. (2013) · Journal of Epidemiology and Community Health · doi:10.1136/jech-2013-203104 · Cited by 2,169 · see citing works
Advanced methods in meta‐analysis: multivariate approach and meta‐regression
van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002) · Statistics in Medicine · doi:10.1002/sim.1040 · Cited by 1,574 · see citing works
A comparison of heterogeneity variance estimators in simulated random‐effects meta‐analyses
Langan, D., Higgins, J. P. T., Jackson, D., Bowden, J., Veroniki, A. A., Kontopantelis, E., Viechtbauer, W., & Simmonds, M. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1316 · Cited by 1,074 · see citing works
Gaussian Predictive Process Models for Large Spatial Data Sets
Banerjee, S., Gelfand, A. E., Finley, A. O., & Sang, H. (2008) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2008.00663.x · Cited by 1,000 · see citing works
Stijnen, T., Hamza, T. H., & Özdemir, P. (2010) · Statistics in Medicine · doi:10.1002/sim.4040 · Cited by 757 · see citing works
Latitude is significantly associated with the prevalence of multiple sclerosis: a meta-analysis
Simpson, S., Blizzard, L., Otahal, P., Van der Mei, I., & Taylor, B. (2011) · Journal of Neurology, Neurosurgery & Psychiatry · doi:10.1136/jnnp.2011.240432 · Cited by 718 · see citing works
Chu, H., & Cole, S. R. (2006) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2006.06.011 · Cited by 708 · see citing works
Self-citationSchwarzer, G., Chemaitelly, H., Abu‐Raddad, L. J., & Rücker, G. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1348 · Cited by 625 · see citing works
Bayesian approaches to random-effects meta-analysis: a comparative study
Smith, T. C., Spiegelhalter, D. J., & Thomas, A. (1995) · Statistics in Medicine · doi:10.1002/sim.4780142408 · Cited by 568 · see citing works
Neuhaus, J. M., Kalbfleisch, J. D., & Hauck, W. W. (1991) · International Statistical Review · doi:10.2307/1403572 · Cited by 548 · see citing works
The Inverse of the Freeman – Tukey Double Arcsine Transformation
Miller, J. J. (1978) · The American Statistician · doi:10.1080/00031305.1978.10479283 · Cited by 501 · see citing works
The binomial distribution of meta-analysis was preferred to model within-study variability
Hamza, T. H., van Houwelingen, H. C., & Stijnen, T. (2007) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2007.03.016 · Cited by 388 · see citing works
Warn, D. E., Thompson, S. G., & Spiegelhalter, D. J. (2002) · Statistics in Medicine · doi:10.1002/sim.1189 · Cited by 277 · see citing works
Marginally Specified Logistic‐Normal Models for Longitudinal Binary Data
Heagerty, P. J. (1999) · Biometrics · doi:10.1111/j.0006-341x.1999.00688.x · Cited by 210 · see citing works
A comparison of seven random‐effects models for meta‐analyses that estimate the summary odds ratio
Jackson, D., Law, M. W.-M., Stijnen, T., Viechtbauer, W., & White, I. R. (2018) · Statistics in Medicine · doi:10.1002/sim.7588 · Cited by 203 · see citing works
When should meta‐analysis avoid making hidden normality assumptions?
Jackson, D., & White, I. R. (2018) · Biometrical Journal · doi:10.1002/bimj.201800071 · Cited by 177 · see citing works
Incidence of maternal peripartum infection: A systematic review and meta-analysis
Woodd, S., Montoya, A., Barreix, M., Pi, L., Calvert, C., Rehman, A. M., Chou, D., & Campbell, O. M. R. (2019) · PLoS Medicine · doi:10.1371/journal.pmed.1002984 · Cited by 163 · see citing works
Use of Generalized Linear Mixed Models for Network Meta-analysis
Tu, Y. (2014) · Medical Decision Making · doi:10.1177/0272989x14545789 · Cited by 92 · see citing works
Chu, H., Nie, L., Chen, Y., Huang, Y., & Sun, W. (2010) · Statistical Methods in Medical Research · doi:10.1177/0962280210393712 · Cited by 78 · see citing works
Self-citationMeta-analysis of binary outcomes via generalized linear mixed models: a simulation study
Bakbergenuly, I., & Kulinskaya, E. (2018) · BMC Medical Research Methodology · doi:10.1186/s12874-018-0531-9 · Cited by 69 · see citing works
Sampling Bias and Logistic Models
McCullagh, P. J. (2008) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2007.00660.x · Cited by 38 · see citing works
Marginalized Models for Moderate to Long Series of Longitudinal Binary Response Data
Schildcrout, J. S., & Heagerty, P. J. (2006) · Biometrics · doi:10.1111/j.1541-0420.2006.00680.x · Cited by 37 · see citing works
Multiple imputation of missing blood pressure covariates in survival analysis
van Buuren, S., Boshuizen, H. C., & Knook, D. L. (1999) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19990330)18:6
Hahn, S., Williamson, P. R., Hutton, J. L., Garner, P., & Flynn, E. V. (2000) · Statistics in Medicine · doi:10.1002/1097-0258(20001230)19:24
Flagged first, then by citations
Research works printed but not linked: 4
- [22]Schwarzer G meta: An R package for meta-analysis. R News 2007; 7(3): 40– 45.
- [23]Agresti A Foundations of Linear and Generalized Linear Models. Hoboken, NJ: John Wiley & Sons, 2015.
- [29]Agresti A Categorical Data Analysis. Third ed. Hoboken, NJ: John Wiley & Sons, 2013.
- [30]Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Boca Raton, FL: CRC Press, 1998.
Cited by
Sorted by citations
Quek, J., Chan, K. E., Wong, Z. Y., Tan, C., Tan, B., Lim, W. H., Tan, D. J. H., Tang, A. S. P., Tay, P., Xiao, J., et al. (2023) · The Lancet Gastroenterology & Hepatology · doi:10.1016/s2468-1253(22)00317-x · Cited by 749 · see citing works
En Li Cho, E., Ang, C. Z., Quek, J., Fu, C. E., Lim, L. K. E., Heng, Z. E. Q., Tan, D. J. H., Lim, W. H., Yong, J. N., Zeng, R., et al. (2023) · Gut · doi:10.1136/gutjnl-2023-330110 · Cited by 380 · see citing works
Xu, C., Fan, S., Tian, Y., Liu, F., Furuya-Kanamori, L., Clark, J., Zhang, C., Li, S., Lin, L., Chu, H., et al. (2025) · BMJ · doi:10.1136/bmj-2024-082068 · Cited by 39 · see citing works
Self-citationOsinga, J. A. J., Derakhshan, A., Feldt-Rasmussen, U., Huang, K., Vrijkotte, T. G. M., Männistö, T., Bassols, J., López-Bermejo, A., Aminorroaya, A., Vafeiadi, M., et al. (2024) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgad564 · Cited by 27 · see citing works
Ye, F., Lee, J. J., Xue, D., & Yu, D. S.-F. (2023) · JAMA Network Open · doi:10.1001/jamanetworkopen.2023.46216 · Cited by 23 · see citing works
- Authors
- Lin, L., & Chu, H.
- Affiliations
- Florida State University (US)
- University of Minnesota (US)
- Corresponding author
- Lin, Lifeng
- Venue
- Epidemiology
- Published
- 2020-09
- Volume
- 31
- Issue
- 5
- Pages
- 713-717
- ISSN
- 1044-3983 (ISSN-L)
- PMC
- PMC7398826
- OpenAlex
- W3043017551
- Cited by
- 345
- References
- 31
- Citations by year
- 2026: 74 · 2025: 76 · 2024: 73 · 2023: 53 · 2022: 36 · 2021: 30 · 2020: 3
- FWCI
- 6.30
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health (UL1TR001427, UL1TR002494)
- National Cancer Institute (P30CA077598)
- U.S. National Library of Medicine (R01LM012982)
- National Center for Advancing Translational Sciences
- 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
- generalized linear mixed models, two-stage algorithm, logit transformation, arcsine transformation, zero counts
- MeSH terms
- Humans, Meta-Analysis as Topic, Linear Models
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