Contextual citations appear beside each decision in the analysis. Cite the source that supports the specific method you used, rather than citing this interface as methodological authority.
Choosing a model and pooling binary outcomes
Deeks JJ, Higgins JPT, Altman DG, McKenzie JE, Veroniki AA. Chapter 10: Analysing data and undertaking meta-analyses. Cochrane Handbook, version 6.5 (2024). Sections 10.4.1, 10.4.4.1, 10.5.2 and 10.10.4.
Read original source (opens in new tab)Odds ratios, log scales and event definitions
Higgins JPT, Li T, Deeks JJ. Chapter 6: Choosing effect measures and computing estimates of effect. Cochrane Handbook, version 6.5 (2024). Sections 6.1.2, 6.3.1, 6.4 and 6.5.2.3.
Read original source (opens in new tab)Original Mantel–Haenszel method
Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst. 1959;22(4):719–748. doi:10.1093/jnci/22.4.719.
Read original source (opens in new tab)Estimating between-study variance
Veroniki AA, et al. Methods to estimate the between-study variance and its uncertainty in meta-analysis. Res Synth Methods. 2016;7(1):55–79. doi:10.1002/jrsm.1164.
Read original source (opens in new tab)Modified Knapp–Hartung confidence intervals
Röver C, Knapp G, Friede T. Hartung-Knapp-Sidik-Jonkman approach and its modification for random-effects meta-analysis with few studies. BMC Med Res Methodol. 2015;15:99. doi:10.1186/s12874-015-0091-1.
Read original source (opens in new tab)The R software used for this analysis
Viechtbauer W. Conducting meta-analyses in R with the metafor package. J Stat Softw. 2010;36(3):1–48. doi:10.18637/jss.v036.i03.
Read original source (opens in new tab)Implementation details and interval options
metafor documentation: rma.uni (REML, DL, test="adhoc" and test="z") and rma.mh. Consult the downloaded session information for the version actually used.
Read original source (opens in new tab)When funnel plots and asymmetry tests are appropriate
Page MJ, Higgins JPT, Sterne JAC. Cochrane Handbook v6.5 (2024), Chapter 13, sections 13.3.4.2 and 13.3.4.4: Assessing risk of bias due to missing evidence.
Read original source (opens in new tab)The 10-study rule and effect-measure restrictions
Sterne JAC, et al. Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials. BMJ. 2011;343:d4002.
Read original source (opens in new tab)Original Egger regression test
Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test. BMJ. 1997;315:629–634.
Read original source (opens in new tab)Implementation of regression tests for asymmetry
metafor documentation: regtest. Original Egger implementation: model="lm", predictor="sei"; a weighted regression with multiplicative dispersion.
Read original source (opens in new tab)Binomial models for single-group proportions
Lin L, Chu H. Meta-analysis of proportions using generalized linear mixed models. Epidemiology. 2020;31(5):713–717.
Read original source (opens in new tab)Estimating a mean from a median and quartiles or range
Luo D, Wan X, Liu J, Tong T. Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range. Stat Methods Med Res. 2018;27(6):1785–1805.
Read original source (opens in new tab)Estimating an SD from a range or interquartile range
Wan X, Wang W, Liu J, Tong T. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol. 2014;14:135.
Read original source (opens in new tab)Estimating an SD from the five-number summary
Shi J, Luo D, Weng H, et al. Optimally estimating the sample standard deviation from the five-number summary. Res Synth Methods. 2020;11(5):641–654.
Read original source (opens in new tab)Checking medians and quartiles for skewed data
Shi J, Luo D, Wan X, et al. Detecting the skewness of data from the five-number summary and its application in meta-analysis. Stat Methods Med Res. 2023;32(7):1338–1360.
Read original source (opens in new tab)Standard error of an AUROC from group sizes
Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology. 1982;143(1):29–36.
Read original source (opens in new tab)Why funnel plots mislead for proportions
Hunter JP, Saratzis A, Sutton AJ, Boucher RH, Sayers RD, Bown MJ. In meta-analyses of proportion studies, funnel plots were found to be an inaccurate method of assessing publication bias. J Clin Epidemiol. 2014;67(8):897–903.
Read original source (opens in new tab)Implementation of logistic meta-analysis
metafor documentation: rma.glmm. Logit-binomial models for proportions; maximum likelihood with adaptive quadrature. MetaLab uses its t-based interval (k − 1 degrees of freedom) for the random-effects model.
Read original source (opens in new tab)Joint synthesis of sensitivity and specificity
Takwoingi Y, et al. Undertaking meta-analysis. Cochrane Handbook for Systematic Reviews of Diagnostic Test Accuracy. 2023. Chapter 10.
Read original source (opens in new tab)How the bivariate and HSROC diagnostic models relate
Harbord RM, Deeks JJ, Egger M, Whiting P, Sterne JAC. A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics. 2007;8(2):239–251.
Read original source (opens in new tab)What a random-effects average means, and prediction intervals
Higgins JPT, Thompson SG, Spiegelhalter DJ. A re-evaluation of random-effects meta-analysis. J R Stat Soc Ser A Stat Soc. 2009;172(1):137–159.
Read original source (opens in new tab)Why to report prediction intervals
IntHout J, Ioannidis JPA, Rovers MM, Goeman JJ. Plea for routinely presenting prediction intervals in meta-analysis. BMJ Open. 2016;6(7):e010247.
Read original source (opens in new tab)Judging consistency from the study results
Guyatt GH, Oxman AD, Kunz R, et al. GRADE guidelines: 7. Rating the quality of evidence: inconsistency. J Clin Epidemiol. 2011;64(12):1294–1302.
Read original source (opens in new tab)Why I² depends on study size
Rücker G, Schwarzer G, Carpenter JR, Schumacher M. Undue reliance on I² in assessing heterogeneity may mislead. BMC Med Res Methodol. 2008;8:79.
Read original source (opens in new tab)Why I² doesn't show how much results vary
Borenstein M, Higgins JPT, Hedges LV, Rothstein HR. Basics of meta-analysis: I² is not an absolute measure of heterogeneity. Res Synth Methods. 2017;8(1):5–18.
Read original source (opens in new tab)Bivariate binomial model for diagnostic accuracy
Chu H, Cole SR. Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalized linear mixed model approach. J Clin Epidemiol. 2006;59(12):1331–1332.
Read original source (opens in new tab)Why diagnostic accuracy needs a different asymmetry test
Deeks JJ, Macaskill P, Irwig L. The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. J Clin Epidemiol. 2005;58(9):882–893.
Read original source (opens in new tab)Implementation of the bivariate binomial model
lme4 documentation: glmer. Binomial models with correlated random effects fitted using the Laplace approximation (nAGQ=1). MetaLab calculates normal (Wald) intervals from the fitted estimates and standard errors, as Cochrane’s MetaDAS macro does.
Read original source (opens in new tab)Adjusted estimates and non-randomised studies
Reeves BC, et al. Cochrane Handbook v6.5 (2024), Chapter 24: Including non-randomized studies on intervention effects.
Read original source (opens in new tab)When AUROC and prediction-model performance can be pooled
Debray TPA, et al. A guide to systematic review and meta-analysis of prediction model performance. BMJ. 2017;356:i6460. doi:10.1136/bmj.i6460.
Read original source (opens in new tab)Pooling AUCs from studies of the same diagnostic test
Zhou XH. Empirical Bayes combination of estimated areas under ROC curves using estimating equations. Med Decis Making. 1996;16(1):24–28. doi:10.1177/0272989X9601600109.
Read original source (opens in new tab)Fixed-effect and random-effects pooling of ROC curves and their areas
Hellmich M, Abrams KR, Sutton AJ. Bayesian approaches to meta-analysis of ROC curves. Med Decis Making. 1999;19(3):252–264. doi:10.1177/0272989X9901900304.
Read original source (opens in new tab)AUROC analysis scale and assumptions
Snell KIE, Ensor J, Debray TPA, Moons KGM, Riley RD. Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures? Stat Methods Med Res. 2018;27(11):3505–3522. doi:10.1177/0962280217705678.
Read original source (opens in new tab)