The DOI matches its Crossref record; 59 of the 59 references it cites were found in a registry or an index.
Arcsine‐based transformations for meta‐analysis of proportions: Pros, cons, and alternatives
Open accessAbstract
Meta‐analyses have been increasingly used to synthesize proportions (eg, disease prevalence) from multiple studies in recent years. Arcsine‐based transformations, especially the Freeman–Tukey double‐arcsine transformation, are popular tools for stabilizing the variance of each study's proportion in two‐step meta‐analysis methods. Although they offer some benefits over the conventional logit transformation, they also suffer from several important limitations (eg, lack of interpretability) and may lead to misleading conclusions. Generalized linear mixed models and Bayesian models are intuitive one‐step alternative approaches, and can be readily implemented via many software programs. This article explains various pros and cons of the arcsine‐based transformations, and discusses the alternatives that may be generally superior to the currently popular practice.
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.
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
Fitting Linear Mixed-Effects Models Using lme4
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015) · Journal of Statistical Software · doi:10.18637/jss.v067.i01 · Cited by 86,835
Baltosser, W. H., & Zar, J. H. (1996) · Ecology · doi:10.2307/2265725 · Cited by 35,166
Cochrane Handbook for Systematic Reviews of Interventions: Cochrane Book Series
(2008) · doi:10.1002/9780470712184 · Cited by 25,048
Conducting 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
Statistical Methods for Rates and Proportions
Fleiss, J. L., Levin, B., & Paik, M. C. (2003) · Wiley Series in Probability and Statistics · doi:10.1002/0471445428 · Cited by 18,646
Cochrane Handbook for Systematic Reviews of Interventions
(2019) · doi:10.1002/9781119536604 · Cited by 14,828
Sterne, J. A. C., Sutton, A. J., Ioannidis, J. P. A., Terrin, N., Jones, D. R., Lau, J., Carpenter, J., Rucker, G., Harbord, R. M., Schmid, C. H., et al. (2011) · BMJ · doi:10.1136/bmj.d4002 · Cited by 7,709
A basic introduction to fixed-effect and random-effects models for meta-analysis
Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2010) · Research Synthesis Methods · doi:10.1002/jrsm.12 · Cited by 6,793 · cited 1×
“Second, as the proportion estimates are usually heterogeneous, the random-effects meta-analysis method is frequently used, assuming that each study's underlying true transformed proportion follows the normal distribution across studies.(22) The arcsine-based transfor-”
MethodFunnel plots for detecting bias in meta-analysis
Sterne, J. A. C., & Egger, M. (2001) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(01)00377-8 · Cited by 3,779 · cited 1×
“For example, metaanalysts frequently use the forest plot to visualize the distributions of study-specific estimates,(56) and the funnel plot to assess potential publication bias or small-study effects.(57,58) Both plots depend on each”
BackgroundReitsma, J. B., Glas, A. S., Rutjes, A. W. S., Scholten, R. J. P. M., Bossuyt, P. M., & Zwinderman, A. H. (2005) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2005.02.022 · Cited by 3,369 · cited 1×
“Besides the arcsine-based transformations, the log and logit transformations are also frequently used for proportions.(10,20,21) Their formulas are more straightforward: the log transformation is yi = g (pi) = logpi, with variance vi = 1/ei − 1/ni, and the logit transformation is yi = g(pi) = log[pi/(1 − pi)], with va…”
MethodTransformations 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 2,628
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
The arcsine is asinine: the analysis of proportions in ecology
Warton, D. I., & Hui, F. K. C. (2011) · Ecology · doi:10.1890/10-0340.1 · Cited by 2,280
Comparison of two methods to detect publication bias in meta-analysis.
Peters, J. L. (2006) · JAMA · doi:10.1001/jama.295.6.676 · Cited by 2,278
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
What to add to nothing? Use and avoidance of continuity corrections in meta‐analysis of sparse data
J. Sweeting, M., J. Sutton, A., & C. Lambert, P. (2004) · Statistics in Medicine · doi:10.1002/sim.1761 · Cited by 1,734
Agresti, A., & Kateri, M. (2011) · International Encyclopedia of Statistical Science · doi:10.1007/978-3-642-04898-2_161 · Cited by 1,111
Estimation of effect size from a series of independent experiments.
Hedges, L. V. (1982) · Psychological Bulletin · doi:10.1037//0033-2909.92.2.490 · Cited by 1,062
A random‐effects regression model for meta‐analysis
Berkey, C. S., Hoaglin, D. C., Mosteller, F., & Colditz, G. A. (1995) · Statistics in Medicine · doi:10.1002/sim.4780140406 · Cited by 879
Turner, R. M., Davey, J., Clarke, M. J., Thompson, S. G., & Higgins, J. P. (2012) · International Journal of Epidemiology · doi:10.1093/ije/dys041 · Cited by 837
Stijnen, T., Hamza, T. H., & Özdemir, P. (2010) · Statistics in Medicine · doi:10.1002/sim.4040 · Cited by 757
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
Chu, H., & Cole, S. R. (2006) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2006.06.011 · Cited by 708
Lange, S., Probst, C., Gmel, G., Rehm, J., Burd, L., & Popova, S. (2017) · JAMA Pediatrics · doi:10.1001/jamapediatrics.2017.1919 · Cited by 669
Schwarzer, G., Chemaitelly, H., Abu‐Raddad, L. J., & Rücker, G. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1348 · Cited by 625
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 · cited 1×
“meta-analysis methods, including generalized linear mixed models (GLMMs) or Bayesian hierarchical models.(11,18,19,37-43)”
MethodThe Inverse of the Freeman – Tukey Double Arcsine Transformation
Miller, J. J. (1978) · The American Statistician · doi:10.1080/00031305.1978.10479283 · Cited by 535
Ismail, Z., Elbayoumi, H., Fischer, C. E., Hogan, D. B., Millikin, C. P., Schweizer, T., Mortby, M. E., Smith, E. E., Patten, S. B., & Fiest, K. M. (2017) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2016.3162 · Cited by 532
Sun, P., Qie, S., Liu, Z., Ren, J., Li, K., & Xi, J. (2020) · Journal of Medical Virology · doi:10.1002/jmv.25735 · Cited by 523
Prevalence of Multiple Forms of Sexting Behavior Among Youth: A Systematic Review and Meta-analysis
Madigan, S., Ly, A., Rash, C. L., Van Ouytsel, J., & Temple, J. R. (2018) · JAMA Pediatrics · doi:10.1001/jamapediatrics.2017.5314 · Cited by 519
The Estimation and Interpretation of Attributable Risk in Health Research
Walter, S. D. (1976) · Biometrics · doi:10.2307/2529268 · Cited by 451
Sobczyk, K., & Kirkner, D. J. (2001) · Modeling and Simulation in Science, Engineering and Technology · doi:10.1007/978-1-4612-0121-2_5 · Cited by 436
Blyth, C. R., & Still, H. A. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477938 · Cited by 434
The binomial distribution of meta-analysis was preferred to model within-study variability
Hamza, T. H., van Houwelingen, H. C., & Stijnen, T. (2008) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2007.03.016 · Cited by 385
How are systematic reviews of prevalence conducted? A methodological study
on behalf of the Prevalence Estimates Reviews – Systematic Review Methodology Group (PERSyst), Borges Migliavaca, C., Stein, C., Colpani, V., Barker, T. H., Munn, Z., & Falavigna, M. (2020) · BMC Medical Research Methodology · doi:10.1186/s12874-020-00975-3 · Cited by 359
Meta-analysis of proportions using generalized linear mixed models.
Lin, L., & Chu, H. (2020) · Epidemiology · doi:10.1097/ede.0000000000001232 · Cited by 345
Self-citationBias caused by sampling error in meta-analysis with small sample sizes
Lin, L. (2018) · PLOS ONE · doi:10.1371/journal.pone.0204056 · Cited by 335
Self-citationThe Transformation of Poisson, Binomial and Negative-Binomial Data
Anscombe, F. J. (1948) · Biometrika · doi:10.2307/2332343 · Cited by 304
Warn, D. E., Thompson, S. G., & Spiegelhalter, D. J. (2002) · Statistics in Medicine · doi:10.1002/sim.1189 · Cited by 277
Rücker, G., Schwarzer, G., Carpenter, J., & Olkin, I. (2009) · Statistics in Medicine · doi:10.1002/sim.3511 · Cited by 252
Mortality in children diagnosed with tuberculosis: a systematic review and meta-analysis
Jenkins, H. E., Yuen, C. M., Rodriguez, C. A., Nathavitharana, R. R., McLaughlin, M. M., Donald, P., Marais, B. J., & Becerra, M. C. (2017) · The Lancet Infectious Diseases · doi:10.1016/s1473-3099(16)30474-1 · Cited by 246
Practical guide to the meta-analysis of rare events
Efthimiou, O. (2018) · Evidence Based Mental Health · doi:10.1136/eb-2018-102911 · Cited by 231
A comparison of seven random‐effects models for meta‐analyses that estimate the summary odds ratio
Jackson, D., Law, M., Stijnen, T., Viechtbauer, W., & White, I. R. (2018) · Statistics in Medicine · doi:10.1002/sim.7588 · Cited by 203
When should meta‐analysis avoid making hidden normality assumptions?
Jackson, D., & White, I. R. (2018) · Biometrical Journal · doi:10.1002/bimj.201800071 · Cited by 178
A systematic review and meta-analysis of the prevalence of left ventricular non-compaction in adults
Ross, S. B., Jones, K., Blanch, B., Puranik, R., McGeechan, K., Barratt, A., & Semsarian, C. (2020) · European Heart Journal · doi:10.1093/eurheartj/ehz317 · Cited by 171
Dendukuri, N., Schiller, I., Joseph, L., & Pai, M. (2012) · Biometrics · doi:10.1111/j.1541-0420.2012.01773.x · Cited by 117
The Uses and Usefulness of Binomial Probability Paper
Mosteller, F. C., & Tukey, J. W. (1949) · Journal of the American Statistical Association · doi:10.1080/01621459.1949.10483300 · Cited by 114
Chu, H., Chen, S., & Louis, T. A. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.0017 · Cited by 87
Exclusion of studies with no events in both arms in meta-analysis impacted the conclusions
Xu, C., Li, L., Lin, L., Chu, H., Thabane, L., Zou, K., & Sun, X. (2020) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2020.03.020 · Cited by 75
Self-citationCorrection for bias in meta‐analysis of little‐replicated studies
Doncaster, C. P., & Spake, R. (2017) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12927 · Cited by 67
Ju, K., Lin, L., Chu, H., Cheng, L.-L., & Xu, C. (2020) · BMC Medical Research Methodology · doi:10.1186/s12874-020-01035-6 · Cited by 61
Self-citationSimulation-Based Comparison of Methods for Meta-Analysis of Proportions and Rates
Trikalinos, T. A., Trow, P., & Schmid, C. H. (2013) · Europe PMC (PubMed Central) · Cited by 54
The Bias and Higher Cumulants of the Logarithm of a Binomial Variate
Pettigrew, H. M., Gart, J. J., & Thomas, D. G. (1986) · Biometrika · doi:10.1093/biomet/73.2.425 · Cited by 44
Negeri, Z., Shaikh, M. R., & Beyene, J. (2018) · Biometrical Journal · doi:10.1002/bimj.201700101 · Cited by 39
Multiple uses of forest plots in presenting analysis results in health research: A Tutorial
Li, G., Zeng, J., Tian, J., Levine, M., & Thabane, L. (2019) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2019.09.021 · Cited by 37
A Unification of Models for Meta-Analysis of Diagnostic Accuracy Studies without a Gold Standard
Liu, Y., Chen, Y., & Chu, H. (2014) · Biometrics · doi:10.1111/biom.12264 · Cited by 33
Using Bayesian Inference to Perform Meta-Analysis
Schmid, C. H. (2001) · Evaluation & the Health Professions · doi:10.1177/01632780122034867 · Cited by 31
A Bayesian multivariate meta‐analysis of prevalence data
Siegel, L. K., Rudser, K. D., Sutcliffe, S., Markland, A. D., Brubaker, L. T., Gahagan, S., Stapleton, A. E., & Chu, H. (2020) · Statistics in Medicine · doi:10.1002/sim.8593 · Cited by 8
Domain of Inverse Double Arcsine TransformationPreprint
Jeong, J. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1811.07827 · Cited by 4
Research works printed but not linked: 3
- Rothman KJ, 2008, Modern Epidemiology
- 10.1037/0033-2909.92.2.490 · DOI · Paper page
- Schwarzer G, 2007, Meta: an R package for meta‐analysis, R News, 7, 40
Cited by
Teo, R. H., Cheng, W. H., Cheng, L. J., Lau, Y., & Lau, S. T. (2023) · Archives of Gerontology and Geriatrics · doi:10.1016/j.archger.2022.104904 · Cited by 160
Qiu, X., Nergiz, A. I., Maraolo, A. E., Bogoch, I. I., Low, N., & Cevik, M. (2021) · Clinical Microbiology and Infection · doi:10.1016/j.cmi.2021.01.011 · Cited by 135
Ribeiro, F., Teixeira-Santos, A. C., Caramelli, P., & Leist, A. K. (2022) · Ageing Research Reviews · doi:10.1016/j.arr.2022.101703 · Cited by 114
“Accordingly, the random effects method was used to estimate the pooled prevalence using the Freeman-Tukey double arcsine transformation that stabilizes the variance of each study’s proportion (Lin and Xu, 2020).”
MethodHuang, G., Chu, H., Chen, R., Liu, D., Banda, K. J., O’Brien, A. P., Jen, H.-J., Chiang, K.-J., Chiou, J.-F., & Chou, K.-R. (2022) · Journal of Global Health · doi:10.7189/jogh.12.05028 · Cited by 64
Stegen, H., Duppen, D., Savieri, P., Stas, L., Pan, H., Aartsen, M., Callewaert, H., Dierckx, E., & De Donder, L. (2024) · International Psychogeriatrics · doi:10.1017/s1041610224000425 · Cited by 42
Metadata
- Authors
- Lin, L., & Xu, C.
- Venue
- Health Science Reports
- Publisher
- Wiley
- Published
- 2020-07-27
- Volume
- 3
- Issue
- 3
- Pages
- e178-e178
- ISSN
- 2398-8835 (ISSN-L)
- OpenAlex
- W3044366033
- Cited by
- 339
- References
- 59
- FWCI
- 24.30
- Type
- journal article
- Language
- en
- Open access
- gold
- Funders
- National Center for Advancing Translational Sciences (UL1 TR001427)
- U.S. National Library of Medicine (R01 LM012982)
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
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.