The metafor Package - analysesA Meta-Analysis Package for R
https://metafor-project.org/
2026-04-17T13:55:55+00:00The metafor Package
https://metafor-project.org/
https://metafor-project.org/lib/exe/fetch.php/wiki:logo.pngtext/html2022-10-19T18:55:11+00:00Anonymous (anonymous@undisclosed.example.com)Berkey et al. (1995)
https://metafor-project.org/doku.php/analyses:berkey1995?rev=1666205711
Berkey et al. (1995)
The Methods and Data
Berkey et al. (1995) describe the meta-analytic random- and mixed-effects models and provide the equation for the empirical Bayes estimator for the amount of (residual) heterogeneity (p. 398). The models and methods are illustrated with the BCG vaccine dataset (Colditz et al., 1994). The data are provided in Table 1 in the article and can be loaded with:$\hat{\tau}^2 = 0.268$$\hat{\mu} = -0.5429$$SE[\hat{\mu}] = 0.1842$$\hat{\tau}^2 = 0.157$$log(RR) = …text/html2024-06-09T16:21:28+00:00Anonymous (anonymous@undisclosed.example.com)Berkey et al. (1998)
https://metafor-project.org/doku.php/analyses:berkey1998?rev=1717950088
Berkey et al. (1998)
The Methods and Data
Berkey et al. (1998) describe a meta-analytic multivariate model for the analysis of multiple correlated outcomes. The use of the model is illustrated with results from 5 trials comparing surgical and non-surgical treatments for medium-severity periodontal disease. Reported outcomes include the change in probing depth (PD) and attachment level (AL) one year after the treatment. The effect size measure used for this meta-analysis was the (raw) mean diff…text/html2025-03-27T08:42:35+00:00Anonymous (anonymous@undisclosed.example.com)Credé et al. (2010)
https://metafor-project.org/doku.php/analyses:crede2010?rev=1743064955
Credé et al. (2010)
The Methods and Data
The meta-analysis by Credé, Roch, and Kieszczynka (2010) examined to what extent class attendance in college is related to college grades and students' grade point average (GPA) more broadly. The studies included in the meta-analysis either reported the correlation between attendance and grades for a sample of students in a particular class or the correlation between attendance and GPA. Aside from the interesting subject matter, the meta-analysis is als…text/html2024-04-18T11:34:47+00:00Anonymous (anonymous@undisclosed.example.com)DerSimonian and Kacker (2007)
https://metafor-project.org/doku.php/analyses:dersimonian2007?rev=1713440087
DerSimonian and Kacker (2007)
The Methods and Data
In this paper, the authors describe a variety of methods for estimating the amount of heterogeneity under a random-effects model. In addition to the well-known DerSimonian-Laird and Cochran estimators (the latter is also known as the Hedges or variance component estimator), the author also describe the Paule-Mandel estimator, a two-step Cochran estimator, and a two-step DerSimonian-Laird estimator.$\tau^2$$\tau^2$$\mu$$\tau^2$$\tau^2$$\tau$$\t…text/html2024-06-09T16:19:37+00:00Anonymous (anonymous@undisclosed.example.com)Gleser & Olkin (2009)
https://metafor-project.org/doku.php/analyses:gleser2009?rev=1717949977
Gleser & Olkin (2009)
Introduction
The chapter on stochastically dependent effect sizes by Gleser and Olkin (2009) in The handbook of research synthesis and meta-analysis (2nd ed.) describes how multiple-treatment and multiple-endpoint studies can be meta-analyzed. In particular, whenever there is at least some overlap in the individuals used to compute multiple effect size estimates in a particular study, then the estimates from that study can no longer be treated as independent. The chapter …text/html2022-08-03T11:18:16+00:00Anonymous (anonymous@undisclosed.example.com)Henmi & Copas (2010)
https://metafor-project.org/doku.php/analyses:henmi2010?rev=1659525496
Henmi & Copas (2010)
The Methods and Data
The data come from studies examining the effectiveness of wrist acupuncture point P6 stimulation for preventing postoperative nausea (Lee & Done, 2004).
library(metafor)
dat <- dat.lee2004
dat <- escalc(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat)text/html2025-09-16T08:56:09+00:00Anonymous (anonymous@undisclosed.example.com)Konstantopoulos (2011)
https://metafor-project.org/doku.php/analyses:konstantopoulos2011?rev=1758012969
Konstantopoulos (2011)
The Methods and Data
Konstantopoulos (2011) describes a three-level meta-analytic model that is applicable when multiple effect size estimates are nested within a higher level grouping variable (e.g., paper, lab, research group, species). One would then expect the underlying true effects to be more similar for the same level of the grouping variable than true effects arising from different levels (i.e., the true effects within the same level may be correlated). We can ac…text/html2020-07-17T19:30:04+00:00Anonymous (anonymous@undisclosed.example.com)
https://metafor-project.org/doku.php/analyses:lipsey2001?rev=1595014204
This document is outdated. For the up-to-date version, go here.text/html2025-09-12T15:01:39+00:00Anonymous (anonymous@undisclosed.example.com)Miller (1978)
https://metafor-project.org/doku.php/analyses:miller1978?rev=1757689299
Miller (1978)
Note: Make sure you read the at the end of this page. In essence, I would strongly advise against using the Freeman-Tukey (double arcsine) transformation when meta-analyzing proportions.
The Purpose and Data
When meta-analyzing proportions, it is usually advantageous to first transform the proportions into a measure that has better statistical properties (i.e., a sampling distribution that is closer to a normal distribution and whose sampling variance can be better approximated…text/html2022-08-03T17:05:08+00:00Anonymous (anonymous@undisclosed.example.com)Morris (2008)
https://metafor-project.org/doku.php/analyses:morris2008?rev=1659546308
Morris (2008)
The Purpose and Data
Morris (2008) discusses various ways for computing a (standardized) effect size measure for pretest posttest control group designs, where the characteristic, response, or dependent variable assessed in the individual studies is a quantitative variable.$$g_T = c(n_T-1) \frac{\bar{x}_{post,T} - \bar{x}_{pre,T}}{SD_{pre,T}}$$$$g_C = c(n_C-1) \frac{\bar{x}_{post,C} - \bar{x}_{pre,C}}{SD_{pre,C}},$$$\bar{x}_{pre,T}$$\bar{x}_{post,T}$$SD_{pre,T}$$c(m) = \sqrt{2/m} …text/html2024-06-18T19:29:44+00:00Anonymous (anonymous@undisclosed.example.com)Normand (1999)
https://metafor-project.org/doku.php/analyses:normand1999?rev=1718738984
Normand (1999)
The Data (Part 1)
The article by Normand (1999) is part of the "Tutorial in Biostatistics" series in the journal Statistics in Medicine and provides a nice introduction to meta-analysis, covering equal- and random-effects models. Two datasets are analyzed in this article. The first is based on data by Hine et al. (1989) regarding the mortality risk due to prophylactic use of lidocaine after a heart attack. The second dataset provides the results from studies on the length of the…text/html2024-06-18T19:30:15+00:00Anonymous (anonymous@undisclosed.example.com)Raudenbush & Bryk (1985)
https://metafor-project.org/doku.php/analyses:raudenbush1985?rev=1718739015
Raudenbush & Bryk (1985)
The Methods and Data
Raudenbush and Bryk (1985) describe the meta-analytic random- and mixed-effects models and describe restricted maximum likelihood estimation for the amount of (residual) heterogeneity (p. 80-82). The models and methods are illustrated with a meta-analytic dataset of studies examining how teachers' expectations about their pupils can influence actual IQ levels (Raudenbush, 1984). The data are provided in Table 1 of the article and can be loaded wit…text/html2024-06-18T19:30:44+00:00Anonymous (anonymous@undisclosed.example.com)Raudenbush (2009)
https://metafor-project.org/doku.php/analyses:raudenbush2009?rev=1718739044
Raudenbush (2009)
The Methods and Data
Raudenbush (2009) is an excellent chapter in The handbook of research synthesis and meta-analysis (2nd ed.) and describes in detail many of the models and methods that are implemented in the rma() function (including the meta-analytic random- and mixed-effects models). The dataset that is used for the illustration of the various models and methods is actually the same that is used in the Raudenbush and Bryk (1985) and provides the results from 19 studies …text/html2022-08-03T17:47:13+00:00Anonymous (anonymous@undisclosed.example.com)Rothman et al. (2008)
https://metafor-project.org/doku.php/analyses:rothman2008?rev=1659548833
Rothman et al. (2008)
The Methods
In chapter 15 of their book, Rothman et al. (2008) describe a variety of methods for conducting stratified analyses in epidemiological research. These methods are actually closely tied to methods used for conducting a meta-analysis, so it may be instructive to examine how the examples from the chapter can be replicated with the metafor package.$0.045$$0.034$$0.036$$0.035$$0.032$$-0.018$$0.087$$1.33$$0.87$$2.03$$\chi_{score} = 1.09$$1.19$$\chi^2_{Wald} = 0.45$$…text/html2022-08-03T11:22:17+00:00Anonymous (anonymous@undisclosed.example.com)Stijnen et al. (2010)
https://metafor-project.org/doku.php/analyses:stijnen2010?rev=1659525737
Stijnen et al. (2010)
The Methods and Data
Dichotomous and event count data (based on which one can calculate effect size or outcome measures, such as odds ratios, incidence rate ratios, proportions, and incidence rates) are often assumed to arise from binomial and Poisson distributed data. Stijnen et al. (2010) describe meta-analytic models that are directly based on these distibutions. The collection of models are essentially special cases of generalized linear (mixed-effects) models (i.e., …text/html2022-08-03T11:22:47+00:00Anonymous (anonymous@undisclosed.example.com)van Houwelingen et al. (1993)
https://metafor-project.org/doku.php/analyses:vanhouwelingen1993?rev=1659525767
van Houwelingen et al. (1993)
The Methods and Data
The paper by van Houwelingen et al. (1993) is an early (and unfortunately often overlooked) paper on meta-analytic methods for 2×2 table data that describes a variety of rather sophisticated models and methods, including the equal- and random-effects conditional logistic models, a nonparametric mixture model based on Laird (1978), and the bivariate binomial-normal model. The models and methods are illustrated with data from 27 studies examinin…text/html2024-08-20T13:17:55+00:00Anonymous (anonymous@undisclosed.example.com)van Houwelingen et al. (2002)
https://metafor-project.org/doku.php/analyses:vanhouwelingen2002?rev=1724159875
van Houwelingen et al. (2002)
The Methods and Data
The article by van Houwelingen et al. (2002) is a sequel to the introductory article by Normand (1999) on methods for meta-analysis and focuses on more advanced techniques, such as meta-regression and multivariate models. The authors mostly use SAS throughout the article for fitting the various models. The analyses are replicated here using R.$\tau^2$$\tau^2$$\tau^2$$\tau^2$$\mu$$\mu$$\hat{\mu}$$\mu$$-0.74$$\tau^2$$\hat{\rho} \approx 0.947$text/html2022-08-03T17:53:49+00:00Anonymous (anonymous@undisclosed.example.com)Viechtbauer (2005)
https://metafor-project.org/doku.php/analyses:viechtbauer2005?rev=1659549229
Viechtbauer (2005)
The Methods and Data
In this paper, I compare the statistical properties of 5 different estimators for the amount of heterogeneity in the context of the random-effects model, including the Hunter-Schmidt (HS), Hedges (HE), DerSimonian-Laird (DL), maximum likelihood (ML), and restricted maximum likelihood (REML) estimator. Two examples are used to illustrate that the various estimators can provide divergent or even conflicting estimates. The first data set provides the result…text/html2022-08-03T17:55:43+00:00Anonymous (anonymous@undisclosed.example.com)Viechtbauer (2007)
https://metafor-project.org/doku.php/analyses:viechtbauer2007a?rev=1659549343
Viechtbauer (2007)
The Methods and Data
Viechtbauer (2007) describes various methods for computing confidence intervals (CIs) for the amount of heterogeneity in random-effects models. An example dataset, based on a meta-analysis by Collins et al. (1985) examining the effectiveness of diuretics in pregnancy for preventing pre-eclampsia, is used in the paper to illustrate the various methods. The data are given in the paper in Table I (p. 44).$\tau^2$$\hat{\tau}^2_{SH}$$\tau^2$$I^2$$H^2$$\tau^2$…text/html2022-08-03T11:24:52+00:00Anonymous (anonymous@undisclosed.example.com)Viechtbauer (2007)
https://metafor-project.org/doku.php/analyses:viechtbauer2007b?rev=1659525892
Viechtbauer (2007)
The Methods and Data
Viechtbauer (2007) is a general article about meta-analysis focusing in particular on random- and mixed-effects (meta-regression) models. An example dataset, based on a meta-analysis by Linde et al. (2005) examining the effectiveness of $\mu$$\alpha = .05$$p = .06$$p = .56$$p = .65$text/html2022-08-03T11:25:19+00:00Anonymous (anonymous@undisclosed.example.com)Yusuf et al. (1985)
https://metafor-project.org/doku.php/analyses:yusuf1985?rev=1659525919
Yusuf et al. (1985)
The Methods and Data
The meta-analysis by Yusuf et al. (1985) on the effectiveness of beta blockers for reducing mortality and reinfarction is usually cited as the reference for what is sometimes called Peto's (one-step or modified Mantel-Haenszel) method for meta-analyzing 2×2 table data. The method provides a weighted estimate of the (log) odds ratio under an equal-effects model and is particularly advantageous when the event of interest is rare. However, it should only b…