Abstract
The meta-analysis of single proportions has become a popular application over the last two decades. Especially, systematic reviews of prevalence studies are conducted in various fields of science, including medicine, ecology, psychology, or social sciences. In this chapter, we illustrate meta-analysis methods to pool single proportions and to compare proportions from two groups. We introduce classic approaches based on the inverse variance method as well as generalized linear mixed models taking the binary structure of the data into account. The most common transformations of proportions and their back-transformations are described both for individual studies and in the meta-analysis setting.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Borges Migliavaca C, Stein C, Colpani V, Barker TH, Munn Z, Falavigna M (2020) How are systematic reviews of prevalence conducted? A methodological study. BMC Med Res Methodol 20(1):96
Munn Z, Moola S, Riitano D, Lisy K (2014) The development of a critical appraisal tool for use in systematic reviews addressing questions of prevalence. Int J Health Policy Manag 3(3):123–128
Meo SA, Sheikh SA, Sattar K, Akram A, Hassan A, Meo AS (2019) Prevalence of Type 2 diabetes mellitus among men in the middle east: a retrospective study. Am J Mens Health 13(3):1557988319848577
Al Kanaani Z (2018) The epidemiology of hepatitis C virus in Pakistan: systematic review and meta-analyses. R Soc Open Sci 5:180257
Papazisis G, Siafis S, Tsakiridis I, Koulas I, Dagklis T, Kouvelas D (2018) Prevalence of cannabis use among medical students: a systematic review and meta-analysis. Subst Abuse Res Treat 12:117822181880597
Barendregt JJ, Doi SA, Lee YY, Norman RE, Vos T (2013) Meta-analysis of prevalence. J Epidemiol Community Health 67(11):974–978
Warton DI, Hui FKC (2011) The arcsine is asinine: the analysis of proportions in ecology. Ecology 92(1):3–10
Hamza TH, van Houwelingen HC, Stijnen T (2008) The binomial distribution of meta-analysis was preferred to model within-study variability. J Clin Epidemiol 61(1):41–51
Jaeger TF (2008) Categorical data analysis: away from ANOVAs (transformation or not) and towards logit mixed models. J Mem Lang 59(4):434–446
Stijnen T, Hamza TH, Ozdemir P (2010) Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Stat Med 29(29):3046–3067
Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rücker G (2019) Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions. Res Synth Methods 10:476–483
Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010) A basic introduction to fixed-effect and random-effects models for meta-analysis. Res Synth Methods 1(2):97–111
Bylsma LC, Gillezeau C, Garawin TA, Kelsh MA, Fryzek JP, Sangaré L (2020) Prevalence of RAS and BRAF mutations in metastatic colorectal cancer patients by tumor sidedness: a systematic review and meta-analysis. Cancer Med 9(3):1044–1057
Berkson J (1944) Application of the logistic function to bio-assay. J Am Stat Assoc 39(227):357–365
Gart JJ, Zweifel JR (1967) On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika 54(1/2):181–187
Anscombe FJ (1948) The transformation of poisson, binomial and negative-binomial data. Biometrika 35:246–254
Freeman MF, Tukey JW (1950) Transformations related to the angular and the square root. Ann Math Stat 21:607–611
Miller JJ (1978) The inverse of the Freeman-Tukey double arcsine transformation. Am Stat 32(4):138
Wilson EB (1927) Probable inference, the law of succession, and statistical inference. J Am Stat Assoc 22(158):209–212
Clopper CJ, Pearson ES (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26(4):404–413
Agresti A, Coull BA (1998) Approximate is better than “exact” for interval estimation of binomial proportions. Am Stat 52(2):119–126
Newcombe RG (1998) Two-sided confidence intervals for the single proportion: comparison of seven methods. Stat Med 17(8):857–872
Veroniki AA, Jackson D, Viechtbauer W, Bender R, Bowden J, Knapp G (2016) Methods to estimate the between-study variance and its uncertainty in meta-analysis. Res Synth Methods 7:55–79
Hartung J (1999) An alternative method for meta-analysis. Biom J 41(8):901–916
Hartung J, Knapp G (2001) A refined method for the meta-analysis of controlled clinical trials with binary outcome. Stat Med 20(24):3875–3889
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009) A re-evaluation of random-effects meta-analysis. J R Stat Soc Ser A Stat Soc 172(1):137–159
Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JP (2012) Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane database of systematic reviews. Int J Epidemiol 41(3):818–827
Fleiss J (1993) Review papers : the statistical basis of meta-analysis. Stat Methods Med Res 2(2):121–145
Mantel N, Haenszel W (1959) Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst 22:719–748
Yusuf S, Peto R, Lewis J, Collins R, Sleight P (1985) Beta blockade during and after myocardial infarction: an overview of the randomized trials. Prog Cardiovasc Dis 27(5):335–371
Greenland S, Robins JM (1985) Estimation of a common effect parameter from sparse follow-up data. Biometrics 41(1):55–68
Greenland S, Salvan A (1990) Bias in the one-step method for pooling study results. Stat Med 9(3):247–252
Brockhaus AC, Bender R, Skipka G (2014) The Peto odds ratio viewed as a new effect measure. Stat Med 33(28):4861–4874
Bradburn MJ, Deeks JJ, Berlin JA, Russell Localio A (2007) Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Stat Med 26(1):53–77
Brockhaus AC, Grouven U, Bender R (2016) Performance of the Peto odds ratio compared to the usual odds ratio estimator in the case of rare events. Biom J 58(6):1428–1444
Emerson JD (1994) Combining estimates of the odds ratio: the state of the art. Stat Methods Med Res 3(2):157–178
Balduzzi S, Rücker G, Schwarzer G (2019) How to perform a meta-analysis with R: a practical tutorial. Evid Based Ment Health 22:153–160
Rutter CM, Gatsonis CA (2001) A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Stat Med 20(19):2865–2884
Reitsma JB, Glas AS, Rutjes AWS, Scholten RJPM, Bossuyt PM, Zwinderman AH (2005) Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. J Clin Epidemiol 58(10):982–990
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Science+Business Media, LLC, part of Springer Nature
About this protocol
Cite this protocol
Schwarzer, G., Rücker, G. (2022). Meta-Analysis of Proportions. In: Evangelou, E., Veroniki, A.A. (eds) Meta-Research. Methods in Molecular Biology, vol 2345. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-1566-9_10
Download citation
DOI: https://doi.org/10.1007/978-1-0716-1566-9_10
Published:
Publisher Name: Humana, New York, NY
Print ISBN: 978-1-0716-1565-2
Online ISBN: 978-1-0716-1566-9
eBook Packages: Springer Protocols