Version:	1.4-0
Date:	2025-02-04
Title:	Meta-Analysis Datasets
Depends:	R (≥ 4.0.0)
Imports:	utils, tools, mathjaxr
Suggests:	metafor, numDeriv, BiasedUrn, dfoptim, igraph, ape, testthat, digest, lme4, clubSandwich, meta, netmeta, mvtnorm, gridExtra, rms, bayesmeta, ellipse
Description:	A collection of meta-analysis datasets for teaching purposes, illustrating/testing meta-analytic methods, and validating published analyses.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
ByteCompile:	TRUE
LazyData:	TRUE
Encoding:	UTF-8
RdMacros:	mathjaxr
BuildManual:	TRUE
URL:	https://github.com/wviechtb/metadat, https://wviechtb.github.io/metadat/
BugReports:	https://github.com/wviechtb/metadat/issues
NeedsCompilation:	no
Packaged:	2025-02-04 21:32:50 UTC; wviechtb
Author:	Wolfgang Viechtbauer [aut, cre], Thomas White [aut], Daniel Noble [aut], Alistair Senior [aut], W. Kyle Hamilton [aut], Guido Schwarzer [dtc]
Maintainer:	Wolfgang Viechtbauer <wvb@metafor-project.org>
Repository:	CRAN
Date/Publication:	2025-02-04 23:10:02 UTC

Meta-Analysis Datasets for R

Description

The metadat package contains a large collection of meta-analysis datasets. These datasets are useful for teaching purposes, illustrating/testing meta-analytic methods, and validating published analyses.

Browsing and Searching for Datasets

A listing of all datasets in the package can be obtained with help(package=metadat). Each datasets is also tagged with one or multiple concept terms. These concept terms refer to various aspects of a dataset, such as the field/topic of research, the outcome measure used for the analysis, the model(s) used for analyzing the data, and the methods/concepts that can be illustrated with the dataset. The datsearch function can be used to search among the existing datasets in the package based on their concept terms or based on a full-text search of their corresponding help files.

You can also read the documentation online at https://wviechtb.github.io/metadat/ (where the output from the example analyses corresponding to each dataset is provided).

Contributing New Datasets

We welcome contributions of new datasets to the package. For each dataset, there must be a citable reference, ideally in a peer-reviewed journal or publication. The general workflow for contributing a new dataset is as follows:

• Install the metadat package in R in the usual manner (i.e., install.packages("metadat")).

• If you are familiar with Git/GitHub and making pull requests, fork the package repository. Otherwise, download the source version of the package from GitHub and unzip the file to some directory on your computer.

• Place the raw data (in a non-binary format) in the data-raw directory. The file should be named dat.<author><year>.<ext>, where <author> is the last name of the first author of the publication from which the data come, <year> is the publication year, and <ext> is the file extension (e.g., .txt, .csv).

• Place a corresponding R script in the data-raw directory named dat.<author><year>.r that reads in the data, possibly does some data cleaning/processing, and then saves the dataset to the data directory (using save), with name dat.<author><year>.rda.

• Start R, load the metadat package (i.e., library(metadat)), and then run the prep_dat function (either set the working directory to the location of the source package beforehand or use the pkgdir argument of the prep_dat function to specify the source package location).

• For a new dataset, this should create a boilerplate template for a corresponding help file in the man directory, named dat.<author><year>.Rd. Edit the help file, adding the title and a short description of the dataset in general, a description of each variable in the dataset, further details on the dataset (e.g., the field of research, how the data was collected, the purpose of the dataset / what it was used for, the effect size or outcome measure used in the analysis, the types of analyses/models that can be illustrated with the dataset), a reference for the source of the dataset, one or multiple concept terms, the name and email address of the contributor of the dataset, and (optionally) example code to illustrate the analysis of the dataset.

• Either make a pull request (if you are familiar with this workflow) or zip up the dat.<author><year>.<ext>, dat.<author><year>.r, dat.<author><year>.rda, and dat.<author><year>.Rd files and open up a new issue at GitHub, attaching the zip file.

• If the above makes no sense to you, you can also email one of the package authors with a cleaned, raw data file in .txt or .csv format, along with a meta-data file (format doesn't matter) that includes the information described above.

Citing the Package

If you use these data, please cite both the metadat package (see citation("metadat") for the reference) and the original source of the data as given under the help file of a dataset.

Bug/Error Reports

If you think you have found an error in an existing dataset or a bug in the package in general, please go to https://github.com/wviechtb/metadat/issues and open up a new issue.

Author(s)

Thomas White, thomas.white@sydney.edu.au
Daniel Noble, daniel.noble@anu.edu.au
Alistair Senior, alistair.senior@sydney.edu.au
W. Kyle Hamilton, whamilton@ucmerced.edu
Wolfgang Viechtbauer, wvb@metafor-project.org

Studies on the Association Between Supervision Quality and Various Outcomes in Social, Mental Health, and Child Welfare Workers

Description

Results from 5 studies examining the association between various measures of supervision quality and various work-related outcomes in social, mental health, and child welfare workers.

Usage

dat.aloe2013

Format

The data frame contains the following columns:

Details

The dataset is based on studies that used regression models to examine the association between some measure of perceived supervision quality (e.g., the quality of the relationship with one's supervisor) and some work-related outcome (e.g., job satisfaction) in social, mental health, and child welfare workers. The dataset was extracted from Aloe and Thompson (2013), which in turn is a subset of the studies included in the meta-analysis by Mor Barak et al. (2009).

The dataset can be used to illustrate the meta-analysis of regression models, using measures such as the (semi-)partial correlation coefficient. For this, the t-statistic from the regression model for the association (i.e., predictor) of interest was extracted from each regression model (tval), as well as the sample size (n), the number of predictors included in the regression model (preds), and the coefficient of determination (i.e., R-squared value) of the regression model (R2). Based on this information, the (semi-)partial correlation coefficient can be computed for each study, as well as its corresponding sampling variance. These values can then be meta-analyzed using standard methods.

Concepts

social work, (semi-)partial correlations, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Aloe, A. M., & Thompson, C. G. (2013). The synthesis of partial effect sizes. Journal of the Society for Social Work and Research, 4(4), 390–405. ⁠https://doi.org/10.5243/jsswr.2013.24⁠

References

Mor Barak, M. E., Travis, D. J., Pyun, H., & Xie, B. (2009). The impact of supervision on worker outcomes: A meta-analysis. Social Service Review, 83(1), 3–32. ⁠https://doi.org/10.1086/599028⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.aloe2013
dat

## Not run: 
### load metafor package
suppressPackageStartupMessages(library(metafor))

### compute the partial correlation coefficients and corresponding sampling variances
dat <- escalc(measure="PCOR", ti=tval, ni=n, mi=preds, data=dat)
dat

### random-effects model
res <- rma(yi, vi, data=dat)
res

### mixed-effects meta-regression model examining the relationship between the partial
### correlation coefficients and the number of predictors included in the models
res <- rma(yi, vi, mods = ~ preds, data=dat)
res

### compute the r-to-z transformed partial correlation coefficients and their variances
dat <- escalc(measure="ZPCOR", ti=tval, ni=n, mi=preds, data=dat)
dat

### random-effects model
res <- rma(yi, vi, data=dat)
res

### back-transformation to the partial correlation scale
predict(res, transf=transf.ztor)

### compute the semi-partial correlation coefficients and their variances
dat <- escalc(measure="SPCOR", ti=tval, ni=n, mi=preds, r2i=R2, data=dat)
dat

### random-effects model
res <- rma(yi, vi, data=dat)
res

## End(Not run)

Studies on the Effectiveness of Oral Anticoagulants in Patients with Coronary Artery Disease

Description

Results from 34 trials examining the effectiveness of oral anticoagulants in patients with coronary artery disease.

Usage

dat.anand1999

Format

The data frame contains the following columns:

Details

The dataset includes the results from 34 randomized clinical trials that examined the effectiveness of oral anticoagulants in patients with coronary artery disease. The results given here are focused on the total mortality in the treatment versus control groups.

Concepts

medicine, cardiology, odds ratios, Mantel-Haenszel method

Note

Strictly speaking, there are only 31 trials, since Breddin et al. (1980) and ATACS (1990) are multiarm trials.

According to a correction, dat.anand1999$ci[29] should be 1. But then dat.anand1999$ci[21] would also have to be 1 (if these data indeed refer to the same control group). This appears contradictory, so this correction was not made.

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Anand, S. S., & Yusuf, S. (1999). Oral anticoagulant therapy in patients with coronary artery disease: A meta-analysis. Journal of the American Medical Association, 282(21), 2058–2067. ⁠https://doi.org/10.1001/jama.282.21.2058⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.anand1999
dat

## Not run: 
### load metafor package
library(metafor)

### High-Intensity OA vs Control
rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
       subset=(intensity=="high" & asp.t==0 & asp.c==0), digits=2)

### High- or Moderate-Intensity OA vs Aspirin
rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
       subset=(intensity %in% c("high","moderate") & asp.t==0 & asp.c==1), digits=2)

### Moderate-Intensity OA vs Control
rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
       subset=(intensity=="moderate" & asp.t==0 & asp.c==0), digits=2)

### High- or Moderate-Intensity OA and Aspirin vs Aspirin
rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
       subset=(intensity %in% c("high","moderate") & asp.t==1 & asp.c==1), digits=2)

### Low-Intensity OA and Aspirin vs Aspirin
rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
       subset=(intensity=="low" & asp.t==1 & asp.c==1), digits=2)

## End(Not run)

Studies on the Association between Recidivism and Mental Health

Description

Results from 17 studies on the association between recidivism and mental health in delinquent juveniles.

Usage

dat.assink2016

Format

The data frame contains the following columns:

Details

The studies included in this dataset (which is a subset of the data used in Assink et al., 2015) compared the difference in recidivism between delinquent juveniles with a mental health disorder and a comparison group of juveniles without a mental health disorder. Since studies differed in the way recidivism was defined and assessed, results are given in terms of standardized mean differences, with positive values indicating a higher prevalence of recidivism in the group of juveniles with a mental health disorder.

Multiple effect size estimates could be extracted from most studies (e.g., for different delinquent behaviors in which juveniles could have recidivated), necessitating the use of appropriate models/methods for the analysis. Assink and Wibbelink (2016) illustrate the use of multilevel meta-analysis models for this purpose.

Concepts

psychology, criminology, standardized mean differences, multilevel models, cluster-robust inference

Note

The year variable is not constant within study 3, as this study refers to two different publications using the same data.

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Assink, M., & Wibbelink, C. J. M. (2016). Fitting three-level meta-analytic models in R: A step-by-step tutorial. The Quantitative Methods for Psychology, 12(3), 154–174. ⁠https://doi.org/10.20982/tqmp.12.3.p154⁠

References

Assink, M., van der Put, C. E., Hoeve, M., de Vries, S. L. A., Stams, G. J. J. M., & Oort, F. J. (2015). Risk factors for persistent delinquent behavior among juveniles: A meta-analytic review. Clinical Psychology Review, 42, 47–61. ⁠https://doi.org/10.1016/j.cpr.2015.08.002⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.assink2016
head(dat, 9)

## Not run: 
### load metafor package
library(metafor)

### fit multilevel model
res <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat)
res

### use cluster-robust inference methods
robust(res, cluster=study, clubSandwich=TRUE)

### LRTs for the variance components
res0 <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat, sigma2=c(0,NA))
anova(res0, res)
res0 <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat, sigma2=c(NA,0))
anova(res0, res)

### examine some potential moderators via meta-regression
rma.mv(yi, vi, mods = ~ pubstatus, random = ~ 1 | study/esid, data=dat)
rma.mv(yi, vi, mods = ~ year, random = ~ 1 | study/esid, data=dat)
dat$deltype <- relevel(factor(dat$deltype), ref="general")
rma.mv(yi, vi, mods = ~ deltype, random = ~ 1 | study/esid, data=dat)
rma.mv(yi, vi, mods = ~ year + deltype, random = ~ 1 | study/esid, data=dat)

### assume that the effect sizes within studies are correlated with rho=0.6
V <- vcalc(vi, cluster=study, obs=esid, data=dat, rho=0.6)
round(V[dat$study %in% c(1,2), dat$study %in% c(1,2)], 4)

### fit multilevel model using this approximate V matrix
res <- rma.mv(yi, V, random = ~ 1 | study/esid, data=dat)
res

### use cluster-robust inference methods
robust(res, cluster=study, clubSandwich=TRUE)

### use a correlation of 0.7 for effect sizes corresponding to the same type of
### delinquent behavior and a correlation of 0.5 for effect sizes corresponding
### to different types of delinquent behavior
V <- vcalc(vi, cluster=study, type=deltype, obs=esid, data=dat, rho=c(0.7, 0.5))

### fit multilevel model using this approximate V matrix
res <- rma.mv(yi, V, random = ~ 1 | study/esid, data=dat)
res

### use cluster-robust inference methods
robust(res, cluster=study, clubSandwich=TRUE)

## End(Not run)

Mortality Outcomes with Hydroxychloroquine and Chloroquine in COVID-19 from an International Collaborative Meta-Analysis of Randomized Trials

Description

Results from 33 trials examining the effectiveness of hydroxychloroquine or chloroquine in patients with COVID-19.

Usage

dat.axfors2021

Format

The data frame contains the following columns:

Details

The dataset includes the results from 33 published and unpublished randomized clinical trials that examined the effectiveness of hydroxychloroquine or chloroquine in patients with COVID-19. The results given here are focused on the total mortality in the treatment versus control groups.

Concepts

medicine, covid-19, odds ratios

Author(s)

W. Kyle Hamilton whamilton@ucmerced.edu https://kylehamilton.com

Source

Axfors, C., Schmitt, A., Janiaud, P., van ’t Hooft, J., Moher, D., Goodman, S., … Hemkens, L. G. (2021, March 9). Hydroxychloroquine and chloroquine for survival in COVID-19: An international collaborative meta-analysis of randomized trials. ⁠https://doi.org/10.17605/OSF.IO/QESV4⁠

References

Axfors, C., Schmitt, A. M., Janiaud, P., van’t Hooft, J., Abd-Elsalam, S., Abdo, E. F., Abella, B. S., Akram, J., Amaravadi, R. K., Angus, D. C., Arabi, Y. M., Azhar, S., Baden, L. R., Baker, A. W., Belkhir, L., Benfield, T., Berrevoets, M. A. H., Chen, C.-P., Chen, T.-C., … Hemkens, L. G. (2021). Mortality outcomes with hydroxychloroquine and chloroquine in COVID-19 from an international collaborative meta-analysis of randomized trials. Nature Communications, 12(1), 2349. ⁠https://doi.org/10.1038/s41467-021-22446-z⁠

Examples

# copy data into 'dat' and examine data
dat <- dat.axfors2021
dat

## Not run: 
# load metafor package
library(metafor)

# calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=hcq_arm_event, n1i=hcq_arm_total,
                            ci=control_arm_event, n2i=control_arm_total, data=dat)

# meta-analysis Hydroxychloroquine
res_hcq <- rma(yi, vi, subset=(hcq_cq=="hcq"), slab = id, data=dat)
print(res_hcq, digits=2)

# meta-analysis Chloroquine
res_cq <- rma(yi, vi, subset=(hcq_cq=="cq"), slab = id, data=dat)
print(res_cq, digits=2)

## End(Not run)

Dataset on Situation Awareness and Task Performance Associations

Description

Results from 77 papers with 678 effects evaluating associations among measures of situation awareness and task performance.

Usage

dat.bakdash2021

Format

The data frame contains the following columns:

Details

The dataset contains behavioral experiments from 77 papers/79 studies with a total of 678 effects, evaluating associations among measures of situation awareness (“knowing what is going on”) and task performance. Examples of situation awareness include knowledge of current vehicle speed in a simulated driving task and location and heading of aircraft in a simulated air traffic control task. Corresponding examples of task performance include “the number of collisions in a simulated driving task” and “subject matter expert rating of conflict management in a simulated air control task” (Bakdash et al. 2021a, p. 2). This dataset and the ‘Examples’ are a highly simplified version of the data and code in Bakdash et al. (2021b; 2021c). The journal article by Bakdash et al. (2021a) describes the systematic review and meta-analysis in detail.

This dataset is used to illustrate multilevel multivariate meta-analytic models for the overall pooled effect and pooled effects by situation awareness measure. We also adjust meta-analytic models using cluster-robust variance estimation / cluster-robust inference with the robust function in metafor. Results are shown graphically in a customized forest plot with a prediction interval (estimated plausible range of individual effects). Last, we create a table summarizing the estimated meta-analytic heterogeneity parameters.

The meta-analytic results show most pooled effect sizes in the positive medium range or less. There was also substantial meta-analytic heterogeneity (estimated systematic variance in true effects), nearing the magnitude of the overall pooled effect. We interpret the meta-analytic results as situation awareness typically having limited validity for task performance (i.e., good situation awareness does not tend to have strong probabilistic links with good performance and vice-versa). More formally, measures of situation awareness do not generally and meaningfully capture cognitive processes and other relevant factors underlying task performance.

Run-Time

The code run-time can be greatly sped-up using a linear algebra library with R that makes use of multiple CPU cores. See: https://www.metafor-project.org/doku.php/tips:speeding_up_model_fitting. To measure the run-time, uncomment these three lines: start.time <- Sys.time(), end.time <- Sys.time(), and end.time - start.time. Run-times on Windows 10 x64 with the Intel Math Kernel Library are:

Concepts

psychology, human factors, engineering, correlation coefficients, multilevel models, multivariate models, cluster-robust inference

Author(s)

Jonathan Bakdash, jonathan.z.bakdash.civ@army.mil, jbakdash@gmail.com
Laura Marusich, laura.m.cooper20.civ@army.mil, lmarusich@gmail.com

Source

Bakdash, J. Z., Marusich, L. R., Cox, K. R., Geuss, M. N., Zaroukian, E. G., & Morris, K. M. (2021b). The validity of situation awareness for performance: A meta-analysis (Code Ocean Capsule). ⁠https://doi.org/10.24433/CO.1682542.v4⁠

Bakdash, J. Z., Marusich, L. R., Cox, K. R., Geuss, M. N., Zaroukian, E. G., & Morris, K. M. (2021c). The validity of situation awareness for performance: A meta-analysis (Systematic Review, Data, and Code). ⁠https://doi.org/10.17605/OSF.IO/4K7ZV⁠

References

Bakdash, J. Z., Marusich, L. R., Cox, K. R., Geuss, M. N., Zaroukian, E. G., & Morris, K. M. (2021a). The validity of situation awareness for performance: A meta-analysis. Theoretical Issues in Ergonomics Science, 1–24. ⁠https://doi.org/10.1080/1463922X.2021.1921310⁠

Supplemental materials: ⁠https://www.tandfonline.com/doi/suppl/10.1080/1463922X.2021.1921310/suppl_file/ttie_a_1921310_sm5524.docx⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bakdash2021
head(dat[c(1,2,6,8:12)])

## Not run: 
#start.time <- Sys.time()

### load metafor
library(metafor)

### multilevel meta-analytic model to get the overall pooled effect
res.overall <- rma.mv(es.z, vi.z, mods = ~ 1,
                      random = ~ 1 | SampleID / Outcome,
                      data = dat,
                      test = "t")
res.overall

### get prediction interval
predict(res.overall)

### cluster-robust variance estimation (CRVE) / cluster-robust inference
res.overall.crve <- robust(res.overall, cluster = SampleID)
res.overall.crve

### get prediction interval
res.overall.crve.pred <- predict(res.overall.crve)
res.overall.crve.pred

### multilevel meta-analytic model for SA measures
res.sa <-  rma.mv(es.z, vi.z, mods = ~ 0 + SA.measure.type,
                  random = ~ 1 | SampleID / Outcome,
                  data = dat,
                  test = "t")
res.sa

### cluster-robust variance estimation (CRVE) / cluster-robust inference
res.sa.crve <- robust(res.sa, cluster = SampleID)
res.sa.crve

### profile likelihood plots
par(mfrow=c(2,1))
profile(res.sa.crve, progbar = FALSE)

### format and combine output of meta-analytic models for the forest plot
all.z        <- c(res.sa.crve$beta,            # SA measures
                  res.overall.crve$beta,       # pooled effect for confidence interval (CI)
                  res.overall.crve$beta)       # pooled effect for prediction interval (PI)

all.ci.lower <- c(res.sa.crve$ci.lb,           # SA measures
                  res.overall.crve.pred$ci.lb, # pooled effect, lower CI
                  res.overall.crve.pred$pi.lb) # pooled effect, lower PI

all.ci.upper <- c(res.sa.crve$ci.ub,           # SA measures
                  res.overall.crve.pred$ci.ub, # pooled effect, upper CI
                  res.overall.crve.pred$pi.ub) # pooled effect, upper PI

### note: there is no p-value for the PI
all.pvals  <- c(res.sa.crve$pval, res.overall.crve$pval)
all.labels <- c(sort(unique(dat$SA.measure.type)), "Overall", "95% Prediction Interval")

### function to round p-values for the forest plot
pvals.round <- function(input) {
  input <- ifelse(input < 0.001, "< 0.001",
           ifelse(input < 0.01, "< 0.01",
           ifelse(input < 0.05 & input >= 0.045, "< 0.05",
           ifelse(round(input, 2) == 1.00, "0.99",
           sprintf("%.2f", round(input, 2))))))}

all.pvals.rounded <- pvals.round(all.pvals)

### forest plot
plot.vals <- data.frame(all.labels, all.z, all.ci.lower, all.ci.upper)

par(mfrow=c(1,1), cex = 1.05)
forest(plot.vals$all.z,
       ci.lb = plot.vals$all.ci.lower,
       ci.ub = plot.vals$all.ci.upper,
       slab  = plot.vals$all.labels,
       psize = 1,
       efac = 0, xlim = c(-1.8, 2.5), clim = c(-1, 1),
       transf = transf.ztor, # transform z to r
       at = seq(-0.5, 1, by = 0.25),
       xlab = expression("Correlation Coefficient"~"("*italic('r')*")"),
       main = "\n\n\nSA Measures",
       ilab = c(all.pvals.rounded, ""), ilab.xpos = 2.45, ilab.pos = 2.5,
       digits = 2, refline = 0, annotate = FALSE, header = FALSE)

### keep trailing zero using sprintf
output <- cbind(sprintf("%.2f", round(transf.ztor(plot.vals$all.z), 2)),
                sprintf("%.2f", round(transf.ztor(plot.vals$all.ci.lower), 2)),
                sprintf("%.2f", round(transf.ztor(plot.vals$all.ci.upper), 2)))

### alignment kludge
annotext <- apply(output, 1, function(x) {paste0("  ", x[1], " [", x[2],", ", x[3], "]")})
text( 1.05, 12:1, annotext, pos = 4, cex = 1.05)
text(-1.475, 14.00, "SA Measure", cex = 1.05)
text( 2.30,  14.00, substitute(paste(italic('p-value'))), cex = 1.05)
text( 1.55,  14.00, "Correlation [95% CI]", cex = 1.05)
abline(h = 2.5)

### black polygon for overall mean CIs
addpoly(all.z[11], ci.lb = all.ci.lower[11], ci.ub = all.ci.upper[11],
        rows = 2, annotate = FALSE, efac = 1.5, transf = transf.ztor)

### white polygon for PI
addpoly(all.z[12], ci.lb = all.ci.lower[12], ci.ub = all.ci.upper[12],
        rows = 1, col = "white", border = "black",
        annotate = FALSE, efac = 1.5, transf = transf.ztor)

par(mfrow=c(1,1), cex = 1) # reset graph parameters to default

### confidence intervals for the variance components
re.CI.variances <- confint(res.overall)
re.CI.variances

sigma1.z <- data.frame(re.CI.variances[[1]]["random"])
sigma2.z <- data.frame(re.CI.variances[[2]]["random"])

### fit model using alternative multivariate parameterization
res.overall.alt <- rma.mv(es.z, vi.z, mods = ~ 1,
                          random = ~ factor(Outcome) | factor(SampleID),
                          data = dat,
                          test = "t")

### confidence intervals for the total amount of heterogeneity variance component
res.overall.alt.tau <- confint(res.overall.alt, tau2=1)$random

### I^2: http://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate
W <- diag(1/dat$vi.z)
X <- model.matrix(res.overall)
P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W

### I^2 (variance due to heterogeneity): 61%
I2 <- 100 * res.overall.alt$tau2 /
      (res.overall.alt$tau2 + (res.overall$k-res.overall$p)/sum(diag(P)))
I2

### 95% CI for I^2 using uncertainty around tau^2
I2.CI.lb <- 100 * res.overall.alt.tau[1,2] /
            (res.overall.alt.tau[1,2] + (res.overall$k-res.overall$p)/sum(diag(P)))
I2.CI.lb

I2.CI.ub <- 100 * res.overall.alt.tau[1,3] /
            (res.overall.alt.tau[1,3] + (res.overall$k-res.overall$p)/sum(diag(P)))
I2.CI.ub

### total amount of heterogeneity (tau)
sqrt(res.overall.alt$tau2)

### heterogeneity table
table.heterogeneity <- data.frame(matrix(ncol = 3, nrow = 4))
colnames(table.heterogeneity) <- c("Parameter Value",
                                   "Lower 95% CI",
                                   "Upper 95% CI")
rownames(table.heterogeneity) <- c("Tau (Total)",
                                   "Tau1 (Between paper)",
                                   "Tau2 (Within paper)",
                                   "I2 (%)")

table.heterogeneity[1,] <- res.overall.alt.tau[2,]
table.heterogeneity[2,] <- sigma1.z[2,]
table.heterogeneity[3,] <- sigma2.z[2,]
table.heterogeneity[4,] <- c(I2, I2.CI.lb, I2.CI.ub)

round(table.heterogeneity, 2)

#end.time <- Sys.time()
#end.time - start.time

## End(Not run)

Studies on Pharmacologic Treatments for Chronic Obstructive Pulmonary Disease

Description

Results from 39 trials examining pharmacologic treatments for chronic obstructive pulmonary disease (COPD).

Usage

dat.baker2009

Format

The data frame contains the following columns:

Details

This dataset comes from a systematic review of randomized controlled trials on pharmacologic treatments for chronic obstructive pulmonary disease (COPD) (Baker et al., 2009).

The primary outcome, occurrence of one or more episodes of COPD exacerbation, is binary (yes / no). For this outcome, five drug treatments (fluticasone, budesonide, salmeterol, formoterol, tiotropium) and two combinations (fluticasone + salmeterol, budesonide + formoterol) were compared to placebo. The authors considered the two combinations as separate treatments instead of evaluating the individual components.

Concepts

medicine, odds ratios, network meta-analysis, component network meta-analysis

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Baker, W. L., Baker, E. L., & Coleman, C. I. (2009). Pharmacologic treatments for chronic obstructive pulmonary disease: A mixed-treatment comparison meta-analysis. Pharmacotherapy: The Journal of Human Pharmacology and Drug Therapy, 29(8), 891–905. ⁠https://doi.org/10.1592/phco.29.8.891⁠

Examples

### Show first 6 rows of the dataset
head(dat.baker2009)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Transform data from long arm-based format to contrast-based
### format. Argument 'sm' has to be used for odds ratio as summary
### measure; by default the risk ratio is used in the metabin function
### called internally.
pw <- pairwise(treatment, exac, total, studlab = paste(study, year),
  data = dat.baker2009, sm = "OR")

### Conduct random effects network meta-analysis (NMA)
### with placebo as reference
net <- netmeta(pw, fixed = FALSE, ref = "plac")

### Show network graph
netgraph(net, seq = "optimal", start = "prcomp",
  labels = gsub("+", " +\n", trts, fixed = TRUE),
  plastic = TRUE, thickness = "se.fixed", number = TRUE,
  points = TRUE, cex.points = 5, col.points = "red",
  offset = 0.025)

### Print and plot results for network meta-analysis
net
forest(net)

### Conduct component network meta-analysis (CNMA)
cnet <- netcomb(net)
cnet

### Compare results of NMA and additive CNMA
nb <- netbind(net, cnet, name = c("Standard NMA", "Additive CNMA"))
forest(nb)

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Effectiveness of Writing-to-Learn Interventions

Description

Results from 48 studies on the effectiveness of school-based writing-to-learn interventions on academic achievement.

Usage

dat.bangertdrowns2004

Format

The data frame contains the following columns:

Details

In each of the studies included in this meta-analysis, an experimental group (i.e., a group of students that received instruction with increased emphasis on writing tasks) was compared against a control group (i.e., a group of students that received conventional instruction) with respect to some content-related measure of academic achievement (e.g., final grade, an exam/quiz/test score). The outcome measure for this meta-analysis was the standardized mean difference (with positive values indicating a higher mean level of academic achievement in the intervention group).

The standardized mean differences given here are bias-corrected and therefore differ slightly from the values reported in the article. Also, since only the total sample size is given in the article, the sampling variances were computed under the assumption that \(n_{i1} = n_{i2} = n_i / 2\).

Concepts

education, standardized mean differences, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Bangert-Drowns, R. L., Hurley, M. M., & Wilkinson, B. (2004). The effects of school-based writing-to-learn interventions on academic achievement: A meta-analysis. Review of Educational Research, 74(1), 29–58. ⁠https://doi.org/10.3102/00346543074001029⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bangertdrowns2004
dat[1:10,-13]

## Not run: 
### load metafor package
library(metafor)

### fit random-effects model
res <- rma(yi, vi, data=dat)
res

### some examples of mixed-effects meta-regression models
res <- rma(yi, vi, mods = ~ factor(grade), data=dat)
res
res <- rma(yi, vi, mods = ~ length, data=dat)
res
res <- rma(yi, vi, mods = ~ info + pers + imag + meta, data=dat)
res

## End(Not run)

Results of 350,757 Coin Flips to Examine Same-Side Bias

Description

Results from 350,757 coin flips by 48 people to examine the presence of same-side bias.

Usage

dat.bartos2023

Format

The data frame contains the following columns:

Details

In a landmark study by Bartoš et al. (2023), 48 people flipped a coin (of various currencies and/or denominations) a total of 350,757 times, recording on each flip whether it landed on heads or tails and whether the coin landed on the same side as where it started or on the different side. The goal of this experiment was to examine the model by Diaconis, Holmes, and Montgomery (2007), according to which flipped coins have a slightly higher than 50% chance (of around 51% according to the D-H-M model) of landing on the same side as where they started.

Concepts

physics, human factors, proportions, multivariate models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Bartoš, F., Sarafoglou, A., Godmann, H. R., Sahrani, A., Leunk, D. K., Gui, P. Y., Voss, D., Ullah, K., Zoubek, M. J., Nippold, F., Aust, F., Vieira, F. F., Islam, C.-G., Zoubek, A. J., Shabani, S., Petter, J., Roos, I. B., Finnemann, A., Lob, A. B., Hoffstadt, M. F., Nak, J., de Ron, J., Derks, K., Huth, K., Terpstra, S., Bastelica, T., Matetovici, M., Ott, V. L., Zetea, A. S., Karnbach, K., Donzallaz, M. C., John, A., Moore, R. M., Assion, F., van Bork, R., Leidinger, T. E., Zhao, X., Motaghi, A. K., Pan, T., Armstrong, H., Peng, T., Bialas, M., Pang, J. Y.-C., Fu, B., Yang, S., Lin, X., Sleiffer, D., Bognar, M., Aczel, B., & Wagenmakers, E.-J. (2023). Fair coins tend to land on the same side they started: Evidence from 350,757 flips. arXiv, 2310.04153, v2. ⁠https://arxiv.org/abs/2310.04153⁠

References

Diaconis, P., Holmes, S., & Montgomery, R. (2007). Dynamical bias in the coin toss. SIAM Review, 49(2), 211–235. ⁠https://doi.org/10.1137/s0036144504446436⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bartos2023
dat

## Not run: 
### load metafor package
library(metafor)

### compute proportions and the corresponding sampling variances
dat <- escalc(measure="PR", xi=same, ni=flips, data=dat, slab=person)
dat

### compute confidence intervals for the individual proportions (as in Table 1)
summary(dat, digits=3)[c(1,6:8,13,14)]

### compute a confidence interval based on the column totals
summary(escalc(measure="PR", xi=sum(dat$same), ni=sum(dat$flips)), digits=3)

### this is the same as meta-analyzing the proportions directly using an equal-effects
### model and also computing the sampling variances under the assumption that the true
### proportions are homogeneous
rma(measure="PR", xi=same, ni=flips, vtype="AV", method="EE", data=dat, digits=3)

### fit a random-effects model
res <- rma(yi, vi, data=dat)
res

### profile likelihood confidence interval for tau^2
confint(res, type="PL")

### forest plot
forest(res, refline=0.5, xlim=c(0.38,0.72), digits=c(3,2), efac=c(0,1))

### funnel plot
funnel(res, xlim=c(0.45,0.6), ylim=c(0,0.02))

### fit a random-effects model excluding those with same-side proportions larger than 0.53
res <- rma(yi, vi, data=dat, subset=yi<=0.53)
res
confint(res, type="PL")

### fit a binomial-normal model
res <- rma.glmm(measure="PLO", xi=same, ni=flips, data=dat)
res
predict(res, transf=plogis)

### conduct a meta-analysis for the proportions of heads (to examine heads-tails bias)
dat <- escalc(measure="PR", xi=hdiff+hsame, ni=flips, data=dat)
res <- rma(yi, vi, data=dat)
res
confint(res, type="PL")

### restructure the dataset for a bivariate meta-analysis of same-side and heads proportions
dat <- dat.bartos2023
dat <- dat[rep(1:nrow(dat), each=2),]
rownames(dat) <- NULL
dat$outcome <- c("heads", "same")
dat <- escalc(measure="PR", xi=hsame+hdiff, ni=flips, data=dat, include=outcome=="heads")
dat <- escalc(measure="PR", xi=hsame+tsame, ni=flips, data=dat, include=outcome=="same")
dat

### construct the 2x2 variance-covariance matrix of the proportions within persons
dat$cov <- with(dat, (hsame/flips * (1-hsame/flips) - hsame/flips * tsame/flips -
                      hsame/flips * hdiff/flips - hdiff/flips * tsame/flips) / flips)
V <- lapply(split(dat, dat$person), \(x) matrix(c(x$vi[1], x$cov, x$vi[2]), nrow=2))

### fit bivariate meta-analysis model
res <- rma.mv(yi, V, mods = ~ 0 + outcome, random = ~ outcome | person, struct="UN", data=dat)
res

### create plot with confidence ellipses ('ellipse' package must be installed)
library(ellipse)
plot(NA, xlim=c(0.45,0.62), ylim=c(0.45,0.62), bty="l", xlab="Pr(heads)", ylab="Pr(same)")
abline(h=0.5, lty="dotted")
abline(v=0.5, lty="dotted")
# add confidence ellipses for persons
invisible(tapply(dat, dat$person, \(x) {
   xy <- ellipse(matrix(c(x$vi[1],x$cov,x$vi[2]), nrow=2), centre=x$yi, level=0.95)
   lines(xy[,1],xy[,2], col="gray80")
}))
# add the points
invisible(tapply(dat, dat$person, \(x) points(x$yi[1], x$yi[2], pch=21, bg="gray80", cex=1.5)))
# add the 95% PI ellipsis based on the model
xy <- ellipse(res$G, centre=coef(res), level=0.95)
lines(xy[,1],xy[,2], col="gray30", lwd=3, lty="dotted")
# add the 95% CI ellipsis based on the model
xy <- ellipse(vcov(res), centre=coef(res), level=0.95)
lines(xy[,1],xy[,2], col="gray30", lwd=3)
# add the point for the pooled effects
points(coef(res)[1], coef(res)[2], pch=21, bg="gray40", cex=2)

## End(Not run)

Studies on the Effectiveness of Practice Facilitation Interventions

Description

Results from 23 studies on the effectiveness of practice facilitation interventions within the primary care practice setting.

Usage

dat.baskerville2012

Format

The data frame contains the following columns:

Details

Baskerville et al. (2012) describe outreach or practice facilitation as a "multifaceted approach that involves skilled individuals who enable others, through a range of intervention components and approaches, to address the challenges in implementing evidence-based care guidelines within the primary care setting". The studies included in this dataset examined the effectiveness of practice facilitation interventions for improving some relevant evidence-based practice behavior. The effect was quantified in terms of a standardized mean difference, comparing the change (from pre- to post-intervention) in the intervention versus the comparison group (or the difference from baseline in prospective cohort studies).

Concepts

medicine, primary care, standardized mean differences, publication bias, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Baskerville, N. B., Liddy, C., & Hogg, W. (2012). Systematic review and meta-analysis of practice facilitation within primary care settings. Annals of Family Medicine, 10(1), 63–74. ⁠https://doi.org/10.1370/afm.1312⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.baskerville2012
dat

## Not run: 
### load metafor package
library(metafor)

### random-effects model
res <- rma(smd, sei=se, data=dat, method="DL")
print(res, digits=2)

### funnel plot
funnel(res, xlab="Standardized Mean Difference", ylim=c(0,0.6))

### rank and regression tests for funnel plot asymmetry
ranktest(res)
regtest(res)

### meta-regression analyses examining various potential moderators
rma(smd, sei=se, mods = ~ score, data=dat, method="DL")
rma(smd, sei=se, mods = ~ alloconc, data=dat, method="DL")
rma(smd, sei=se, mods = ~ blind,    data=dat, method="DL")
rma(smd, sei=se, mods = ~ itt,      data=dat, method="DL")
rma(smd, sei=se, mods = ~ duration, data=dat, method="DL")
rma(smd, sei=se, mods = ~ tailor,   data=dat, method="DL")
rma(smd, sei=se, mods = ~ pperf,    data=dat, method="DL")
rma(smd, sei=se, mods = ~ I(meetings * hours), data=dat, method="DL")

## End(Not run)

Studies on Ketotifen Alone or as Additional Medication for Long-Term Control of Asthma and Wheeze in Children

Description

Results from 10 trials reporting the physicians' judgement on the overall efficacy of ketotifen for long-term control of asthma and wheeze in children.

Usage

dat.bassler2004

Format

The data frame contains the following columns:

Details

Results from 10 trials reporting the physicians' judgement on the overall efficacy of Ketotifen for long-term control of asthma and wheeze in children. A prespecified subgroup analysis was conducted to evaluate whether the treatment effect is different in trials with adequate blinding compared to trials with inadequate / unclear blinding.

This data set is used as an example in Schwarzer et al. (2015).

Concepts

risk ratios, medicine, subgroup analysis

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Bassler D., Mitra A. A. D., Ducharme F. M., Forster J., & Schwarzer, G. (2004). Ketotifen alone or as additional medication for long-term control of asthma and wheeze in children. Cochrane Database of Systematic Reviews, 1, CD001384. ⁠https://doi.org/10.1002/14651858.CD001384.pub2⁠

References

Schwarzer, G., Carpenter, J. R., & Rücker, G. (2015). Meta-analysis with R. Cham, Switzerland: Springer.

Examples

### Show full data set
dat.bassler2004

## Not run: 
### Load meta package
suppressPackageStartupMessages(library("meta"))

### Use DerSimonian-Laird estimator (which was the default in meta in the year 2015).
### Furthermore, print meta-analysis results with two digits.
oldset <- settings.meta(method.tau = "DL", digits = 2)

### Calculate experimental and control event rates
with(dat.bassler2004, summary(Ee / Ne))
with(dat.bassler2004, summary(Ec / Nc))

### Conduct meta-analysis using the inverse variance method
mb3 <- metabin(Ee, Ne, Ec, Nc, method = "I",
               data = dat.bassler2004, studlab = study)
mb3

### Conduct subgroup analysis comparing trials with adequate blinding
### to trials with inadequate or unclear blinding
mb3s <- update(mb3, subgroup = blind, print.subgroup.name = FALSE)
mb3s

### Conduct subgroup analysis assuming common between-study variance in subgroups
mb3s.c <- update(mb3s, tau.common = TRUE)
mb3s.c

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Effectiveness of the BCG Vaccine Against Tuberculosis

Description

Results from 13 studies examining the effectiveness of the Bacillus Calmette-Guerin (BCG) vaccine against tuberculosis.

Usage

dat.bcg

Format

The data frame contains the following columns:

Details

The 13 studies provide data in terms of \(2 \times 2\) tables in the form:

The goal of the meta-analysis was to examine the overall effectiveness of the BCG vaccine for preventing tuberculosis and to examine moderators that may potentially influence the size of the effect.

The dataset has been used in several publications to illustrate meta-analytic methods (see ‘References’).

Concepts

medicine, risk ratios, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Colditz, G. A., Brewer, T. F., Berkey, C. S., Wilson, M. E., Burdick, E., Fineberg, H. V., & Mosteller, F. (1994). Efficacy of BCG vaccine in the prevention of tuberculosis: Meta-analysis of the published literature. Journal of the American Medical Association, 271(9), 698–702. ⁠https://doi.org/10.1001/jama.1994.03510330076038⁠

References

Berkey, C. S., Hoaglin, D. C., Mosteller, F., & Colditz, G. A. (1995). A random-effects regression model for meta-analysis. Statistics in Medicine, 14(4), 395–411. ⁠https://doi.org/10.1002/sim.4780140406⁠

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589–624. ⁠https://doi.org/10.1002/sim.1040⁠

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. ⁠https://doi.org/10.18637/jss.v036.i03⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bcg
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg,
                            ci=cpos, di=cneg, data=dat,
                            slab=paste0(author, ", ", year))
dat

### random-effects model
res <- rma(yi, vi, data=dat)
res

### average risk ratio with 95% CI
predict(res, transf=exp)

### mixed-effects model with absolute latitude and publication year as moderators
res <- rma(yi, vi, mods = ~ ablat + year, data=dat)
res

### predicted average risk ratios for 10-60 degrees absolute latitude
### holding the publication year constant at 1970
predict(res, newmods=cbind(seq(from=10, to=60, by=10), 1970), transf=exp)

### note: the interpretation of the results is difficult because absolute
### latitude and publication year are strongly correlated (the more recent
### studies were conducted closer to the equator)
plot(ablat ~ year, data=dat, pch=19, xlab="Publication Year", ylab="Absolute Lattitude")
cor(dat$ablat, dat$year)

## End(Not run)

Studies on Bone-Marrow Transplantation versus Chemotherapy for the Treatment of Leukemia

Description

Results from controlled and uncontrolled studies on the effectiveness of allogeneic bone-marrow transplantation (BMT) and conventional chemotherapy (CMO) in the treatment of acute nonlymphocytic leukemia.

Usage

dat.begg1989

Format

The data frame contains the following columns:

Details

The dataset includes the results from controlled and uncontrolled studies on the 2-year disease-free survival rate in patients with acute nonlymphocytic leukemia receiving either allogeneic bone-marrow transplantation (BMT) or conventional chemotherapy (CMO). In the controlled (two-arm) studies (studies 1-4), a cohort of patients in complete remission and potentially eligible for BMT was assembled, and those who consented and for whom a donor could be found received BMT, with the remaining patients used as controls (receiving CMO). In the uncontrolled (one-arm) studies (studies 5-16), only a single group was studied, receiving either BMT or CMO.

The data in this dataset were obtained from Table 1 in Begg and Pilote (1991, p. 902).

Concepts

medicine, oncology, single-arm studies, multilevel models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Begg, C. B., & Pilote, L. (1991). A model for incorporating historical controls into a meta-analysis. Biometrics, 47(3), 899–906. ⁠https://doi.org/10.2307/2532647⁠

References

Begg, C. B., Pilote, L., & McGlave, P. B. (1989). Bone marrow transplantation versus chemotherapy in acute non-lymphocytic leukemia: A meta-analytic review. European Journal of Cancer and Clinical Oncology, 25(11), 1519–1523. ⁠https://doi.org/10.1016/0277-5379(89)90291-5⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.begg1989
dat

## Not run: 
### load metafor package
library(metafor)

### turn trt and arms into factors and set reference levels
dat$trt  <- relevel(factor(dat$trt), ref="CMO")
dat$arms <- relevel(factor(dat$arms), ref="2")

### create data frame with the treatment differences for the controlled studies
dat2 <- data.frame(yi = dat$yi[c(1,3,5,7)] - dat$yi[c(2,4,6,8)],
                   vi = dat$vi[c(1,3,5,7)] + dat$vi[c(2,4,6,8)])
dat2

### DerSimonian and Laird method using the treatment differences
res <- rma(yi, vi, data=dat2, method="DL", digits=2)
res

### Begg & Pilote (1991) model incorporating the uncontrolled studies
res <- rma.mv(yi, vi, mods = ~ trt, random = ~ 1 | study,
              data=dat, method="ML", digits=2)
res

### model involving bias terms for the uncontrolled studies
res <- rma.mv(yi, vi, mods = ~ trt + trt:arms, random = ~ 1 | study,
              data=dat, method="ML", digits=2)
res

### model with a random treatment effect
res <- rma.mv(yi, vi, mods = ~ trt, random = list(~ 1 | study, ~ trt | study),
              struct="UN", tau2=c(0,NA), rho=0, data=dat, method="ML", digits=2)
res

### model with a random treatment effect, but with equal variances in both arms
res <- rma.mv(yi, vi, mods = ~ trt, random = list(~ 1 | study, ~ trt | study),
              struct="CS", rho=0, data=dat, method="ML", digits=2)
res

## End(Not run)

Studies on Treatments for Periodontal Disease

Description

Results from 5 trials comparing surgical and non-surgical treatments for medium-severity periodontal disease one year after treatment.

Usage

dat.berkey1998

Format

The data frame contains the following columns:

Details

The dataset includes the results from 5 trials that compared surgical and non-surgical methods for the treatment of medium-severity periodontal disease. Reported outcomes include the change in probing depth (PD) and attachment level (AL) one year after the treatment. The outcome measure used for this meta-analysis was the (raw) mean difference, calculated in such a way that positive values indicate that surgery was more effective than non-surgical treatment in decreasing the probing depth and increasing the attachment level (so, the results from the various trials indicate that surgery is preferable for reducing the probing depth, while non-surgical treatment is preferable for increasing the attachment level). Since each trial provides effect size estimates for both outcomes, the estimates are correlated. A multivariate model can be used to meta-analyze the two outcomes simultaneously.

The v1i and v2i values are the variances and covariances of the observed effects. In particular, for each study, variables v1i and v2i form a \(2 \times 2\) variance-covariance matrix of the observed effects, with the diagonal elements corresponding to the sampling variances of the mean differences (the first for probing depth, the second for attachment level) and the off-diagonal value corresponding to the covariance of the two mean differences. Below, the full (block diagonal) variance-covariance for all studies is constructed from these two variables.

Concepts

medicine, dentistry, raw mean differences, multivariate models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Berkey, C. S., Antczak-Bouckoms, A., Hoaglin, D. C., Mosteller, F., & Pihlstrom, B. L. (1995). Multiple-outcomes meta-analysis of treatments for periodontal disease. Journal of Dental Research, 74(4), 1030–1039. ⁠https://doi.org/10.1177/00220345950740040201⁠

Berkey, C. S., Hoaglin, D. C., Antczak-Bouckoms, A., Mosteller, F., & Colditz, G. A. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine, 17(22), 2537–2550. ⁠https://doi.org/10.1002/(sici)1097-0258(19981130)17:22<2537::aid-sim953>3.0.co;2-c⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.berkey1998
dat

## Not run: 
### load metafor package
library(metafor)

### construct block diagonal var-cov matrix of the observed outcomes based on variables v1i and v2i
V <- vcalc(vi=1, cluster=author, rvars=c(v1i, v2i), data=dat)

### fit multiple outcomes (meta-regression) model (with REML estimation)
res <- rma.mv(yi, V, mods = ~ 0 + outcome, random = ~ outcome | trial, struct="UN", data=dat)
print(res, digits=3)

### test/estimate difference between the two outcomes
anova(res, X=c(1,-1))

### fit model including publication year as moderator for both outcomes (with ML estimation)
res <- rma.mv(yi, V, mods = ~ 0 + outcome + outcome:I(year - 1983),
              random = ~ outcome | trial, struct="UN", data=dat, method="ML")
print(res, digits=3)

## End(Not run)

Dataset on How Maternal Diet Impacts Copying Styles in Rodents

Description

Results from 46 studies synthesising maternal nutritional effects on coping styles in rodents.

Usage

dat.besson2016

Format

The data frame contains the following columns:

Details

Data from experiments where dams were subject to caloric or protein restriction or were overfed around gestation were included. Offspring activity, exploration, or anxiety were measured outcomes variables from maternal experimental treatments. Multilevel meta-analysis and meta-regression models were used to analyze the meta-analytic data.

Concepts

ecology, evolution, standardized mean differences

Author(s)

Daniel Noble, daniel.noble@anu.edu.au

Source

Besson, A. A., Lagisz, M., Senior, A. M., Hector, K. L., & Nakagawa, S. (2016). Effect of maternal diet on offspring coping styles in rodents: A systematic review and meta-analysis. Biological Reviews, 91(4), 1065–1080. ⁠https://doi.org/10.1111/brv.12210⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.besson2016
head(dat)

## Not run: 
### load metafor
library(metafor)

### compute SD from SE
dat$sd_c <- with(dat, con_se * sqrt(con_n))
dat$sd_e <- with(dat, exp_se * sqrt(exp_n))

### compute standardized mean differences and corresponding sampling variances
dat <- escalc(measure="SMD", m1i=exp_mean, m2i=con_mean, sd1i=sd_e, sd2i=sd_c,
              n1i=exp_n, n2i=con_n, data=dat, add.measure=TRUE)

### fit model
mod1 <- rma.mv(yi ~ 1, V = vi, random = list(~ 1 | study_ID, ~ 1 | comp_ID), data = dat)
mod1

## End(Not run)

Studies on the Reliability of the CES-D Scale

Description

Results from 9 studies on the reliability of the Center for Epidemiologic Studies Depression (CES-D) Scale administered to children providing care to an elderly parent.

Usage

dat.bonett2010

Format

The data frame contains the following columns:

Details

The Center for Epidemiologic Studies Depression (CES-D) Scale is a 20-item questionnaire assessing various symptoms of depression, with each item scored on a 4-point scale. The scale has been used in several studies to examine depressive symptoms in children providing care to an elderly parent. The dataset includes information on the reliability of the scale as measured with Cronbach's alpha in 9 such studies. Also, the gender composition of the children in each sample is indicated.

Concepts

psychology, Cronbach's alpha, reliability generalization, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Bonett, D. G. (2010). Varying coefficient meta-analytic methods for alpha reliability. Psychological Methods, 15(4), 368–385. ⁠https://doi.org/10.1037/a0020142⁠

References

Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics, 27(4), 335–340. ⁠https://doi.org/10.3102/10769986027004335⁠

Hakstian, A. R., & Whalen, T. E. (1976). A k-sample significance test for independent alpha coefficients. Psychometrika, 41(2), 219–231. ⁠https://doi.org/10.1007/BF02291840⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bonett2010
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis using the raw alpha values
res <- rma(measure="ARAW", ai=ai, mi=mi, ni=ni, data=dat)
res

### meta-analysis using transformed alpha values (using the
### transformation suggested by Hakstian & Whalen, 1976)
res <- rma(measure="AHW", ai=ai, mi=mi, ni=ni, data=dat)
res
predict(res, transf=transf.iahw)

### meta-analysis using transformed alpha values (using the
### transformation suggested by Bonett, 2002)
res <- rma(measure="ABT", ai=ai, mi=mi, ni=ni, data=dat)
res
predict(res, transf=transf.iabt)

### forest plot
forest(res, slab=source, xlim=c(0,4.5),
       atransf=transf.iabt, refline=coef(res))

### examine whether female/mixed samples yield different alphas (with raw alphas)
res <- rma(measure="ARAW", ai=ai, mi=mi, ni=ni, mods = ~ caregivers, data=dat)
res
predict(res, newmods=c(0,1), digits=2)

## End(Not run)

Studies on Gender Differences in Grant and Fellowship Awards

Description

Results from 21 studies on gender differences in grant and fellowship awards.

Usage

dat.bornmann2007

Format

The data frame contains the following columns:

Details

The studies in this dataset examine whether the chances of receiving a grant or fellowship award differs for men and women. Note that many studies provide multiple comparisons (e.g., for different years / cohorts / disciplines). A multilevel meta-analysis model can be used to account for the multilevel structure in these data.

Concepts

sociology, odds ratios, multilevel models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Bornmann, L., Mutz, R., & Daniel, H. (2007). Gender differences in grant peer review: A meta-analysis. Journal of Informetrics, 1(3), 226–238. ⁠https://doi.org/10.1016/j.joi.2007.03.001⁠

References

Marsh, H. W., Bornmann, L., Mutz, R., Daniel, H.-D., & O'Mara, A. (2009). Gender effects in the peer reviews of grant proposals: A comprehensive meta-analysis comparing traditional and multilevel approaches. Review of Educational Research, 79(3), 1290–1326. ⁠https://doi.org/10.3102/0034654309334143⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bornmann2007
head(dat, 16)

## Not run: 
### load metafor package
library(metafor)

### calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=waward, n1i=wtotal, ci=maward, n2i=mtotal, data=dat)

### fit multilevel meta-analysis model
res <- rma.mv(yi, vi, random = ~ 1 | study/obs, data=dat)
res

### estimated average odds ratio (with 95% CI/PI)
predict(res, transf=exp, digits=2)

### test for a difference between fellowship and grant applications
res <- rma.mv(yi, vi, mods = ~ type, random = ~ 1 | study/obs, data=dat)
res
predict(res, newmods=0:1, transf=exp, digits=2)

## End(Not run)

Studies on the Association between Handedness and Eye-Dominance

Description

Results from 47 studies on the association between handedness and eye-dominance.

Usage

dat.bourassa1996

Format

The data frame contains the following columns:

Details

The 47 studies included in this meta-analysis examined the association between handedness and eye-dominance (ocular dominance or eyedness). Results are given in terms of \(2 \times 2\) tables, indicating the number of left-handed left-eyed, left-handed right-eyed, right-handed left-eyed, and right-handed right-eyed individuals in each sample. Note that some studies included multiple (independent) samples, so that the meta-analysis included 54 samples in total. Also, for some studies, the combined data of the males and females are further broken down into the two subgroups.

In some studies, there was indication that the selection of subjects was not random with respect to handedness and/or eyedness. While this should not influence the size of the association as measured with the odds ratio, this invalidates those studies for assessing the overall percentage of left-eyed and left-handed individuals.

Handedness was assessed in the individual studies either based on a questionnaire or based on task performance. Eyedness was assessed based on various methods: E.1 methods are based on task performance, while E.2.a denotes assessment based on a questionnaire. The performance based methods could be further broken down into: E.1.a.i (monocular procedure with object/instrument held in one hand), E.1.a.ii (monocular procedure with object/instrument held in both hands), E.1.b (binocular procedure), E.1.c (a combination of the previous methods), and E.1.d (some other method).

Concepts

psychology, odds ratios, multilevel models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Bourassa, D. C., McManus, I. C., & Bryden, M. P. (1996). Handedness and eye-dominance: A meta-analysis of their relationship. Laterality, 1(1), 5–34. ⁠https://doi.org/10.1080/713754206⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.bourassa1996
head(dat, 10)

## Not run: 
### load metafor package
library(metafor)

### calculate log(OR) and corresponding sampling variance with 1/2 correction
dat <- escalc(measure="OR", ai=lh.le, bi=lh.re, ci=rh.le, di=rh.re, data=dat, add=1/2, to="all")
head(dat, 10)

### overall association between handedness and eyedness
res <- rma(yi, vi, data=dat, subset=sex=="combined")
res
predict(res, transf=exp, digits=2)

### multilevel model to account for heterogeneity at the study and sample levels
res <- rma.mv(yi, vi, random = ~ 1 | study/sample, data=dat, subset=sex=="combined")
res
predict(res, transf=exp, digits=2)

### restructure the dataset to keep only the male/female data when it is reported
### separately and the combined data when this is the only data reported
dat <- lapply(split(dat, dat$sample), function(x) {
   if (nrow(x) == 3L) {
      x[-which(x$sex == "combined"),]
   } else {
      x
   }
})
dat <- do.call(rbind, dat)
rownames(dat) <- NULL
dat

### multilevel model to account for heterogeneity at the study, sample, and subgroup levels
res <- rma.mv(yi, vi, random = ~ 1 | study/sample/sex, data=dat)
res
predict(res, transf=exp, digits=2)

## End(Not run)

Studies on the Effectiveness of Intensive Versus Moderate Statin Therapy for Preventing Coronary Death or Myocardial Infarction

Description

Results from 4 trials examining the effectiveness of intensive (high dose) versus moderate (standard dose) statin therapy for preventing coronary death or myocardial infarction.

Usage

dat.cannon2006

Format

The data frame contains the following columns:

Details

The data were obtained from Figures 2, 3, 4, and 5 in Cannon et al. (2006). The authors used the Mantel-Haenszel method for combining the results from the 4 trials. This approach is implemented in the rma.mh function.

Concepts

medicine, cardiology, odds ratios, Mantel-Haenszel method

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Cannon, C. P., Steinberg, B. A., Murphy, S. A., Mega, J. L., & Braunwald, E. (2006). Meta-analysis of cardiovascular outcomes trials comparing intensive versus moderate statin therapy. Journal of the American College of Cardiology, 48(3), 438–445. ⁠https://doi.org/10.1016/j.jacc.2006.04.070⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.cannon2006
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of log odds ratios using the MH method for endpoint 1
res <- rma.mh(measure="OR", ai=ep1t, n1i=nt, ci=ep1c, n2i=nc, data=dat, slab=trial)
print(res, digits=2)

### forest plot
forest(res, xlim=c(-.8,0.8), atransf=exp, at=log(c(2/3, 1, 3/2)),
       cex=1.2, xlab="Odds Ratio")
mtext("(high dose better)", side=1, line=par("mgp")[1]-0.5, at=log(2/3), cex=1.2, font=3)
mtext("(standard dose better)", side=1, line=par("mgp")[1]-0.5, at=log(3/2), cex=1.2, font=3)

## End(Not run)

Studies on the Relationship between Course Instructor Ratings and Student Achievement

Description

Results from 20 studies on the correlation between course instructor ratings and student achievement.

Usage

dat.cohen1981

Format

The data frame contains the following columns:

Details

The studies included in this dataset examined to what extent students' ratings of a course instructor correlated with their achievement in the course. Instead of correlating individual ratings and achievement scores, the studies were carried out in multisection courses, in which the sections had different instructors but all sections used a common achievement measure (e.g., a final exam). The correlation coefficients reflect the correlation between the mean instructor rating and the mean achievement score of each section. Hence, the unit of analysis are the sections, not the individuals.

Note that this dataset (extracted from Table A.3 in Cooper & Hedges, 1994) only contains studies with at least 10 sections.

Concepts

education, correlation coefficients

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Cooper, H., & Hedges, L. V. (1994). Appendix A: Data Sets. In H. Cooper & L. V. Hedges (Eds.), The handbook of research synthesis (pp. 543–547). New York: Russell Sage Foundation.

References

Cohen, P. A. (1981). Student ratings of instruction and student achievement: A meta-analysis of multisection validity studies. Review of Educational Research, 51(3), 281–309. ⁠https://doi.org/10.3102/00346543051003281⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.cohen1981
dat[c(1,4,5)]

## Not run: 
### load metafor package
library(metafor)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat[c(1,4,5)])
dat

### meta-analysis of the transformed correlations using a random-effects model
res <- rma(yi, vi, data=dat, digits=2)
res

### predicted average correlation with 95% CI
predict(res, transf=transf.ztor)

## End(Not run)

Studies on the Effectiveness of the BCG Vaccine Against Tuberculosis

Description

Results from 13 studies examining the effectiveness of the Bacillus Calmette-Guerin (BCG) vaccine against tuberculosis.

Usage

dat.colditz1994

Format

The data frame contains the following columns:

Details

The 13 studies provide data in terms of \(2 \times 2\) tables in the form:

The goal of the meta-analysis was to examine the overall effectiveness of the BCG vaccine for preventing tuberculosis and to examine moderators that may potentially influence the size of the effect.

The dataset has been used in several publications to illustrate meta-analytic methods (see ‘References’).

Concepts

medicine, risk ratios, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Colditz, G. A., Brewer, T. F., Berkey, C. S., Wilson, M. E., Burdick, E., Fineberg, H. V., & Mosteller, F. (1994). Efficacy of BCG vaccine in the prevention of tuberculosis: Meta-analysis of the published literature. Journal of the American Medical Association, 271(9), 698–702. ⁠https://doi.org/10.1001/jama.1994.03510330076038⁠

References

Berkey, C. S., Hoaglin, D. C., Mosteller, F., & Colditz, G. A. (1995). A random-effects regression model for meta-analysis. Statistics in Medicine, 14(4), 395–411. ⁠https://doi.org/10.1002/sim.4780140406⁠

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589–624. ⁠https://doi.org/10.1002/sim.1040⁠

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. ⁠https://doi.org/10.18637/jss.v036.i03⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.colditz1994
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg,
                            ci=cpos, di=cneg, data=dat,
                            slab=paste0(author, ", ", year))
dat

### random-effects model
res <- rma(yi, vi, data=dat)
res

### average risk ratio with 95% CI
predict(res, transf=exp)

### mixed-effects model with absolute latitude and publication year as moderators
res <- rma(yi, vi, mods = ~ ablat + year, data=dat)
res

### predicted average risk ratios for 10-60 degrees absolute latitude
### holding the publication year constant at 1970
predict(res, newmods=cbind(seq(from=10, to=60, by=10), 1970), transf=exp)

### note: the interpretation of the results is difficult because absolute
### latitude and publication year are strongly correlated (the more recent
### studies were conducted closer to the equator)
plot(ablat ~ year, data=dat, pch=19, xlab="Publication Year", ylab="Absolute Lattitude")
cor(dat$ablat, dat$year)

## End(Not run)

Studies on the Treatment of Upper Gastrointestinal Bleeding by a Histamine H2 Antagonist

Description

Results from studies examining the effectiveness of histamine H2 antagonists (cimetidine or ranitidine) in treating patients with acute upper gastrointestinal hemorrhage.

Usage

dat.collins1985a

Format

The data frame contains the following columns:

Details

The data were obtained from Tables 1 and 2 in Collins and Langman (1985). The authors used Peto's (one-step) method for meta-analyzing the 27 trials. This approach is implemented in the rma.peto function. Using the same dataset, van Houwelingen, Zwinderman, and Stijnen (1993) describe some alternative approaches for analyzing these data, including fixed- and random-effects conditional logistic models. Those are implemented in the rma.glmm function.

Concepts

medicine, odds ratios, Peto's method, generalized linear models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Collins, R., & Langman, M. (1985). Treatment with histamine H2 antagonists in acute upper gastrointestinal hemorrhage. New England Journal of Medicine, 313(11), 660–666. ⁠https://doi.org/10.1056/NEJM198509123131104⁠

References

van Houwelingen, H. C., Zwinderman, K. H., & Stijnen, T. (1993). A bivariate approach to meta-analysis. Statistics in Medicine, 12(24), 2273–2284. ⁠https://doi.org/10.1002/sim.4780122405⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.collins1985a
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of log ORs using Peto's method (outcome: persistent or recurrent bleedings)
res <- rma.peto(ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat)
print(res, digits=2)

### meta-analysis of log ORs using a conditional logistic regression model (FE model)
res <- rma.glmm(measure="OR", ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat,
                model="CM.EL", method="FE")
summary(res)
predict(res, transf=exp, digits=2)

### plot the likelihoods of the odds ratios
llplot(measure="OR", ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat,
       lwd=1, refline=NA, xlim=c(-4,4), drop00=FALSE)

### meta-analysis of log odds ratios using a conditional logistic regression model (RE model)
res <- rma.glmm(measure="OR", ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat,
                model="CM.EL", method="ML")
summary(res)
predict(res, transf=exp, digits=2)

### meta-analysis of log ORs using Peto's method (outcome: need for surgery)
res <- rma.peto(ai=o.xti, n1i=nti, ci=o.xci, n2i=nci, data=dat)
print(res, digits=2)

### meta-analysis of log ORs using Peto's method (outcome: death)
res <- rma.peto(ai=d.xti, n1i=nti, ci=d.xci, n2i=nci, data=dat)
print(res, digits=2)

## End(Not run)

Studies on the Effects of Diuretics in Pregnancy

Description

Results from 9 studies examining the effects of diuretics in pregnancy on various outcomes.

Usage

dat.collins1985b

Format

The data frame contains the following columns:

Details

The 9 studies in this dataset examined the effects of diuretics in pregnancy on various outcomes, including the presence of any form of pre-eclampsia, perinatal death, stillbirth, and neonatal death.

Concepts

medicine, obstetrics, odds ratios, Peto's method

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Collins, R., Yusuf, S., & Peto, R. (1985). Overview of randomised trials of diuretics in pregnancy. British Medical Journal, 290(6461), 17–23. ⁠https://doi.org/10.1136/bmj.290.6461.17⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.collins1985b
dat

## Not run: 
### load metafor package
library(metafor)

### calculate (log) odds ratio and sampling variance
dat <- escalc(measure="OR", n1i=pre.nti, n2i=pre.nci, ai=pre.xti, ci=pre.xci, data=dat)
summary(dat, digits=2, transf=exp)

### meta-analysis using Peto's method for any form of pre-eclampsia
rma.peto(n1i=pre.nti, n2i=pre.nci, ai=pre.xti, ci=pre.xci, data=dat, digits=2)

### meta-analysis including only studies where oedema was not a diagnostic criterion
rma.peto(n1i=pre.nti, n2i=pre.nci, ai=pre.xti, ci=pre.xci, data=dat, digits=2, subset=(oedema==0))

### meta-analyses of mortality outcomes (perinatal deaths, stillbirths, and neonatal deaths)
rma.peto(n1i=fup.nti, n2i=fup.nci, ai=ped.xti, ci=ped.xci, data=dat, digits=2)
rma.peto(n1i=fup.nti, n2i=fup.nci, ai=stb.xti, ci=stb.xci, data=dat, digits=2)
rma.peto(n1i=fup.nti, n2i=fup.nci, ai=ned.xti, ci=ned.xci, data=dat, digits=2)

## End(Not run)

Studies on the Relationship between the Competitive State Anxiety Inventory-2 and Sport Performance

Description

Results from 10 studies on the relationship between the Competitive State Anxiety Inventory-2 (CSAI-2) and sport performance.

Usage

dat.craft2003

Format

The data frame contains the following columns:

Details

The 10 studies included in this dataset are a subset of the studies included in the meta-analysis by Craft et al. (2003) on the relationship between the Competitive State Anxiety Inventory-2 (CSAI-2) and sport performance.

The CSAI-2 has three subscales: cognitive anxiety (acog), somatic anxiety (asom), and self-confidence (conf). The studies included in this dataset administered the CSAI-2 prior to some sport competition and then measured sport performance based on the competition. Most studies provided all 6 correlations (3 for the correlations among the 3 subscales and 3 for the correlations between the subscales and sport performance), but 2 studies (with study numbers 6 and 17) only provided a subset.

Concepts

psychology, correlation coefficients, multivariate models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Becker, B. J., & Aloe, A. M. (2019). Model-based meta-analysis and related approaches. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (3nd ed., pp. 339–363). New York: Russell Sage Foundation.

References

Craft, L. L., Magyar, T. M., Becker, B. J., & Feltz, D. L. (2003). The relationship between the Competitive State Anxiety Inventory-2 and sport performance: A meta-analysis. Journal of Sport and Exercise Psychology, 25(1), 44–65. ⁠https://doi.org/10.1123/jsep.25.1.44⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.craft2003
head(dat, 18)

## Not run: 
### load metafor package
library(metafor)

### construct dataset and var-cov matrix of the correlations
tmp <- rcalc(ri ~ var1 + var2 | study, ni=ni, data=dat)
V <- tmp$V
dat <- tmp$dat

### examine data for study 1
dat[dat$study == 1,]
V[dat$study == 1, dat$study == 1]

### examine data for study 6
dat[dat$study == 6,]
V[dat$study == 6, dat$study == 6]

### examine data for study 17
dat[dat$study == 17,]
V[dat$study == 17, dat$study == 17]

### multivariate random-effects model
res <- rma.mv(yi, V, mods = ~ 0 + var1.var2, random = ~ var1.var2 | study, struct="UN", data=dat)
res

## End(Not run)

Studies on the Relationship between Class Attendance and Grades in College Students

Description

Results from 68 studies on the relationship between class attendence and class performance and/or grade point average in college students.

Usage

dat.crede2010

Format

The data frame contains the following columns:

Details

The 68 studies included in this dataset provide information about the relationship between class attendance of college students and their performance (i.e., grade) in the class and/or their overall grade point average. Some studies included multiple samples and hence the dataset actually contains 97 correlation coefficients.

The dataset was obtained via personal communication. Note that this dataset differs just slightly from the one used by Credé et al. (2010).

Concepts

education, correlation coefficients, multilevel models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Personal communication.

References

Credé, M., Roch, S. G., & Kieszczynka, U. M. (2010). Class attendance in college: A meta-analytic review of the relationship of class attendance with grades and student characteristics. Review of Educational Research, 80(2), 272–295. ⁠https://doi.org/10.3102/0034654310362998⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.crede2010
head(dat, 18)

## Not run: 
### load metafor package
library(metafor)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)

############################################################################

### meta-analysis for the relationship between attendance and grades
res <- rma(yi, vi, data=dat, subset=criterion=="grade")
res

### estimated average correlation with 95% CI/PI
predict(res, transf=transf.ztor, digits=2)

### examine if relationship between attendance and grades differs for nonscience/science classes
res <- rma(yi, vi, mods = ~ class, data=dat, subset=criterion=="grade")
res

### estimated average correlations for nonscience and science classes
predict(res, newmods=c(0,1), transf=transf.ztor, digits=2)

### examine if relationship between attendance and grades has changed over time
res <- rma(yi, vi, mods = ~ year, data=dat, subset=criterion=="grade")
res

############################################################################

### meta-analysis for the relationship between attendance and GPA
res <- rma(yi, vi, data=dat, subset=criterion=="gpa")
res

### estimated average correlation with 95% CI/PI
predict(res, transf=transf.ztor, digits=2)

### examine if relationship between attendance and GPA has changed over time
res <- rma(yi, vi, mods = ~ year, data=dat, subset=criterion=="gpa")
res

############################################################################

### use a multilevel model to examine the relationship between attendance and grades
res <- rma.mv(yi, vi, random = ~ 1 | studyid/sampleid, data=dat, subset=criterion=="grade")
res
predict(res, transf=transf.ztor, digits=2)

### use a multilevel model to examine the relationship between attendance and gpa
res <- rma.mv(yi, vi, random = ~ 1 | studyid/sampleid, data=dat, subset=criterion=="gpa")
res
predict(res, transf=transf.ztor, digits=2)

## End(Not run)

Duchenne Muscular Dystrophy (DMD) Prevalence Data

Description

26 studies reporting estimates of the birth prevalence of Duchenne muscular dystrophy.

Usage

dat.crisafulli2020

Format

The data frame contains the following columns:

Details

Duchenne muscular dystrophy (DMD) is a rare disease that is caused by a genetic mutation and is characterized by impairment through muscle weakness and a reduced life expectancy.

Crisafulli et al. (2020) reported on a systematic review of data on the epidemiology of DMD, including estimates of the birth prevalence (which is of the order of a few per ten thousand). One of the originally reported studies (Koenig, 2019) is omitted here, as it constitutes an obvious outlier, and the reliability of the reported data is doubtful; Crisafulli et al. (2020) pointed out that “Concerning birth prevalence, Koenig et al. were found to be outliers. This study had problems with data collection in the last study year, as due to privacy issues, DMD cases were under-reported.”

Concepts

medicine, epidemiology, proportions, dose-response models

Author(s)

Christian Roever, christian.roever@med.uni-goettingen.de

Source

Crisafulli, S., Sultana, J., Fontana, A., Salvo, F., Messina, S., & Trifiro, G. (2020). Global epidemiology of Duchenne muscular dystrophy: an updated systematic review and meta-analysis. Orphanet Journal of Rare Diseases, 15, 141. ⁠https://doi.org/10.1186/s13023-020-01430-8⁠

Examples

# show (some) data
head(dat.crisafulli2020)

## Not run: 
# compute logarithmic proportions and associated standard errors
library(metafor)
logp <- escalc(measure="PLN",
               xi=cases, ni=total, slab=study,
               data=dat.crisafulli2020)

# perform meta-analysis
rma01 <- rma.uni(logp)

# show results
rma01

# illustrate in a forest plot
forest(rma01, xlim=c(-12,-5))

## End(Not run)

Studies on Potassium Supplementation to Reduce Diastolic Blood Pressure

Description

Results from 21 cross-over studies evaluating the effect of potassium supplementation to reduce diastolic blood pressure.

Usage

dat.curtin2002

Format

The data frame contains the following columns:

Details

Results from 21 cross-over studies evaluating the effect of potassium supplementation to reduce diastolic blood pressure (Curtin et al., 2002, Table II).

This data set is used as an example in Schwarzer et al. (2015), Chapter 2.

Concepts

raw mean differences

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Curtin, F., Altman, D. G., & Elbourne, D. (2002). Meta-analysis combining parallel and cross-over clinical trials. I: Continuous outcomes. Statistics in Medicine, 21(15), 2131–2144. ⁠https://doi.org/10.1002/sim.1205⁠

References

Schwarzer, G., Carpenter, J. R., & Rücker, G. (2015). Meta-analysis with R. Cham, Switzerland: Springer.

Examples

### Show first five studies
head(dat.curtin2002, 5)

## Not run: 
### Load meta package
suppressPackageStartupMessages(library("meta"))

### Use DerSimonian-Laird estimator (which was the default in meta in the year 2015).
### Furthermore, print meta-analysis results with two digits.
oldset <- settings.meta(method.tau = "DL", digits = 2)

### Conduct meta-analysis
mg2 <- metagen(mean, SE, studlab = paste(author, year),
               data = dat.curtin2002, sm = "MD")
mg2

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Effects of Elevated CO2 Levels on Woody Plant Mass

Description

Results from studies examining the effects of elevated CO2 levels on woody plant mass.

Usage

dat.curtis1998

Format

The data frame contains the following columns:

Details

The studies included in this dataset compared the total above- plus below-ground biomass (in grams) for plants that were either exposed to ambient (around 35 Pa) and elevated CO2 levels (around twice the ambient level). The co2.ambi and co2.elev variables indicate the CO2 levels in the control and treatment groups, respectively (with the units variable specifying the units for the CO2 exposure levels). Many of the studies also varied one or more additional environmental variables (defined by the xtrt and level variables):

• NONE = no additional treatment factor

• FERT = soil fertility (either a CONTROL, HIGH, or LOW level)

• LIGHT = light treatment (always a LOW light level)

• FERT+L = soil fertility and light (a LOW light and soil fertility level)

• H2O = well watered vs drought (either a WW or DRT level)

• TEMP = temperature treatment (either a HIGH or LOW level)

• OZONE = ozone exposure (either a HIGH or LOW level)

• UVB = ultraviolet-B radiation exposure (either a HIGH or LOW level)

In addition, the studies differed with respect to various design variables, including CO2 exposure duration (time), growing method (pot: number = pot size in liters; GRND = plants rooted in ground; HYDRO = solution or aeroponic culture), CO2 exposure facility (method: GC = growth chamber; GH = greenhouse; OTC = field-based open-top chamber), and planting stock (stock: SEED = plants started from seeds; SAP = plants started from cuttings). The goal of the meta-analysis was to examine the effects of elevated CO2 levels on plant physiology and growth and the interacting effects of the environmental (and design) variables.

Concepts

ecology, ratios of means

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hedges, L. V., Gurevitch, J., & Curtis, P. S. (1999). The meta-analysis of response ratios in experimental ecology. Ecology, 80(4), 1150–1156. ⁠https://doi.org/10.1890/0012-9658(1999)080[1150:TMAORR]2.0.CO;2⁠ (data obtained from Ecological Archives, E080-008-S1, at: ⁠https://doi.org/10.6084/m9.figshare.c.3297278⁠)

References

Curtis, P. S., & Wang, X. (1998). A meta-analysis of elevated CO2 effects on woody plant mass, form, and physiology. Oecologia, 113(3), 299–313. ⁠https://doi.org/10.1007/s004420050381⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.curtis1998
head(dat)

## Not run: 
### load metafor package
library(metafor)

### calculate (log transformed) ratios of means and corresponding sampling variances
dat <- escalc(measure="ROM", m1i=m1i, sd1i=sd1i, n1i=n1i,
                             m2i=m2i, sd2i=sd2i, n2i=n2i, data=dat)
head(dat)

### meta-analysis using a random-effects model
res <- rma(yi, vi, method="DL", data=dat)
res

### average ratio of means with 95% CI
predict(res, transf=exp, digits=2)

### meta-analysis for plants grown under nutrient stress
res <- rma(yi, vi, method="DL", data=dat, subset=(xtrt=="FERT" & level=="LOW"))
predict(res, transf=exp, digits=2)

### meta-analysis for plants grown under low light conditions
res <- rma(yi, vi, method="DL", data=dat, subset=(xtrt=="LIGHT" & level=="LOW"))
predict(res, transf=exp, digits=2)

## End(Not run)

Studies on the Effectiveness of Antihistamines in Reducing Symptoms of the Common Cold

Description

Results from 9 studies on the effectiveness of antihistamines in reducing the severity of runny nose and sneezing in the common cold.

Usage

dat.dagostino1998

Format

The data frame contains the following columns:

Details

The studies for this meta-analysis were assembled to examine the effectiveness of antihistamines in reducing the severity of runny nose and sneezing in the common cold. Effectiveness was measured after one and two days of treatment in terms of 4 different outcome variables:

1. rnic1 and rnic2 (continuous): incremental change (improvement) in runny nose severity at day 1 and day 2,

2. rngoal1 and rngoal2 (dichotomous): reaching the goal of therapy (of at least a 50% reduction in runny nose severity) at day 1 and day 2,

3. snic1 and snic2 (continuous): incremental change (improvement) in sneezing severity at day 1 and day 2, and

4. rngoal1 and rngoal2 (dichotomous): reaching the goal of therapy (of at least a 50% reduction in sneezing severity) at day 1 and day 2.

For the continuous outcomes, standardized mean differences can be computed to quantify the difference between the treatment and control groups. For the dichotomous outcomes, one can compute (log) odds ratios to quantify the difference between the treatment and control groups.

Concepts

medicine, standardized mean differences, odds ratios, multivariate models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

D'Agostino, R. B., Sr., Weintraub, M., Russell, H. K., Stepanians, M., D'Agostino, R. B., Jr., Cantilena, L. R., Jr., Graumlich, J. F., Maldonado, S., Honig, P., & Anello, C. (1998). The effectiveness of antihistamines in reducing the severity of runny nose and sneezing: A meta-analysis. Clinical Pharmacology & Therapeutics, 64(6), 579–596. ⁠https://doi.org/10.1016/S0009-9236(98)90049-2⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.dagostino1998
head(dat, 16)

## Not run: 
### load metafor package
library(metafor)

### compute standardized mean differences and corresponding sampling variances
dat <- escalc(measure="SMD", m1i=mt, m2i=mc, sd1i=sdt, sd2i=sdc, n1i=nt, n2i=nc, data=dat,
              add.measure=TRUE)

### compute log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR",  ai=xt, ci=xc, n1i=nt, n2i=nc, data=dat,
              replace=FALSE, add.measure=TRUE, add=1/2, to="all")

### inspect data for the first study
head(dat, 8)

### fit a random-effects model for incremental change in runny nose severity at day 1
res <- rma(yi, vi, data=dat, subset=outcome=="rnic1")
res

### fit a random-effects model for reaching the goal of therapy for runny nose severity at day 1
res <- rma(yi, vi, data=dat, subset=outcome=="rngoal1")
res
predict(res, transf=exp)

### construct approximate V matrix assuming a correlation of 0.7 for sampling errors within studies
dat$esid <- ave(dat$study, dat$study, FUN=seq)
V <- vcalc(vi, cluster=study, obs=esid, rho=0.7, data=dat)

### fit a model for incremental change in runny nose severity at day 1 and at day 2, allowing for
### correlated sampling errors (no random effects added, since there does not appear to be any
### noteworthy heterogeneity in these data)
res <- rma.mv(yi, V, mods = ~ 0 + outcome, data=dat, subset=outcome %in% c("rnic1","rnic2"))
res

### test if there is a difference in effects at day 1 and day 2
anova(res, X=c(1,-1))

## End(Not run)

Studies on Topical plus Systemic Antibiotics to Prevent Respiratory Tract Infections

Description

Results from 16 studies examining the effectiveness of topical plus systemic antibiotics to prevent respiratory tract infections (RTIs).

Usage

dat.damico2009

Format

The data frame contains the following columns:

Details

The dataset includes the results from 16 studies that examined the effectiveness of topical plus systemic antibiotics versus no prophylaxis to prevent respiratory tract infections (RTIs).

Concepts

medicine, odds ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

D'Amico, R., Pifferi, S., Torri, V., Brazzi, L., Parmelli, E., & Liberati, A. (2009). Antibiotic prophylaxis to reduce respiratory tract infections and mortality in adults receiving intensive care. Cochrane Database of Systematic Reviews, 4, CD000022. ⁠https://doi.org/10.1002/14651858.CD000022.pub3⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.damico2009
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of the (log) odds ratios using the Mantel-Haenszel method
rma.mh(measure="OR", ai=xt, n1i=nt, ci=xc, n2i=nc, data=dat, digits=2)

### calculate log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=xt, n1i=nt, ci=xc, n2i=nc, data=dat)

### meta-analysis using a random-effects model
res <- rma(yi, vi, data=dat, method="DL")
res
predict(res, transf=exp, digits=2)

## End(Not run)

Studies on Standard Care Quality and HAART-Adherence

Description

Results from 13 trials providing information about standard care quality and HAART-adherence in control groups.

Usage

dat.debruin2009

Format

The data frame contains the following columns:

Details

Highly active antiretroviral therapy (HAART) refers to a combination of multiple antiretroviral drugs that can effectively suppress the HIV virus. However, achieving viral suppression (to the point that the virus becomes essentially undetectable in a blood sample) requires high levels of adherence to an often complicated medication regimen. A number of trials have examined various interventions that aim to increase adherence levels. In each trial, patients receiving the intervention are compared to patients in a control group receiving standard care (often referred to as ‘care as usual’). However, the quality of standard care can vary substantially between these studies. de Bruin et al. (2009) assessed the quality of standard care provided (based on a quantification of the number of behavior change techniques applied) and examined to what extent the quality of standard care was related to the proportion of patients achieving effective viral suppression in the control groups.

Concepts

psychology, medicine, proportions, single-arm studies, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

de Bruin, M., Viechtbauer, W., Hospers, H. J., Schaalma, H. P., & Kok, G. (2009). Standard care quality determines treatment outcomes in control groups of HAART-adherence intervention studies: Implications for the interpretation and comparison of intervention effects. Health Psychology, 28(6), 668–674. ⁠https://doi.org/10.1037/a0015989⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.debruin2009
dat

## Not run: 
### load metafor package
library(metafor)

### calculate proportions and corresponding sampling variances
dat <- escalc(measure="PR", xi=xi, ni=ni, data=dat)
dat

### random-effects model
res <- rma(yi, vi, data=dat)
print(res, digits=2)

### mixed-effects meta-regression model with all predictors/covariates
res <- rma(yi, vi, mods = ~ scq + ethnicity + patients + select + sens, data=dat)
print(res, digits=3)

### mixed-effects meta-regression model with scq and ethnicity as predictors/covariates
res <- rma(yi, vi, mods = ~ scq + ethnicity, data=dat)
print(res, digits=3)

## End(Not run)

Studies on Antithrombotic Treatments to Prevent Strokes

Description

Results from 20 trials examining the effectiveness of antithrombotic treatments to prevent strokes in patients with non-valvular atrial fibrillation.

Usage

dat.dogliotti2014

Format

The data frame contains the following columns:

Details

This dataset comes from a systematic review aiming to estimate the effects of eight antithrombotic treatments including placebo in reducing the incidence of major thrombotic events in patients with non-valvular atrial fibrillation (Dogliotti et al., 2014).

The review included 20 studies with 79,808 participants, four studies are three-arm studies. The primary outcome is stroke reduction (yes / no).

Concepts

medicine, odds ratios, network meta-analysis, Mantel-Haenszel method

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Dogliotti, A., Paolasso, E., & Giugliano, R. P. (2014). Current and new oral antithrombotics in non-valvular atrial fibrillation: A network meta-analysis of 79808 patients. Heart, 100(5), 396–405. ⁠https://doi.org/10.1136/heartjnl-2013-304347⁠

Examples

### Show first 7 rows / 3 studies of the dataset
head(dat.dogliotti2014, 7)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Change appearance of confidence intervals
cilayout("(", "-")

### Transform data from long arm-based format to contrast-based
### format. Argument 'sm' has to be used for odds ratio as summary
### measure; by default the risk ratio is used in the metabin function
### called internally.
pw <- pairwise(treat = treatment, n = total, event = stroke,
  studlab = study, data = dat.dogliotti2014, sm = "OR")

### Print log odds ratios (TE) and standard errors (seTE)
head(pw, 5)[, 1:5]

### Conduct network meta-analysis (NMA) with placebo as reference
net <- netmeta(pw, ref = "plac")

### Details on excluded study
selvars <- c("studlab", "event1", "n1", "event2", "n2")
subset(pw, studlab == "WASPO, 2007")[, selvars]

### Show network graph
netgraph(net, seq = "optimal", number = TRUE)

### Conduct Mantel-Haenszel NMA
net.mh <- netmetabin(pw, ref = "plac")

### Compare results of inverse variance and Mantel-Haenszel NMA
nb <- netbind(net, net.mh, random = FALSE,
  name = c("Inverse variance", "Mantel-Haenszel"))
forest(nb, xlim = c(0.15, 2), at = c(0.2, 0.5, 1, 2))

### Print and plot results for inverse variance NMA
net
forest(net)

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on Safety of Inhaled Medications for Chronic Obstructive Pulmonary Disease

Description

Results from 41 trials examining the safety of inhaled medications in patients with chronic obstructive pulmonary disease.

Usage

dat.dong2013

Format

The data frame contains the following columns:

Details

This network meta-analysis compared the safety of inhaled medications in patients with chronic obstructive pulmonary disease (Dong et al., 2013).

Mortality was reported in 41 randomized trials, with a total of 52 462 patients. Mortality was low, with 2 408 deaths (4.6%) reported across all studies. There were nine studies that reported zero events in at least one of the treatment arms and three additional studies had zero events in all treatment arms.

This dataset was used in Efthimiou et al. (2019) to illustrate the Mantel-Haenszel method for network meta-analysis.

Concepts

medicine, odds ratios, network meta-analysis, Mantel-Haenszel method

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Dong, Y.-H., Lin, H.-H., Shau, W.-Y., Wu, Y.-C., Chang, C.-H., & Lai, M.-S. (2013). Comparative safety of inhaled medications in patients with chronic obstructive pulmonary disease: Systematic review and mixed treatment comparison meta-analysis of randomised controlled trials. Thorax, 68(1), 48–56. ⁠https://doi.org/10.1136/thoraxjnl-2012-201926⁠

References

Efthimiou, O., Rücker, G., Schwarzer, G., Higgins, J., Egger, M., & Salanti, G. (2019). A Mantel-Haenszel model for network meta-analysis of rare events. Statistics in Medicine, 38(16), 2992–3012. ⁠https://doi.org/10.1002/sim.8158⁠

Examples

### Show first 6 rows / 3 studies of the dataset
head(dat.dong2013)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Change appearance of confidence intervals
cilayout("(", "-")

### Transform data from long arm-based format to contrast-based
### format. Argument 'sm' has to be used for odds ratio as summary
### measure; by default the risk ratio is used in the metabin function
### called internally.
pw <- pairwise(treatment, death, randomized, studlab = id,
  data = dat.dong2013, sm = "OR")

### Calculated log odds ratios (TE) and standard errors (seTE)
pw[1:3, 1:9]

### Conduct Mantel-Haenszel network meta-analysis (NMA)
net <- netmetabin(pw, ref = "plac")

### Network graph
netgraph(net, seq = "optimal", col = "black", plastic = FALSE,
  points = TRUE, pch = 21, cex.points = 3, col.points = "black",
  bg.points = "gray", thickness = "se.fixed",
  number.of.studies = TRUE)

### Show results for Mantel-Haenszel NMA
net
forest(net)

### League table with network estimates in lower triangle and direct
### estimates in upper triangle
netleague(net)

### Assess inconsistency
print(netsplit(net), show = "both", ci = TRUE, overall = FALSE,
  nchar.trts = 6)

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on Complementary and Alternative Medicine for Irritable Bowel Syndrome

Description

Results from 19 trials examining complementary and alternative medicine (CAM) for irritable bowel syndrome (IBS).

Usage

dat.dorn2007

Format

The data frame contains the following columns:

Details

The dataset includes the results from 19 randomized clinical trials that examined the effectiveness of complementary and alternative medicine (CAM) for irritable bowel syndrome (IBS).

Concepts

medicine, alternative medicine, risk ratios

Note

The data were extracted from Table I in Dorn et al. (2009). Comparing the funnel plot in Figure 1 with the one obtained below indicates that the data for study 5 (Davis et al., 2006) in the table were not the ones that were used in the actual analyses.

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Dorn, S. D., Kaptchuk, T. J., Park, J. B., Nguyen, L. T., Canenguez, K., Nam, B. H., Woods, K. B., Conboy, L. A., Stason, W. B., & Lembo, A. J. (2007). A meta-analysis of the placebo response in complementary and alternative medicine trials of irritable bowel syndrome. Neurogastroenterology & Motility, 19(8), 630–637. ⁠https://doi.org/10.1111/j.1365-2982.2007.00937.x⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.dorn2007
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=x.a, n1i=n.a, ci=x.p, n2i=n.p, data=dat)

### random-effects model
res <- rma(yi, vi, data=dat, digits=2, method="DL")
res

### estimated average risk ratio
predict(res, transf=exp)

### funnel plot with study 5 highlighted in red
funnel(res, atransf=exp, at=log(c(0.1, 0.2, 0.5, 1, 2, 5, 10)),
       ylim=c(0,1), steps=6, las=1, col=ifelse(id == 5, "red", "black"))

### change log risk ratio for study 5
dat$yi[5] <- -0.44

### results are now more in line with what is reported in the paper
### (although the CI in the paper is not wide enough)
res <- rma(yi, vi, data=dat, digits=2, method="DL")
predict(res, transf=exp)

### funnel plot with study 5 highlighted in red
funnel(res, atransf=exp, at=log(c(0.1, 0.2, 0.5, 1, 2, 5, 10)),
       ylim=c(0,1), steps=6, las=1, col=ifelse(id == 5, "red", "black"))

## End(Not run)

Nitrogen dioxide data set

Description

Nine studies investigating the effect of NO2 exposure on respiratory illness in children.

Usage

dat.dumouchel1994

Format

The data frame contains the following columns:

Details

Hasselblad et al. (1992) investigated the effects of nitrogen dioxide (NO2) exposure on the occurrence of respiratory illness in children. Their data were picked up by DuMouchel (1994) as an illustrative example in his article on Bayesian meta-analysis, and were also part of his “hblm” S-Plus software package. DuMouchel's dataset differs slightly from the figures quoted by Hasselblad et al. (1992), apparently because he had additional, more detailed data available.

The data set features three study-level covariables reflecting characteristics of the study designs, namely, whether the quoted estimate had been adjusted for parents' smoking status, whether NO2 exposure had been measured directly (or presence of a gas stove in the household had been used as a proxy instead), and whether the quoted effect had been adjusted for gender. Inclusion of the covariables allows to account for the studies' design features, quantify their effects, and adjust for these.

Concepts

medicine, odds ratios, meta-regression

Author(s)

Christian Roever, christian.roever@med.uni-goettingen.de

Source

DuMouchel, W. H. (1994). Hierarchical Bayes linear models for meta-analysis. Technical Report 27, National Institute of Statistical Sciences (NISS); Research Triangle Park, NC, USA. ⁠https://www.niss.org/research/technical-reports/hierarchical-bayes-linear-models-meta-analysis-1994⁠

References

Hasselblad, V., Eddy, D. M., & Kotchmar, D. J. (1992). Synthesis of environmental evidence: Nitrogen dioxide epidemiology studies. Journal of the Air and Waste Management Association, 42(5), 662–671. ⁠https://doi.org/10.1080/10473289.1992.10467018⁠

Examples

# show data:
dat.dumouchel1994

## Not run: 
# derive effect sizes (log-ORs):
library(metafor)
no2 <- escalc(measure="OR", yi=log(or),
              sei=(log(upper)-log(lower))/(2*qnorm(0.975)),
              slab=study, data=dat.dumouchel1994)
summary(no2)

# compute overall meta-analysis:
library(bayesmeta)
bm01 <- bayesmeta(no2, tau.prior="DuMouchel")

# show results:
bm01
forestplot(bm01)
traceplot(bm01)

# perform meta-regression;
# specify regressor matrix:
X <- model.matrix( ~ smoke + no2 + gender, data=no2)
colnames(X) <- c("intercept", "smoke", "no2", "gender")

# perform regression:
bm02 <- bmr(no2, X=X, tau.prior="DuMouchel")

# show results:
bm02
forestplot(bm02)
#forestplot(bm02, xlab="log-OR",
#           X.mean=rbind("none"      = c(1,0,0,0),
#                        "smoke"     = c(1,1,0,0),
#                        "no2"       = c(1,0,1,0),
#                        "gender"    = c(1,0,0,1),
#                        "all three" = c(1,1,1,1)))
traceplot(bm02)

## End(Not run)

Studies on the Effectiveness of Intravenous Magnesium in Acute Myocardial Infarction

Description

Results from 16 trials examining the effectiveness of intravenous magnesium in the prevention of death following acute myocardial infarction.

Usage

dat.egger2001

Format

The data frame contains the following columns:

Details

The dataset includes the results from 16 randomized clinical trials that examined the effectiveness of intravenous magnesium in the prevention of death following acute myocardial infarction. Studies 1-7 were included in the meta-analyses by Teo et al. (1991) and Horner (1992) and were combined with the results from the LIMIT-2 trial (Woods et al., 1992) in Yusuf et al. (1993), suggesting that magnesium is an effective treatment for reducing mortality. However, the results from the ISIS-4 mega trial (ISIS-4 Collaborative Group, 1995) indicated no reduction in mortality with magnesium treatment. Publication bias has been suggested as one possible explanation for the conflicting findings (Egger & Davey Smith, 1995).

The present dataset includes some additional trials and are based on Table 18.2 from Egger, Davey Smith, and Altman (2001).

Concepts

medicine, cardiology, Peto's method, publication bias

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Egger, M., Davey Smith, G., & Altman, D. G. (Eds.) (2001). Systematic reviews in health care: Meta-analysis in context (2nd ed.). London: BMJ Books.

References

Egger, M., & Davey Smith, G. (1995). Misleading meta-analysis: Lessons from “an effective, safe, simple” intervention that wasn't. British Medical Journal, 310(6982), 752–754. ⁠https://doi.org/10.1136/bmj.310.6982.752⁠

Horner, S. M. (1992). Efficacy of intravenous magnesium in acute myocardial infarction in reducing arrhythmias and mortality: Meta-analysis of magnesium in acute myocardial infarction. Circulation, 86(3), 774–779. ⁠https://doi.org/10.1161/01.cir.86.3.774⁠

ISIS-4 Collaborative Group (1995). ISIS-4: A randomised factorial trial assessing early oral captopril, oral mononitrate, and intravenous magnesium sulphate in 58,050 patients with suspected acute myocardial infarction. Lancet, 345(8951), 669–685. ⁠https://doi.org/10.1016/S0140-6736(95)90865-X⁠

Teo, K. K., Yusuf, S., Collins, R., Held, P. H., & Peto, R. (1991). Effects of intravenous magnesium in suspected acute myocardial infarction: Overview of randomised trials. British Medical Journal, 303(6816), 1499–1503. ⁠https://doi.org/10.1136/bmj.303.6816.1499⁠

Woods, K. L., Fletcher, S., Roffe, C., & Haider, Y. (1992). Intravenous magnesium sulphate in suspected acute myocardial infarction: Results of the second Leicester Intravenous Magnesium Intervention Trial (LIMIT-2). Lancet, 339(8809), 1553–1558. ⁠https://doi.org/10.1016/0140-6736(92)91828-v⁠

Yusuf, S., Teo, K., & Woods, K. (1993). Intravenous magnesium in acute myocardial infarction: An effective, safe, simple, and inexpensive treatment. Circulation, 87(6), 2043–2046. ⁠https://doi.org/10.1161/01.cir.87.6.2043⁠

See Also

dat.li2007

Examples

### copy data into 'dat' and examine data
dat <- dat.egger2001
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of trials 1-7 using Peto's method (as in Teo et al., 1991)
res <- rma.peto(ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, subset=1:7)
print(res, digits=2)

### meta-analysis of trials 1-7 and LIMIT-2 (as in Yusuf et al., 1993)
res <- rma.peto(ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, subset=c(1:7,14))
print(res, digits=2)

### meta-analysis of all trials except ISIS-4
res <- rma.peto(ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, subset=-16)
print(res, digits=2)
predict(res, transf=exp, digits=2)

### meta-analysis of all trials including ISIS-4
res <- rma.peto(ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat)
print(res, digits=2)
predict(res, transf=exp, digits=2)

### contour-enhanced funnel plot centered at 0
funnel(res, refline=0, level=c(90, 95, 99), shade=c("white", "gray", "darkgray"))

## End(Not run)

Studies on Radiation Therapy with or without Adjuvant Chemotherapy in Patients with Malignant Gliomas

Description

Results from 17 trials comparing post-operative radiation therapy with and without adjuvant chemotherapy in patients with malignant gliomas.

Usage

dat.fine1993

Format

The data frame contains the following columns:

Details

The 17 trials report the post-operative survival of patients with malignant gliomas receiving either radiation therapy with adjuvant chemotherapy or radiation therapy alone. Survival was assessed at 6, 12, 18, and 24 months in all but one study (which assessed survival only at 12 and at 24 months).

The data were reconstructed by Trikalinos and Olkin (2012) based on Table 2 in Fine et al. (1993) and Table 3 in Dear (1994). The data can be used to illustrate how a meta-analysis can be conducted of effect sizes reported at multiple time points using a multivariate model.

Concepts

medicine, oncology, odds ratios, longitudinal models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Dear, K. B. G. (1994). Iterative generalized least squares for meta-analysis of survival data at multiple times. Biometrics, 50(4), 989–1002. ⁠https://doi.org/10.2307/2533438⁠

Trikalinos, T. A., & Olkin, I. (2012). Meta-analysis of effect sizes reported at multiple time points: A multivariate approach. Clinical Trials, 9(5), 610–620. ⁠https://doi.org/10.1177/1740774512453218⁠

References

Fine, H. A., Dear, K. B., Loeffler, J. S., Black, P. M., & Canellos, G. P. (1993). Meta-analysis of radiation therapy with and without adjuvant chemotherapy for malignant gliomas in adults. Cancer, 71(8), 2585–2597. ⁠https://doi.org/10.1002/1097-0142(19930415)71:8<2585::aid-cncr2820710825>3.0.co;2-s⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.fine1993
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log(ORs) and sampling variances for each time point
dat <- escalc(measure="OR", ai=e1i, n1i=nei, ci=c1i, n2i=nci, data=dat, var.names=c("y1i","v1i"))
dat <- escalc(measure="OR", ai=e2i, n1i=nei, ci=c2i, n2i=nci, data=dat, var.names=c("y2i","v2i"))
dat <- escalc(measure="OR", ai=e3i, n1i=nei, ci=c3i, n2i=nci, data=dat, var.names=c("y3i","v3i"))
dat <- escalc(measure="OR", ai=e4i, n1i=nei, ci=c4i, n2i=nci, data=dat, var.names=c("y4i","v4i"))

### calculate the covariances (equations in Appendix of Trikalinos & Olkin, 2012)
dat$v12i <- with(dat, nei / (e1i * (nei - e2i)) + nci / (c1i * (nci - c2i)))
dat$v13i <- with(dat, nei / (e1i * (nei - e3i)) + nci / (c1i * (nci - c3i)))
dat$v14i <- with(dat, nei / (e1i * (nei - e4i)) + nci / (c1i * (nci - c4i)))
dat$v23i <- with(dat, nei / (e2i * (nei - e3i)) + nci / (c2i * (nci - c3i)))
dat$v24i <- with(dat, nei / (e2i * (nei - e4i)) + nci / (c2i * (nci - c4i)))
dat$v34i <- with(dat, nei / (e3i * (nei - e4i)) + nci / (c3i * (nci - c4i)))

### create dataset in long format
dat.long <- data.frame(study=rep(1:nrow(dat), each=4), time=1:4,
                       yi=c(t(dat[c("y1i","y2i","y3i","y4i")])),
                       vi=c(t(dat[c("v1i","v2i","v3i","v4i")])))

### var-cov matrices of the studies
V <- lapply(split(dat, dat$study),
            function(x) matrix(c( x$v1i, x$v12i, x$v13i, x$v14i,
                                 x$v12i,  x$v2i, x$v23i, x$v24i,
                                 x$v13i, x$v23i,  x$v3i, x$v34i,
                                 x$v14i, x$v24i, x$v34i,  x$v4i), nrow=4, ncol=4, byrow=TRUE))

### remove rows for the missing time points in study 17
dat.long <- na.omit(dat.long)

### remove corresponding rows/columns from var-cov matrix
V[[17]] <- V[[17]][c(2,4),c(2,4)]

### make a copy of V
Vc <- V

### replace any (near) singular var-cov matrices with ridge corrected versions
repl.Vi <- function(Vi) {
   res <- eigen(Vi)
   if (any(res$values <= 0.08)) {
      round(res$vectors %*% diag(res$values + 0.08) %*% t(res$vectors), 12)
   } else {
      Vi
   }
}
Vc <- lapply(Vc, repl.Vi)

### do not correct var-cov matrix of study 17
Vc[[17]] <- V[[17]]

### construct block diagonal matrix
Vc <- bldiag(Vc)

### multivariate fixed-effects model
res <- rma.mv(yi, Vc, mods = ~ 0 + factor(time), method="FE", data=dat.long)
print(res, digits=3)

### multivariate random-effects model with heteroscedastic AR(1) structure for the true effects
res <- rma.mv(yi, Vc, mods = ~ 0 + factor(time), random = ~ time | study,
              struct="HAR", data=dat.long, control=list(optimizer="hjk"))
print(res, digits=3)

### profile the variance components
par(mfrow=c(2,2))
profile(res, tau2=1, xlim=c(  0, 0.2))
profile(res, tau2=2, xlim=c(  0, 0.2))
profile(res, tau2=3, xlim=c(  0, 0.2))
profile(res, tau2=4, xlim=c(0.1, 0.3))

### profile the autocorrelation coefficient
par(mfrow=c(1,1))
profile(res, rho=1)

## End(Not run)

Studies on Dopamine Agonists to Reduce “Off-Time” in Patients with Advanced Parkinson Disease

Description

Results from 7 trials examining the effectiveness of four dopamine agonists and placebo to reduce “off-time” in patients with advanced Parkinson disease.

Usage

dat.franchini2012

Format

The data frame contains the following columns:

Details

This network meta-analysis compared the effectiveness of four active treatments and placebo in patients with advanced Parkinson disease (Franchini et al., 2012). The outcome is mean lost work-time reduction in patients given dopamine agonists as adjunct therapy. The data are given as sample size, mean, and standard deviation in each trial arm.

This dataset was used as an example in the supplemental material of Dias et al. (2013) where placebo is coded as 1 and the four active drugs as 2 to 5.

Concepts

medicine, raw mean differences, network meta-analysis

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Dias, S., Sutton, A. J., Ades, A. E., & Welton, N. J. (2013). Evidence synthesis for decision making 2: A generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Medical Decision Making, 33(5), 607–617. ⁠https://doi.org/10.1177/0272989X12458724⁠

Franchini, A. J., Dias, S., Ades, A. E., Jansen, J. P., & Welton, N. J. (2012). Accounting for correlation in network meta-analysis with multi-arm trials. Research Synthesis Methods, 3(2), 142–160. ⁠https://doi.org/10.1002/jrsm.1049⁠

Examples

### Show results from first three studies; third study is a three-arm
### study
head(dat.franchini2012, 3)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print mean differences with two digits
oldset <- settings.meta(digits = 2)

### Transform data from wide arm-based format to contrast-based
### format. Argument 'sm' must not be provided as the mean difference
### is the default in R function metacont() called internally.
pw <- pairwise(list(Treatment1, Treatment2, Treatment3),
  n = list(n1, n2, n3),
  mean = list(y1, y2, y3),
  sd = list(sd1, sd2, sd3),
  data = dat.franchini2012, studlab = Study, sm = "MD")

### Show calculated mean differences (TE) for first three studies
pw[1:5, c(3:7, 10, 1)]

### Conduct network meta-analysis
net <- netmeta(pw)
net

### Draw network graph
netgraph(net, points = TRUE, cex.points = 3, cex = 1.5,
  plastic = TRUE, thickness = "se.fixed",
  iterate = TRUE, start = "eigen")

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Association Between the CASP8 -652 6N del Promoter Polymorphism and Breast Cancer Risk

Description

Results from 4 case-control studies examining the association between the CASP8 -652 6N del promoter polymorphism and breast cancer risk.

Usage

dat.frank2008

Format

The data frame contains the following columns:

Details

The 4 studies included in this dataset are case-control studies that have examined the association between the CASP8 -652 6N del promoter polymorphism and breast cancer risk. Breast cancer cases and controls were genotyped and either had a homozygous insertion, a heterozygous insertion/deletion, or a homozygous deletion polymorphism.

Ziegler et al. (2011) used the same dataset to illustrate the use of meta-analytic methods to examine deviations from Hardy-Weinberg equilibrium across multiple studies. The relative excess heterozygosity (REH) is the proposed measure for such a meta-analysis, which can be computed by setting measure="REH".

Concepts

medicine, oncology, genetics, odds ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Frank, B., Rigas, S. H., Bermejo, J. L., Wiestler, M., Wagner, K., Hemminki, K., Reed, M. W., Sutter, C., Wappenschmidt, B., Balasubramanian, S. P., Meindl, A., Kiechle, M., Bugert, P., Schmutzler, R. K., Bartram, C. R., Justenhoven, C., Ko, Y.-D., Brüning, T., Brauch, H., Hamann, U., Pharoah, P. P. D., Dunning, A. M., Pooley, K. A., Easton, D. F., Cox, A. & Burwinkel, B. (2008). The CASP8 -652 6N del promoter polymorphism and breast cancer risk: A multicenter study. Breast Cancer Research and Treatment, 111(1), 139–144. ⁠https://doi.org/10.1007/s10549-007-9752-z⁠

References

Ziegler, A., Steen, K. V. & Wellek, S. (2011). Investigating Hardy-Weinberg equilibrium in case-control or cohort studies or meta-analysis. Breast Cancer Research and Treatment, 128(1), 197–201. ⁠https://doi.org/10.1007/s10549-010-1295-z⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.frank2008
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log odds ratios comparing ins/del versus ins/ins
dat <- escalc(measure="OR", ai=bc.ins.del, bi=bc.ins.ins,
                            ci=ct.ins.del, di=ct.ins.ins, data=dat)

### fit random-effects model and get the pooled odds ratio (with 95% CI)
res <- rma(yi, vi, data=dat)
res
predict(res, transf=exp, digits=2)

### calculate log odds ratios comparing del/del versus ins/ins
dat <- escalc(measure="OR", ai=bc.del.del, bi=bc.ins.ins,
                            ci=ct.del.del, di=ct.ins.ins, data=dat)

### fit random-effects model and get the pooled odds ratio (with 95% CI)
res <- rma(yi, vi, data=dat)
res
predict(res, transf=exp, digits=2)

### calculate log odds ratios comparing ins/del+del/del versus ins/ins
dat <- escalc(measure="OR", ai=bc.ins.del+bc.del.del, bi=bc.ins.ins,
                            ci=ct.ins.del+ct.del.del, di=ct.ins.ins, data=dat)

### fit random-effects model and get the pooled odds ratio (with 95% CI)
res <- rma(yi, vi, data=dat)
res
predict(res, transf=exp, digits=2)

############################################################################

### compute the relative excess heterozygosity in the controls
dat <- escalc(measure="REH", ai=ct.ins.ins, bi=ct.ins.del, ci=ct.del.del,
              slab=study, data=dat)

### fit random-effects model and get the pooled REH value (with 90% CI)
res <- rma(yi, vi, data=dat, level=90)
res
predict(res, transf=exp, digits=2)

### draw forest plot
forest(res, atransf=exp, xlim=c(-1.4,1.4), at=log(c(0.5,5/7,1,7/5,2)))
segments(log(5/7), -2, log(5/7), res$k+1, lty="dotted")
segments(log(7/5), -2, log(7/5), res$k+1, lty="dotted")

## End(Not run)

Studies on Low Dosage Tricyclic Antidepressants for the Treatment of Depression

Description

Results on depression severity from 17 studies comparing low dosage tricyclic antidepressants (TCA) and placebo for the treatment of depression.

Usage

dat.furukawa2003

Format

The data frame contains the following columns:

Details

Furukawa et al. (2003) carried out a systematic review comparing low dosage tricyclic antidepressants (TCA) with placebo for the treatment of depression. They reported the effect on presence/absence of depression and on depression severity at various time points. Here we focus on depression severity at four weeks. Most studies used some version of the Hamilton Depression Rating Scale, however, some studies used the Montgomery-Asberg Depression Rating Scale. Accordingly, it is not possible to pool the estimated effects directly.

This data set is used as an example in Schwarzer et al. (2015).

Concepts

standardized mean differences

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Furukawa, T. A., McGuire, H., & Barbui, C. (2003). Low dosage tricyclic antidepressants for depression. Cochrane Database of Systematic Reviews, 3, CD003197. ⁠https://doi.org/10.1002/14651858.CD003197⁠

References

Schwarzer, G., Carpenter, J. R., & Rücker, G. (2015). Meta-analysis with R. Cham, Switzerland: Springer.

Examples

### Show first five studies
head(dat.furukawa2003, 5)

## Not run: 
### Load meta package
suppressPackageStartupMessages(library("meta"))

### Use RevMan5 settings
oldset <- settings.meta("RevMan5", digits = 2)

### Conduct random effects meta-analysis with Hedges' g as effect measure
mc2 <- metacont(Ne, Me, Se, Nc, Mc, Sc, common = FALSE,
                data = dat.furukawa2003, sm = "SMD")
mc2

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Effectiveness of Self-Management Education and Regular Medical Review for Adults with Asthma

Description

Results from 15 trials examining the effectiveness of self-management education and regular medical review for adults with asthma.

Usage

dat.gibson2002

Format

The data frame contains the following columns:

Details

Asthma management guidelines typically recommend for patients to receive education and regular medical review. While self-management programs have been shown to increase patient knowledge, it is less clear to what extent they actually impact health outcomes. The systematic review by Gibson et al. (2002) examined the effectiveness of self-management education and regular medical review for adults with asthma. In each study, participants receiving a certain management intervention were compared against those in a control/comparison group with respect to a variety of health outcomes. One of the outcomes examined in a number of studies was the number of days off work/school.

The majority of studies reporting this outcome provided means and standard deviations allowing a meta-analysis of standardized mean differences. Seven studies also reported the number of participants who had one or more days off work/school in each group. These studies could be meta-analyzed using, for example, (log) risk ratios. Finally, one could also consider a combined analysis based on standardized mean differences computed from the means and standard deviations where available and using probit transformed risk differences (which also provide estimates of the standardized mean difference) for the remaining studies.

Some degree of patient education was provided in all studies. In addition, the type variable indicates what additional intervention components were included in each study:

1. optimal self-management (writing action plan, self-monitoring, regular medical review),

2. self-monitoring and regular medical review,

3. self-monitoring only,

4. regular medical review only,

5. written action plan only.

Concepts

medicine, primary care, risk ratios, standardized mean differences

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Gibson, P. G., Powell, H., Wilson, A., Abramson, M. J., Haywood, P., Bauman, A., Hensley, M. J., Walters, E. H., & Roberts, J. J. L. (2002). Self-management education and regular practitioner review for adults with asthma. Cochrane Database of Systematic Reviews, 3, CD001117. ⁠https://doi.org/10.1002/14651858.CD001117⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.gibson2002
dat

## Not run: 
### load metafor package
library(metafor)

### compute standardized mean differences and corresponding sampling variances
dat <- escalc(measure="SMD", m1i=m1i, sd1i=sd1i, n1i=n1i, m2i=m2i, sd2i=sd2i, n2i=n2i, data=dat)
dat

### fit an equal-effects model to the standardized mean differences (as in Gibson et al., 2002)
res <- rma(yi, vi, data=dat, method="EE")
print(res, digits=2)

### compute log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=ai, bi=bi, ci=ci, di=di, data=dat)
dat

### fit an equal-effects model to the log risk ratios
res <- rma(yi, vi, data=dat, method="EE")
print(res, digits=2)
predict(res, transf=exp, digits=2)

### note: Gibson et al. (2002) used the Mantel-Haenszel method for their analysis
rma.mh(measure="RR", ai=ai, bi=bi, ci=ci, di=di, data=dat, digits=2)

### compute standardized mean differences where possible and otherwise probit transformed
### risk differences (which also provide estimates of the standardized mean differences)
dat <- escalc(measure="SMD", m1i=m1i, sd1i=sd1i, n1i=n1i,
                             m2i=m2i, sd2i=sd2i, n2i=n2i, data=dat, add.measure=TRUE)
dat <- escalc(measure="PBIT", ai=ai, bi=bi, ci=ci, di=di, data=dat, replace=FALSE, add.measure=TRUE)
dat

### fit a random-effects model to these estimates
res <- rma(yi, vi, data=dat)
print(res, digits=2)

### meta-regression model examining if there are systematic differences based on the
### type of measure used (there are only 2 studies where measure="PBIT", so this isn't
### very conclusive here, but shown for illustration purposes)
res <- rma(yi, vi, mods = ~ measure, data=dat)
print(res, digits=2)
predict(res, newmods=1, digits=2)

## End(Not run)

Studies on the Effectiveness of Injected Cholera Vaccines

Description

Results from 17 studies on the effectiveness of injected vaccines against cholera.

Usage

dat.graves2010

Format

The data frame contains the following columns:

Details

Cholera is an infection caused by certain strains of the bacterium Vibrio cholerae. When untreated, mortality rates can be as high as 50-60%. Proper sanitation practices are usually effective in preventing outbreaks, but a number of oral and injectable vaccines have also been developed. The Cochrane review by Graves et al. (2010) examined the effectiveness of injectable vaccines for preventing cholera cases and death. The present dataset includes results from 17 studies that reported the number of cholera cases in vaccinated and placebo/comparison groups up to 7 months after the treatment.

Concepts

medicine, risk ratios, Mantel-Haenszel method

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Graves, P. M., Deeks, J. J., Demicheli, V., & Jefferson, T. (2010). Vaccines for preventing cholera: Killed whole cell or other subunit vaccines (injected). Cochrane Database of Systematic Reviews, 8, CD000974. ⁠https://doi.org/10.1002/14651858.CD000974.pub2⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.graves2010
dat

## Not run: 
### load metafor package
library(metafor)

### analysis using the Mantel-Haenszel method
rma.mh(measure="RR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, digits=2)

## End(Not run)

Studies on Interventions to Reduce Mortality after Liver Transplantation

Description

Results from 14 trials examining the mortality risk of interventions for decreasing blood loss and blood transfusion requirements during liver transplantation.

Usage

dat.gurusamy2011

Format

The data frame contains the following columns:

Details

This network meta-analysis compared the effectiveness of seven interventions for decreasing blood loss and blood transfusion requirements during liver transplantation (Gurusamy et al., 2011).

Fourteen studies reported mortality at 60 days, in 1,002 patients. Forty-five deaths were reported across all studies (4.5%). Six studies observed deaths in all treatment arms while three studies did not observe any deaths.

This dataset was used in Efthimiou et al. (2019) to introduce the Mantel-Haenszel method for network meta-analysis.

One of the treatments (solvent detergent plasma) was only included in one study with zero events in both treatment arms; this study was excluded from all network meta-analyses. In addition, no death was observed in the antithrombin III arm of the only study evaluating this treatment which was excluded from the Mantel-Haenszel network meta-analysis.

Concepts

medicine, odds ratios, network meta-analysis, Mantel-Haenszel method

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Gurusamy, K. S., Pissanou, T., Pikhart, H., Vaughan, J., Burroughs, A. K., & Davidson, B. R. (2011). Methods to decrease blood loss and transfusion requirements for liver transplantation. Cochrane Database of Systematic Reviews, 12, CD009052. ⁠https://doi.org/10.1002/14651858.CD009052.pub2⁠

References

Efthimiou, O., Rücker, G., Schwarzer, G., Higgins, J., Egger, M., & Salanti, G. (2019). A Mantel-Haenszel model for network meta-analysis of rare events. Statistics in Medicine, 38(16), 2992–3012. ⁠https://doi.org/10.1002/sim.8158⁠

Examples

### Show first 6 rows of the dataset
head(dat.gurusamy2011)

### Only study evaluating solvent detergent plasma
subset(dat.gurusamy2011, study == "Williamson 1999")

### Only study evaluating antithrombin III
subset(dat.gurusamy2011, study == "Baudo 1992")

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Change appearance of confidence intervals
cilayout("(", "-")

### Transform data from long arm-based format to contrast-based
### format. Argument 'sm' has to be used for odds ratio as summary
### measure; by default the risk ratio is used in the metabin function
### called internally.
pw <- pairwise(treatment, death, n, studlab = study,
  data = dat.gurusamy2011, sm = "OR")

### Conduct Mantel-Haenszel network meta-analysis (NMA)
net.MH <- netmetabin(pw, ref = "cont")

### Conduct inverse variance (IV) network meta-analysis
net.IV <- netmeta(pw, ref = "cont")

### Network graph (Mantel-Haenszel NMA)
netgraph(net.MH, seq = "optimal", col = "black", plastic = FALSE,
  points = TRUE, pch = 21, cex.points = 3, col.points = "black",
  bg.points = "gray", thickness = "se.fixed",
  number.of.studies = TRUE)

### Full network graph (based on inverse variance method, including
### study comparing Antithrombin III with Control/Placebo)
netgraph(net.IV,
  seq = "optimal", col = "black", plastic = FALSE,
  points = TRUE, pch = 21, cex.points = 3, col.points = "black",
  bg.points = "gray", thickness = "se.fixed",
  number.of.studies = TRUE)

### Compare results for Mantel-Haenszel and IV NMA
forest(netbind(net.MH, net.IV,
  random = FALSE, name = c("MH NMA", "IV NMA")))

### Show results for Mantel-Haenszel NMA
net.MH
forest(net.MH)

### League table with network estimates in lower triangle and direct
### estimates in upper triangle
netleague(net.MH)

### Assess inconsistency
print(netsplit(net.MH), show = "both", ci = TRUE, overall = FALSE,
  nchar.trts = 6)

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Risk of Lung Cancer in Women Exposed to Environmental Tobacco Smoke

Description

Results from 37 studies on the risk of lung cancer in women exposed to environmental tobacco smoke (ETS) from their smoking spouse.

Usage

dat.hackshaw1998

Format

The data frame contains the following columns:

Details

The dataset includes the results from 37 studies (4 cohort, 33 case-control) examining if women (who are lifelong nonsmokers) have an elevated risk for lung cancer due to exposure to environmental tobacco smoke (ETS) from their smoking spouse. Values of the log odds ratio greater than 0 indicate an increased risk of cancer in exposed women compared to women not exposed to ETS from their spouse.

Note that the log odds ratios and corresponding sampling variances were back-calculated from the reported odds ratios and confidence interval (CI) bounds (see ‘Examples’). Since the reported values were rounded to some extent, this introduces some minor inaccuracies into the back-calculations. The overall estimate reported in Hackshaw et al. (1997) and Hackshaw (1998) can be fully reproduced though.

Concepts

medicine, oncology, epidemiology, smoking, odds ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hackshaw, A. K., Law, M. R., & Wald, N. J. (1997). The accumulated evidence on lung cancer and environmental tobacco smoke. British Medical Journal, 315(7114), 980–988. ⁠https://doi.org/10.1136/bmj.315.7114.980⁠

Hackshaw, A. K. (1998). Lung cancer and passive smoking. Statistical Methods in Medical Research, 7(2), 119–136. ⁠https://doi.org/10.1177/096228029800700203⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hackshaw1998
head(dat, 10)

## Not run: 
### load metafor package
library(metafor)

### random-effects model using the log odds ratios
res <- rma(yi, vi, data=dat, method="DL")
res

### estimated average odds ratio with CI (and prediction interval)
predict(res, transf=exp, digits=2)

### illustrate how the log odds ratios and corresponding sampling variances
### can be back-calculated based on the reported odds ratios and CI bounds
dat$yi <- NULL
dat$vi <- NULL
dat <- data.frame(dat)
head(dat, 10)
dat <- conv.wald(out=or, ci.lb=or.lb, ci.ub=or.ub, data=dat, transf=log)
head(dat, 10)

## End(Not run)

Studies on the Effectiveness of Different Rehydration Solutions for the Prevention of Unscheduled Intravenous Infusion in Children with Diarrhoea

Description

Results from 12 trials examining the effectiveness of a reduced versus standard rehydration solution for the prevention of unscheduled intravenous infusion in children with diarrhoea.

Usage

dat.hahn2001

Format

The data frame contains the following columns:

Details

The dataset includes the results from 12 randomized clinical trials that examined the effectiveness of a reduced osmolarity oral rehydration solution (total osmolarity <250 mmol/l with reduced sodium) with a standard WHO oral rehydration solution (sodium 90 mmol/l, glucose 111mmol/l, total osmolarity 311 mmol/l) for the prevention of unscheduled intravenous infusion in children with diarrhoea.

Concepts

medicine, odds ratios, Mantel-Haenszel method

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hahn, S., Kim, Y., & Garner, P. (2001). Reduced osmolarity oral rehydration solution for treating dehydration due to diarrhoea in children: Systematic review. British Medical Journal, 323(7304), 81–85. ⁠https://doi.org/10.1136/bmj.323.7304.81⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hahn2001
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of (log) odds rations using the Mantel-Haenszel method
res <- rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, digits=2, slab=study)
res

### forest plot (also show studies that were excluded from the analysis)
options(na.action="na.pass")
forest(res, atransf=exp, xlim=c(-11,9), at=log(c(0.01, 0.1, 1, 10, 100)))
options(na.action="na.omit")

## End(Not run)

Studies Comparing Objective and Subjective Olfactory Loss in COVID-19 Patients

Description

Results from 35 studies measuring olfactory loss in COVID-19 patients using either objective or subjective measures.

Usage

dat.hannum2020

Format

The data frame contains the following columns:

Details

One of the symptoms of COVID-19 infection is olfactory loss (loss of smell) either recently acquired anosmia (complete loss of smell) or hyposmia (partial loss of smell). One challenge to reaching this symptom is the wide range of reported prevalence for this symptom ranging from 5 percent to 98 percent. In this dataset studies were grouped into one of two groups based on the type of method used to measure smell loss (either subjective measures, such as self-reported smell loss, or objective measures using rated stimuli).

Concepts

medicine, covid-19, proportions

Author(s)

W. Kyle Hamilton whamilton@ucmerced.edu https://kylehamilton.com

Source

Ramirez VA , Hannum ME, Lipson SJ, Herriman RD, Toskala AK, Lin C, Joseph PV, Reed DR. 2020. COVID-19 Smell Loss Prevalence Tracker. Available from: ⁠https://vicente-ramirez.shinyapps.io/COVID19_Olfactory_Dashboard/⁠ and ⁠https://github.com/vramirez4/OlfactoryLoss⁠ (accessed August 11, 2021)

References

Hannum, M. E., Ramirez, V. A., Lipson, S. J., Herriman, R. D., Toskala, A. K., Lin, C., Joseph, P. V., & Reed, D. R. (2020). Objective sensory testing methods reveal a higher prevalence of olfactory loss in COVID-19 positive patients compared to subjective methods: A systematic review and meta-analysis. Chemical Senses, 45(9), 865–874. ⁠https://doi.org/10.1093/chemse/bjaa064⁠

Examples

# copy data into 'dat' and examine data
dat <- dat.hannum2020
dat

## Not run: 
# load metafor package
library(metafor)

# compute effect size
dat <- escalc(measure="PR", xi=xi, ni=ni, data=dat)

# split data into objective and subjective datasets
dat_split <- split(dat, dat$objectivity)
dat_objective <- dat_split[["Objective"]]
dat_subjective <- dat_split[["Subjective"]]

# random-effects model all studies
res_all <- rma(yi, vi, data=dat)
print(res_all, digits=2)

# random-effects model objective
res_objective <- rma(yi, vi, data=dat_objective)
print(res_objective, digits=2)

# random-effects model subjective
res_subjective <- rma(yi, vi, data=dat_subjective)
print(res_subjective, digits=2)

## End(Not run)

Studies on the Effectiveness of Warfarin for Preventing Strokes

Description

Results from 6 clinical trials examining the effectiveness of adjusted-dose warfarin for preventing strokes in patients with atrial fibrillation.

Usage

dat.hart1999

Format

The data frame contains the following columns:

Details

The 6 studies provide data with respect to the number of strokes in the warfarin and the comparison (placebo or control) group. In addition, the number of patients and the total person-time (in years) is provided for the two groups. The goal of the meta-analysis was to examine the effectiveness of adjusted-dose warfarin for preventing strokes in patients with atrial fibrillation.

Concepts

medicine, cardiology, incidence rates

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hart, R. G., Benavente, O., McBride, R., & Pearce, L. A. (1999). Antithrombotic therapy to prevent stroke in patients with atrial fibrillation: A meta-analysis. Annals of Internal Medicine, 131(7), 492–501. ⁠https://doi.org/10.7326/0003-4819-131-7-199910050-00003⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hart1999
dat

## Not run: 
### load metafor package
library(metafor)

### calculate log incidence rate ratios and corresponding sampling variances
dat <- escalc(measure="IRR", x1i=x1i, x2i=x2i, t1i=t1i, t2i=t2i, data=dat)
dat

### meta-analysis of log incidence rate ratios using a random-effects model
res <- rma(yi, vi, data=dat)
res

### average incidence rate ratio with 95% CI
predict(res, transf=exp)

### forest plot with extra annotations
par(mar=c(5,4,1,2))
forest(res, xlim=c(-11, 5), at=log(c(0.05, 0.25, 1, 4)), atransf=exp,
       slab=paste0(study, " (", year, ")"),
       ilab=cbind(paste(x1i, "/", t1i, sep=" "),
                  paste(x2i, "/", t2i, sep=" ")),
       ilab.xpos=c(-6.5,-4), cex=0.85, header="Study (Year)")
op <- par(cex=0.85, font=2)
text(c(-6.5,-4), 8.5, c("Warfarin", "Control"))
text(c(-6.5,-4), 7.5, c("Strokes / PT", "Strokes / PT"))
segments(x0=-8, y0=8, x1=-2.75, y1=8)
par(op)

### meta-analysis of incidence rate differences using a random-effects model
res <- rma(measure="IRD", x1i=x1i, x2i=x2i, t1i=t1i, t2i=t2i, data=dat)
res

## End(Not run)

Studies on the Effectiveness of Nicotine Replacement Therapy for Smoking Cessation

Description

Results from 133 studies examining the effectiveness of nicotine replacement therapy (NRT) for smoking cessation at 6+ months of follow-up.

Usage

dat.hartmannboyce2018

Format

The data frame contains the following columns:

Details

The dataset includes the results from 133 studies examining the effectiveness of nicotine replacement therapy (NRT) for smoking cessation. The results given in this dataset pertain to abstinence at 6+ months of follow-up. NRT was provided to participants in the treatment groups in various forms as indicated by the treatment variable (e.g., gum, patch, inhalator). Note that the dataset includes 136 rows, since a few studies included multiple treatments.

Concepts

medicine, smoking, risk ratios, Mantel-Haenszel method

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hartmann‐Boyce, J., Chepkin, S. C., Ye, W., Bullen, C. & Lancaster, T. (2018). Nicotine replacement therapy versus control for smoking cessation. Cochrane Database of Systematic Reviews, 5, CD000146. ⁠https://doi.org//10.1002/14651858.CD000146.pub5⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hartmannboyce2018
head(dat, 10)

## Not run: 
### load metafor package
library(metafor)

### turn treatment into a factor with the desired ordering
dat$treatment <- factor(dat$treatment, levels=unique(dat$treatment))

### meta-analysis per treatment using the M-H method
lapply(split(dat, dat$treatment), function(x)
       rma.mh(measure="RR", ai=x.nrt,  n1i=n.nrt,
                            ci=x.ctrl, n2i=n.ctrl, data=x, digits=2))

### all combined
rma.mh(measure="RR", ai=x.nrt,  n1i=n.nrt,
                     ci=x.ctrl, n2i=n.ctrl, data=dat, digits=2)

## End(Not run)

Studies on the Effectiveness of Counseling for Smoking Cessation

Description

Results from 24 studies on the effectiveness of various counseling types for smoking cessation.

Usage

dat.hasselblad1998

Format

The data frame contains the following columns:

Details

The dataset includes the results from 24 studies on the effectiveness of various counseling types for smoking cessation (i.e., self-help, individual counseling, group counseling, and no contact). The dataset indicates the total number of individuals within each study arm and the number that were abstinent from 6 to 12 months. The majority of the studies compared two interventions types against each other, while 2 studies compared three types against each other simultaneously.

The data can be used for a ‘network meta-analysis’ (also called a ‘mixed treatment comparison’). The code below shows how such an analysis can be conducted using an arm-based and a contrast-based model (see Salanti et al., 2008, for more details).

Concepts

medicine, psychology, smoking, odds ratios, network meta-analysis

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Hasselblad, V. (1998). Meta-analysis of multitreatment studies. Medical Decision Making, 18(1), 37–43. ⁠https://doi.org/10.1177/0272989X9801800110⁠

References

Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 357–376). New York: Russell Sage Foundation.

Law, M., Jackson, D., Turner, R., Rhodes, K., & Viechtbauer, W. (2016). Two new methods to fit models for network meta-analysis with random inconsistency effects. BMC Medical Research Methodology, 16, 87. ⁠https://doi.org/10.1186/s12874-016-0184-5⁠

Salanti, G., Higgins, J. P. T., Ades, A. E., & Ioannidis, J. P. A. (2008). Evaluation of networks of randomized trials. Statistical Methods in Medical Research, 17(3), 279–301. ⁠https://doi.org/10.1177/0962280207080643⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hasselblad1998
dat

## Not run: 
### load metafor package
library(metafor)

### create network graph ('igraph' package must be installed)
library(igraph, warn.conflicts=FALSE)
pairs <- data.frame(do.call(rbind,
   sapply(split(dat$trt, dat$study), function(x) t(combn(x,2)))), stringsAsFactors=FALSE)
lvls <- c("no_contact", "self_help", "ind_counseling", "grp_counseling")
pairs$X1 <- factor(pairs$X1, levels=lvls)
pairs$X2 <- factor(pairs$X2, levels=lvls)
tab <- table(pairs[,1], pairs[,2])
tab # adjacency matrix
g <- graph_from_adjacency_matrix(tab, mode = "plus", weighted=TRUE, diag=FALSE)
vertex_attr(g, "name") <- c("No Contact", "Self-Help",
                            "Individual\nCounseling", "Group\nCounseling")
plot(g, edge.curved=FALSE, edge.width=E(g)$weight, layout=layout_on_grid,
     vertex.size=45, vertex.color="lightgray", vertex.label.color="black", vertex.label.font=2)

### calculate log odds for each study arm
dat <- escalc(measure="PLO", xi=xi, ni=ni, add=1/2, to="all", data=dat)
dat

### convert trt variable to factor with desired ordering of levels
dat$trt <- factor(dat$trt, levels=c("no_contact", "self_help", "ind_counseling", "grp_counseling"))

### add a space before each level (this makes the output a bit more legible)
levels(dat$trt) <- paste0(" ", levels(dat$trt))

### network meta-analysis using an arm-based model with fixed study effects
### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons
res <- rma.mv(yi, vi, mods = ~ 0 + factor(study) + trt,
              random = ~ trt | study, rho=1/2, data=dat, btt="trt")
res

### all pairwise odds ratios of interventions versus no contact
predict(res, newmods=cbind(matrix(0, nrow=3, ncol=24), diag(3)),
        intercept=FALSE, transf=exp, digits=2)

### all pairwise odds ratios comparing interventions (ic vs sh, gc vs sh, and gc vs ic)
predict(res, newmods=cbind(matrix(0, nrow=3, ncol=24), rbind(c(-1,1,0), c(-1,0,1), c(0,-1,1))),
        intercept=FALSE, transf=exp, digits=2)

### forest plot of ORs of interventions versus no contact
forest(c(0,res$beta[25:27]), sei=c(0,res$se[25:27]), psize=1, xlim=c(-3,4), digits=c(2,1), efac=2,
       slab=c("No Contact", "Self-Help", "Individual Counseling", "Group Counseling"),
       atransf=exp, at=log(c(0.5, 1, 2, 4, 8)), xlab="Odds Ratio for Intervention vs. No Contact",
       header=c("Intervention", "Odds Ratio [95% CI]"))

############################################################################

### restructure dataset to a contrast-based format
dat <- to.wide(dat.hasselblad1998, study="study", grp="trt", ref="no_contact", grpvars=6:7)

### calculate log odds ratios for each treatment comparison
dat <- escalc(measure="OR", ai=xi.1, n1i=ni.1,
                            ci=xi.2, n2i=ni.2, add=1/2, to="all", data=dat)
dat

### calculate the variance-covariance matrix of the log odds ratios for multitreatment studies
### see Gleser & Olkin (2009), equation (19.11), for the covariance equation
calc.v <- function(x) {
   v <- matrix(1/(x$xi.2[1] + 1/2) + 1/(x$ni.2[1] - x$xi.2[1] + 1/2), nrow=nrow(x), ncol=nrow(x))
   diag(v) <- x$vi
   v
}
V <- bldiag(lapply(split(dat, dat$study), calc.v))

### add contrast matrix to dataset
dat <- contrmat(dat, grp1="trt.1", grp2="trt.2")
dat

### network meta-analysis using a contrast-based random-effects model
### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons
res <- rma.mv(yi, V, mods = ~ 0 + self_help + ind_counseling + grp_counseling,
              random = ~ comp | study, rho=1/2, data=dat)
res

### predicted odds ratios of interventions versus no contact
predict(res, newmods=diag(3), transf=exp, digits=2)

### fit random inconsistency effects model (see Law et al., 2016)
res <- rma.mv(yi, V, mods = ~ 0 + self_help + ind_counseling + grp_counseling,
              random = list(~ comp | study, ~ comp | design), rho=1/2, phi=1/2, data=dat)
res

## End(Not run)

Studies on Prophylactic Use of Lidocaine After a Heart Attack

Description

Results from 6 studies evaluating mortality from prophylactic use of lidocaine in acute myocardial infarction.

Usage

dat.hine1989

Format

The data frame contains the following columns:

Details

Hine et al. (1989) conducted a meta-analysis of death rates in randomized controlled trials in which prophylactic lidocaine was administered to patients with confirmed or suspected acute myocardial infarction. The dataset describes the mortality at the end of the assigned treatment period for control and intravenous lidocaine treatment groups for six studies. The question of interest is whether there is a detrimental effect of lidocaine. Because the studies were conducted to compare rates of arrhythmias following a heart attack, the studies, taken individually, are too small to detect important differences in mortality rates.

The data in this dataset were obtained from Table I in Normand (1999, p. 322).

Concepts

medicine, cardiology, risk differences

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Normand, S. T. (1999). Meta-analysis: Formulating, evaluating, combining, and reporting. Statistics in Medicine, 18(3), 321–359. ⁠https://doi.org/10.1002/(sici)1097-0258(19990215)18:3<321::aid-sim28>3.0.co;2-p⁠

References

Hine, L. K., Laird, N., Hewitt, P., & Chalmers, T. C. (1989). Meta-analytic evidence against prophylactic use of lidocaine in acute myocardial infarction. Archives of Internal Medicine, 149(12), 2694–2698. ⁠https://doi.org/10.1001/archinte.1989.00390120056011⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.hine1989
dat

## Not run: 
### load metafor package
library(metafor)

### calculate risk differences and corresponding sampling variances
dat <- escalc(measure="RD", n1i=n1i, n2i=n2i, ai=ai, ci=ci, data=dat)
dat

### meta-analysis of risk differences using a random-effects model
res <- rma(yi, vi, data=dat)
res

## End(Not run)

Studies on Deep-Brain Stimulation in Patients with Parkinson's disease

Description

Results from 46 studies examining the effects of deep-brain stimulation on motor skills of patients with Parkinson's disease.

Usage

dat.ishak2007

Format

The data frame contains the following columns:

Details

Deep-brain stimulation (DBS), which is delivered through thin surgically implanted wires in specific areas of the brain and controlled by the patient, is meant to provide relief of the debilitating symptoms of Parkinson's disease. The dataset includes the results from 46 studies examining the effects of DBS of the subthalamic nucleus on motor functioning, measured with the Unified Parkinson's Disease Rating Scale (UPDRS). The effect size measure for this meta-analysis was the mean difference of the scores while the stimulator is active and the baseline scores (before implantation of the stimulator). Since lower scores on the UPDRS indicate better functioning, negative numbers indicate improvements in motor skills. Effects were generally measured at 3, 6, and 12 months after implantation of the stimulator, with some studies also including a further long-term follow-up. However, the number of measurements differed between studies - hence the missing data on some of the measurement occasions.

Since the same patients were followed over time within a study, effect size estimates from multiple measurement occasions are likely to be correlated. A multivariate model accounting for the correlation in the effects can be used to meta-analyze these data. A difficulty with this approach is the lack of information about the correlation of the measurements over time in the individual studies. The approach taken by Ishak et al. (2007) was to assume an autoregressive (AR1) structure for the estimates within the individual studies. In addition, the correlation in the true effects was modeled, again using an autoregressive structure.

Concepts

medicine, raw mean differences, longitudinal models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Ishak, K. J., Platt, R. W., Joseph, L., Hanley, J. A., & Caro, J. J. (2007). Meta-analysis of longitudinal studies. Clinical Trials, 4(5), 525–539. ⁠https://doi.org/10.1177/1740774507083567⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.ishak2007
head(dat, 5)

## Not run: 
### load metafor package
library(metafor)

### create long format dataset
dat <- reshape(dat, direction="long", idvar="study", v.names=c("yi","vi"),
               varying=list(c(2,4,6,8), c(3,5,7,9)))
dat <- dat[order(study, time),]

### remove missing measurement occasions from dat.long
dat <- dat[!is.na(yi),]
rownames(dat) <- NULL
head(dat, 8)

### construct the full (block diagonal) V matrix with an AR(1) structure
### assuming an autocorrelation of 0.97 as estimated by Ishak et al. (2007)
V <- vcalc(vi, cluster=study, time1=time, phi=0.97, data=dat)

### plot data
with(dat, interaction.plot(time, study, yi, type="b", pch=19, lty="solid", xaxt="n",
          legend=FALSE, xlab="Time Point", ylab="Mean Difference", bty="l"))
axis(side=1, at=1:4, lab=c("1 (3 months)", "2 (6 months)", "3 (12 months)", "4 (12+ months)"))

### multivariate model with heteroscedastic AR(1) structure for the true effects
res <- rma.mv(yi, V, mods = ~ 0 + factor(time), random = ~ time | study,
              struct = "HAR", data = dat)
print(res, digits=2)

## End(Not run)

Studies on the Effectiveness of Coaching for the SAT

Description

Results from studies examining the effectiveness of coaching on the performance on the Scholastic Aptitude Test (SAT).

Usage

dat.kalaian1996

Format

The data frame contains the following columns:

Details

The effectiveness of coaching for the Scholastic Aptitude Test (SAT) has been examined in numerous studies. This dataset contains standardized mean differences comparing the performance of a coached versus uncoached group on the verbal and/or math subtest of the SAT. Studies may report a standardized mean difference for the verbal subtest, the math subtest, or both. In the latter case, the two standardized mean differences are not independent (since they were measured in the same group of subjects). The number of hours of coaching (variable hrs), whether the study was conducted by the Educational Testing Service (variable ets), whether homework was assigned outside of the coaching course (variable homework), and the study type (variable type) may be potential moderators of the treatment effect.

Concepts

education, standardized mean differences, multivariate models, meta-regression

Note

The dataset was obtained from Table 1 in Kalaian and Raudenbush (1996). However, there appear to be some inconsistencies between the data in the table and those that were actually used for the analyses (see ‘Examples’).

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Kalaian, H. A., & Raudenbush, S. W. (1996). A multivariate mixed linear model for meta-analysis. Psychological Methods, 1(3), 227–235. ⁠https://doi.org/10.1037/1082-989X.1.3.227⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.kalaian1996
head(dat, 12)

## Not run: 
### load metafor package
library(metafor)

### check ranges
range(dat$yi[dat$outcome == "verbal"]) # -0.35 to 0.74 according to page 230
range(dat$yi[dat$outcome == "math"])   # -0.53 to 0.60 according to page 231

### comparing this with Figure 1 in the paper reveals some discrepancies
par(mfrow=c(1,2), mar=c(5,5,1,3.4))
plot(log(dat$hrs[dat$outcome == "verbal"]), dat$yi[dat$outcome == "verbal"],
     pch=19, col=rgb(0,0,0,0.4), xlab="Log(Coaching Hours)", ylab="Effect Size (verbal)",
     xlim=c(1,6), ylim=c(-0.5,1), xaxs="i", yaxs="i")
abline(h=c(-0.5,0,0.5), lty="dotted")
abline(v=log(c(5,18)),  lty="dotted")
plot(log(dat$hrs[dat$outcome == "math"]), dat$yi[dat$outcome == "math"],
     pch=19, col=rgb(0,0,0,0.4), xlab="Log(Coaching Hours)", ylab="Effect Size (math)",
     xlim=c(1,6), ylim=c(-1.0,1), xaxs="i", yaxs="i")
abline(h=c(-0.5,0,0.5), lty="dotted")
abline(v=log(c(5,18)),  lty="dotted")

### construct variance-covariance matrix assuming rho = 0.66 for effect sizes
### corresponding to the 'verbal' and 'math' outcome types
V <- vcalc(vi, cluster=study, type=outcome, data=dat, rho=0.66)

### fit multivariate random-effects model
res <- rma.mv(yi, V, mods = ~ 0 + outcome,
              random = ~ outcome | study, struct="UN",
              data=dat, digits=3)
res

### test whether the effect differs for the math and verbal subtest
anova(res, X=c(1,-1))

### log-transform and mean center the hours of coaching variable
dat$loghrs <- log(dat$hrs) - mean(log(dat$hrs), na.rm=TRUE)

### fit multivariate model with log(hrs) as moderator
res <- rma.mv(yi, V, mods = ~ 0 + outcome + outcome:loghrs,
              random = ~ outcome | study, struct="UN",
              data=dat, digits=3)
res

### fit model with tau2 = 0 for outcome verbal (which also constrains rho = 0)
res <- rma.mv(yi, V, mods = ~ 0 + outcome + outcome:loghrs,
              random = ~ outcome | study, struct="UN", tau2=c(NA,0),
              data=dat, digits=3)
res

## End(Not run)

Studies on the Accuracy of Venous Ultrasonography for the Diagnosis of Deep Venous Thrombosis

Description

Results from diagnostic accuracy studies examining the accuracy of venous ultrasonography for the diagnosis of deep venous thrombosis.

Usage

dat.kearon1998

Format

The data frame contains the following columns:

Details

The studies included in the dataset examined the accuracy of venous ultrasonography for the diagnossis of a first deep venous thrombosis in symptomatic and asymptomatic patients. Cases and non-cases were determined based on contrast venography. Venous ultrasonography was then used to make a diagnosis, leading to a given number of true positives and negatives.

A subset of this dataset (using only the studies with asymptomatic patients) was used by Deeks et al. (2005) to illustrate methods for detecting publication bias (or small-study effects) in meta-analyses of diagnostic accuracy studies.

Concepts

medicine, odds ratios, diagnostic accuracy studies, multivariate models, publication bias

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Kearon, C., Julian, J. A., Math, M., Newman, T. E., & Ginsberg, J. S. (1998). Noninvasive diagnosis of deep venous thrombosis. Annals of Internal Medicine, 128(8), 663–677. ⁠https://doi.org/10.7326/0003-4819-128-8-199804150-00011⁠

References

Deeks, J. J., Macaskill, P., & Irwig, L. (2005). The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. Journal of Clinical Epidemiology, 58(9), 882–893. ⁠https://doi.org/10.1016/j.jclinepi.2005.01.016⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.kearon1998
head(dat)

## Not run: 
### load metafor package
library(metafor)

### calculate diagnostic log odds ratios and corresponding sampling variances
dat <- escalc(measure="OR", ai=tp, n1i=np, ci=nn-tn, n2i=nn, data=dat, add=1/2, to="all")
head(dat)

### fit random-effects model for the symptomatic patients
res <- rma(yi, vi, data=dat, subset=patients=="symptomatic")
res

### fit random-effects model for the asymptomatic patients
res <- rma(yi, vi, data=dat, subset=patients=="asymptomatic")
res

### estimated average diagnostic odds ratio (with 95% CI)
predict(res, transf=exp, digits=2)

### regression test for funnel plot asymmetry using SE as predictor
reg <- regtest(res, model="lm")
reg

### corresponding funnel plot
funnel(res, atransf=exp, xlim=c(0,7), at=log(c(1,10,100,1000)), ylim=c(0,1.5), steps=4)
ys <- seq(0, 2, length=100)
lines(coef(reg$fit)[1] + coef(reg$fit)[2]*ys, ys, lwd=2, lty=3)

### regression test for funnel plot asymmetry using total sample size as predictor
reg <- regtest(res, model="lm", predictor="ni")
reg

### corresponding funnel plot
funnel(res, yaxis="ni", atransf=exp, xlim=c(0,7), at=log(c(1,10,100,1000)), ylim=c(0,300), steps=4)
ys <- seq(0, 300, length=100)
lines(coef(reg$fit)[1] + coef(reg$fit)[2]*ys, ys, lwd=2, lty=3)

### regression test for funnel plot asymmetry using 1/sqrt(ESS) as predictor (Deeks et al., 2005)
dat$invessi <- 1/(4*dat$np) + 1/(4*dat$nn)
tmp <- rma(yi, invessi, data=dat, subset=patients=="asymptomatic")
reg <- regtest(tmp, model="lm")
reg

### corresponding funnel plot
funnel(tmp, atransf=exp, xlim=c(0,7), at=log(c(1,10,100,1000)), ylim=c(0,0.15), steps=4,
       refline=coef(res), level=0, ylab="1/root(ess)")
ys <- seq(0, 0.2, length=100)
lines(coef(reg$fit)[1] + coef(reg$fit)[2]*ys, ys, lwd=2, lty=3)

### convert data to long format
dat <- to.long(measure="OR", ai=tp, n1i=np, ci=tn, n2i=nn,
               data=dat.kearon1998, subset=patients=="asymptomatic", append=FALSE)
dat$group <- factor(dat$group, levels=c(1,2), labels=c("sensitivity", "specificity"))
dat

### calculate logit-transformed sensitivities
dat <- escalc(measure="PLO", xi=out1, mi=out2, data=dat, add=1/2, to="all",
              include=group=="sensitivity")
dat

### calculate logit-transformed specificities
dat <- escalc(measure="PLO", xi=out1, mi=out2, data=dat, add=1/2, to="all",
              include=group=="specificity")
dat

### bivariate random-effects model for logit sensitivity and specificity
res <- rma.mv(yi, vi, mods = ~ 0 + group, random = ~ group | study, struct="UN", data=dat)
res

### estimated average sensitivity and specificity based on the model
predict(res, newmods = rbind(c(1,0),c(0,1)), transf=transf.ilogit, tau2.levels=c(1,2), digits=2)

### estimated average diagnostic odds ratio based on the model
predict(res, newmods = c(1,1), transf=exp, digits=2)

## End(Not run)

Studies on Differences in Planning Performance in Schizophrenia Patients versus Healthy Controls

Description

Results from 31 studies examining differences in planning performance in schizophrenia patients versus healthy controls.

Usage

dat.knapp2017

Format

The data frame contains the following columns:

Details

The studies included in this dataset examined differences between schizophrenia patients and healthy controls with respect to their performance on the tower of London test (https://en.wikipedia.org/wiki/Tower_of_London_test) or a similar cognitive tasks measuring planning ability. The outcome measure for this meta-analysis was the standardized mean difference (with positive values indicating better performance in the healthy controls compared to the schizophrenia patients).

The dataset has a more complex structure for several reasons:

1. Studies 2, 3, 9, and 20 included more than one schizophrenia patient group and the standardized mean differences were computed by comparing these groups against a single healthy control group.

2. Studies 6, 12, 14, 15, 18, 19, 22, and 26 had the patients and controls complete different tasks of varying complexity (essentially the average number of moves required to complete a task). Study 6 also included two different task types.

3. Study 24 provides two standardized mean differences, one for men and the other for women.

4. Study 29 provides three standardized mean differences, corresponding to the three different COMT Val158Met genotypes (val/val, val/met, and met/met).

All 4 issues described above lead to a multilevel structure in the dataset, with multiple standardized mean differences nested within some of the studies. Issues 1. and 2. also lead to correlated sampling errors.

Concepts

psychology, standardized mean differences, multilevel models, multivariate models, cluster-robust inference, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Knapp, F., Viechtbauer, W., Leonhart, R., Nitschke, K., & Kaller, C. P. (2017). Planning performance in schizophrenia patients: A meta-analysis of the influence of task difficulty and clinical and sociodemographic variables. Psychological Medicine, 47(11), 2002–2016. ⁠https://doi.org/10.1017/S0033291717000459⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.knapp2017
dat[-c(1:2)]

## Not run: 
### load metafor package
library(metafor)

### fit a standard random-effects model ignoring the issues described above
res <- rma(yi, vi, data=dat)
res

### fit a multilevel model with random effects for studies and comparisons within studies
### (but this ignored the correlation in the sampling errors)
res <- rma.mv(yi, vi, random = ~ 1 | study/comp, data=dat)
res

### create variable that indicates the task and difficulty combination as increasing integers
dat$task.diff <- unlist(lapply(split(dat, dat$study), function(x) {
   task.int <- as.integer(factor(x$task))
   diff.int <- as.integer(factor(x$difficulty))
   diff.int[is.na(diff.int)] <- 1
   paste0(task.int, ".", diff.int)}))

### construct correlation matrix for two tasks with four different difficulties where the
### correlation is 0.4 for different difficulties of the same task, 0.7 for the same
### difficulty of different tasks, and 0.28 for different difficulties of different tasks
R <- matrix(0.4, nrow=8, ncol=8)
R[5:8,1:4] <- R[1:4,5:8] <- 0.28
diag(R[1:4,5:8]) <- 0.7
diag(R[5:8,1:4]) <- 0.7
diag(R) <- 1
rownames(R) <- colnames(R) <- paste0(rep(1:2, each=4), ".", 1:4)
R

### construct an approximate V matrix accounting for the use of shared groups and
### for correlations among tasks/difficulties as specified in the R matrix above
V <- vcalc(vi, cluster=study, grp1=group1, grp2=group2, w1=n_sz, w2=n_hc,
           obs=task.diff, rho=R, data=dat)

### correlation matrix for study 3 with four patient groups and a single control group
round(cov2cor(V[dat$study == 3, dat$study == 3]), 2)

### correlation matrix for study 6 with two tasks with four difficulties
cov2cor(V[dat$study == 6, dat$study == 6])

### correlation matrix for study 24 with two independent groups
cov2cor(V[dat$study == 24, dat$study == 24])

### correlation matrix for study 29 with three independent groups
cov2cor(V[dat$study == 29, dat$study == 29])

### fit multilevel model as above, but now use this V matrix in the model
res <- rma.mv(yi, V, random = ~ 1 | study/comp, data=dat)
res
predict(res, digits=2)

### use cluster-robust inference methods based on this model
robust(res, cluster=study)

### use methods from the clubSandwich package
robust(res, cluster=study, clubSandwich=TRUE)

### examine if task difficulty is a potential moderator of the effect
res <- rma.mv(yi, V, mods = ~ difficulty, random = ~ 1 | study/comp, data=dat)
res
sav <- robust(res, cluster=study)
sav
sav <- robust(res, cluster=study, clubSandwich=TRUE)
sav

### draw bubble plot
regplot(sav, xlab="Task Difficulty", ylab="Standardized Mean Difference", las=1, digits=1, bty="l")

## End(Not run)

Studies on the Effects of Modified School Calendars on Student Achievement

Description

Results from 56 studies on the effects of modified school calendars on student achievement.

Usage

dat.konstantopoulos2011

Format

The data frame contains the following columns:

Details

Instead of following the more traditional school calendar with a long summer break (in addition to a short winter and spring break), some schools have switched to a modified school calendar comprising more frequent but shorter intermittent breaks (e.g., 9 weeks of school followed by 3 weeks off), while keeping the total number of days at school approximately the same. The effects of using such a modified calendar on student achievement have been examined in a number of studies and were meta-analyzed by Cooper et al. (2003).

The dataset (taken from Konstantopoulos, 2011) contains the results from 56 studies, each comparing the level of academic achievement in a group of students following a modified school calendar with that of a group of students following a more traditional school calendar. The difference between the two groups was quantified in terms of a standardized mean difference (with positive values indicating a higher mean level of achievement in the group following the modified school calendar).

The studies were conducted at various schools that were clustered within districts. The data therefore have a multilevel structure, with schools nested within districts. A multilevel meta-analysis of these data can be used to estimate and account for the amount of heterogeneity between districts and between schools within districts.

Concepts

education, standardized mean differences, multilevel models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Konstantopoulos, S. (2011). Fixed effects and variance components estimation in three-level meta-analysis. Research Synthesis Methods, 2(1), 61–76. ⁠https://doi.org/10.1002/jrsm.35⁠

References

Cooper, H., Valentine, J. C., Charlton, K., & Melson, A. (2003). The effects of modified school calendars on student achievement and on school and community attitudes. Review of Educational Research, 73(1), 1–52. ⁠https://doi.org/10.3102/00346543073001001⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.konstantopoulos2011
dat

## Not run: 
### load metafor package
library(metafor)

### fit random-effects model
res <- rma(yi, vi, data=dat)
print(res, digits=3)

### fit random-effects model using rma.mv()
res <- rma.mv(yi, vi, random = ~ 1 | study, data=dat)
print(res, digits=3)

### fit multilevel random-effects model
res.ml <- rma.mv(yi, vi, random = ~ 1 | district/school, data=dat)
print(res.ml, digits=3)

### profile variance components
profile(res.ml, progbar=FALSE)

### fit multivariate parameterization of the model
res.mv <- rma.mv(yi, vi, random = ~ school | district, data=dat)
print(res.mv, digits=3)

### tau^2 = sum of the two variance components from the multilevel model
round(sum(res.ml$sigma2), digits=3)

### rho = intraclass correlation coefficient based on the multilevel model
round(res.ml$sigma2[1] / sum(res.ml$sigma2), digits=3)

## End(Not run)

Studies on the Effectiveness of CBT for Reducing Recidivism

Description

Results from 58 studies on the effectiveness of cognitive-behavioral therapy (CBT) for reducing recidivism in juvenile and adult offenders.

Usage

dat.landenberger2005

Format

The data frame contains the following columns:

Details

Landenberger and Lipsey (2005) conducted a meta-analysis of 58 experimental and quasi-experimental studies of the effects of cognitive-behavioral therapy (CBT) on the recidivism rates of adult and juvenile offenders (see also Lipsey et al., 2007). The present dataset includes the results of these studies and a range of potential moderator variables to identify factors associated with variation in treatment effects.

Concepts

psychology, criminology, odds ratios, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Personal communication.

References

Landenberger, N. A., & Lipsey, M. W. (2005). The positive effects of cognitive-behavioral programs for offenders: A meta-analysis of factors associated with effective treatment. Journal of Experimental Criminology, 1, 451–476. ⁠https://doi.org/10.1007/s11292-005-3541-7⁠

Lipsey, M. W., Landenberger, N. A., & Wilson, S. J. (2007). Effects of cognitive-behavioral programs for criminal offenders. Campbell Systematic Reviews, 3(1), 1–27. ⁠https://doi.org/10.4073/csr.2007.6⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.landenberger2005
head(dat)

## Not run: 
### load metafor package
library(metafor)

### calculate log odds ratios (for non-recidivism in CBT vs. control groups) and sampling variances
dat <- escalc(measure="OR", ai=n.cbt.non, bi=n.cbt.rec, ci=n.ctrl.non, di=n.ctrl.rec, data=dat)

### fit random-effects model
res <- rma(yi, vi, data=dat)
res

### estimated average OR and corresponding 95% CI/PI
predict(res, transf=exp, digits=2)

### examine if number of treatment sessions per week is a potential moderator
res <- rma(yi, vi, mods = ~ sessions, data=dat)
res

### predicted ORs for 1, 2, 5, or 10 sessions per week
predict(res, newmods=c(1,2,5,10), transf=exp, digits=2)

## End(Not run)

Studies on the Effectiveness of Azithromycin for Treating Lower Respiratory Tract Infections

Description

Results from 15 studies on the effectiveness of azithromycin versus amoxycillin or amoxycillin/clavulanic acid (amoxyclav) in the treatment of acute lower respiratory tract infections.

Usage

dat.laopaiboon2015

Format

The data frame contains the following columns:

Details

Azithromycin is an antibiotic useful for the treatment of a number of bacterial infections. Laopaiboon et al. (2015) conducted a meta-analysis of trials comparing the effectiveness of azithromycin versus amoxycillin or amoxycillin/clavulanic acid (amoxyclav) in the treatment of acute lower respiratory tract infections, including acute bacterial bronchitis, acute exacerbations of chronic bronchitis, and pneumonia. The results from 15 trials are included in this dataset.

Concepts

medicine, risk ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Laopaiboon, M., Panpanich, R., & Swa Mya, K. (2015). Azithromycin for acute lower respiratory tract infections. Cochrane Database of Systematic Reviews, 3, CD001954. ⁠https://doi.org/10.1002/14651858.CD001954.pub4⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.laopaiboon2015
dat

## Not run: 
### load metafor package
library(metafor)

### analysis using the Mantel-Haenszel method
rma.mh(measure="RR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, digits=3)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat)

### random-effects model
res <- rma(yi, vi, data=dat)
res

### average risk ratio with 95% CI
predict(res, transf=exp)

## End(Not run)

Studies on Intravenous Streptokinase for Acute Myocardial Infarction

Description

Results from 33 trials comparing intravenous streptokinase versus placebo or no therapy in patients who had been hospitalized for acute myocardial infarction.

Usage

dat.lau1992

Format

The data frame contains the following columns:

Details

In the paper by Lau et al. (1992), the data are used to illustrate the idea of a cumulative meta-analysis, where the results are updated as each trial is added to the dataset. See ‘Examples’ for code that replicates the results and shows corresponding forest plots.

Concepts

medicine, cardiology, odds ratios, cumulative meta-analysis

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Lau, J., Antman, E. M., Jimenez-Silva, J., Kupelnick, B., Mosteller, F., & Chalmers, T. C. (1992). Cumulative meta-analysis of therapeutic trials for myocardial infarction. New England Journal of Medicine, 327(4), 248–254. ⁠https://doi.org/10.1056/NEJM199207233270406⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.lau1992
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of log odds ratios using the MH method
res <- rma.mh(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, slab=trial)
print(res, digits=2)

### forest plot
forest(res, xlim=c(-11,9), atransf=exp, at=log(c(0.01, 0.1, 1, 10, 100)),
       ilab=dat$year, ilab.xpos=-7)
text(-7, 35, "Year", font=2)

### cumulative meta-analysis
sav <- cumul(res)

### forest plot of the cumulative results
forest(sav, xlim=c(-5,4), atransf=exp, at=log(c(0.1, 0.5, 1, 2, 10)),
       ilab=dat$year, ilab.xpos=-3)
text(-3, 35, "Year", font=2)
id <- c(4, 8, 15, 33) # rows for which the z/p-values should be shown (as in Lau et al., 1992)
text(1.1, (res$k:1)[id], paste0("z = ", fmtx(sav$zval[id], digits=2),
                                fmtp(sav$pval[id], pname=", p", equal=TRUE, sep=TRUE, add0=TRUE)))

## End(Not run)

Studies on Acupoint P6 Stimulation for Preventing Nausea

Description

Results from studies examining the effectiveness of wrist acupuncture point P6 stimulation for preventing postoperative nausea.

Usage

dat.lee2004

Format

The data frame contains the following columns:

Details

Postoperative nausea and vomiting are common complications following surgery and anaesthesia. As an alternative to drug therapy, acupuncture has been studied as a potential treatment in several trials. The dataset contains the results from 16 clinical trials examining the effectiveness of wrist acupuncture point P6 stimulation for preventing postoperative nausea.

Concepts

medicine, alternative medicine, risk ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Lee, A., & Done, M. L. (2004). Stimulation of the wrist acupuncture point P6 for preventing postoperative nausea and vomiting. Cochrane Database of Systematic Reviews, 3, CD003281. ⁠https://doi.org/10.1002/14651858.CD003281.pub2⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.lee2004
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis based on log risk ratios
res <- rma(measure="RR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat)
res
predict(res, transf=exp, digits=2)

## End(Not run)

The Effect of Red on Perceived Attractiveness

Description

Results from studies in which participants rated the attractiveness of photos that featured red or a control color. See OSF project at ⁠https://osf.io/xy47p/⁠.

Usage

dat.lehmann2018

Format

The data frame contains the following columns:

Details

This is data from a meta-analysis of studies that test the red-romance hypothesis, which is that the color red enhances heterosexual attraction in romantic contexts. Analyzing male participants only, the meta-analysis should show a small, statistically significant effect (d = 0.26 [0.12, 0.40], p = .0004, N = 2,961). Analyzing female participants only should show a very small effect (d = 0.13 [0.01, 0.25], p = .03, N = 2,739). The analyses in the published meta-analysis found clear evidence of upward bias in the estimate for female participants and equivocal evidence for male participants. Moderator analyses suggest effect sizes may have declined over time (both genders), may be largest when an original shade of red is used (men only), and may be smaller in pre-registered studies (women only).

Concepts

psychology, attraction, standardized mean differences

Author(s)

Robert Calin-Jageman, rcalinjageman@dom.edu, https://calin-jageman.net

Source

Lehmann, G. K., Elliot, A. J., & Calin-Jageman, R. J. (2018). Meta-analysis of the effect of red on perceived attractiveness. Evolutionary Psychology, 16(4). ⁠https://doi.org/10.1177/1474704918802412⁠ ⁠https://osf.io/xy47p/⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.lehmann2018
head(dat)

## Not run: 
### load metafor package
library(metafor)

### meta-analyses for male and female participants
red_romance_malep   <- dat[dat$Gender == "Males", ]
red_romance_femalep <- dat[dat$Gender == "Females", ]

res_malep <- rma(yi, vi, data=red_romance_malep, test="knha")
res_malep
res_femalep <- rma(yi, vi, data=red_romance_femalep, test="knha")
res_femalep

## End(Not run)

Studies on the Effectiveness of Intravenous Magnesium in Acute Myocardial Infarction

Description

Results from 22 trials examining the effectiveness of intravenous magnesium in the prevention of death following acute myocardial infarction.

Usage

dat.li2007

Format

The data frame contains the following columns:

Details

The dataset includes the results from 22 randomized clinical trials that examined the effectiveness of intravenous magnesium in the prevention of death following acute myocardial infarction. It is similar to the dataset dat.egger2001, with some slight differences in the included trials and data used.

Concepts

medicine, cardiology, odds ratios, publication bias

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Li, J., Zhang, Q., Zhang, M., & Egger, M. (2007). Intravenous magnesium for acute myocardial infarction. Cochrane Database of Systematic Reviews, 2, CD002755. ⁠https://doi.org/10.1002/14651858.CD002755.pub2⁠

See Also

dat.egger2001

Examples

### copy data into 'dat' and examine data
dat <- dat.li2007
dat

## Not run: 
### load metafor package
library(metafor)

### meta-analysis of all trials except ISIS-4
res <- rma(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, method="EE", subset=-14)
print(res, digits=2)
predict(res, transf=exp, digits=2)

### meta-analysis of all trials including ISIS-4
res <- rma(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, method="EE")
print(res, digits=2)
predict(res, transf=exp, digits=2)

### contour-enhanced funnel plot centered at 0
funnel(res, refline=0, level=c(90, 95, 99), shade=c("white", "gray", "darkgray"))

## End(Not run)

Studies on the Association Between Maternal Size, Offspring Size, and Number of Offsprings

Description

Results from studies examining the association between maternal size, offspring size, and number of offsprings.

Usage

dat.lim2014

Format

The object is a list containing data frames m_o_size, m_o_fecundity, o_o_unadj, and o_o_adj that contain the following columns and the corresponding phylogenetic trees called m_o_size_tree, m_o_fecundity_tree, o_o_unadj_tree, and o_o_adj_tree:

Details

The object dat.lim2014 includes 4 datasets:

Objects m_o_size_tree, m_o_fecundity_tree, o_o_unadj_tree, and o_o_adj_tree are the corresponding phylogenetic trees for the species included in each of these datasets.

Concepts

ecology, evolution, correlation coefficients, multilevel models, phylogeny

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Lim, J. N., Senior, A. M., & Nakagawa, S. (2014). Heterogeneity in individual quality and reproductive trade-offs within species. Evolution, 68(8), 2306–2318. ⁠https://doi.org/10.1111/evo.12446⁠

References

Cinar, O., Nakagawa, S., & Viechtbauer, W. (in press). Phylogenetic multilevel meta-analysis: A simulation study on the importance of modelling the phylogeny. Methods in Ecology and Evolution. ⁠https://doi.org/10.1111/2041-210X.13760⁠

Hadfield, J. D., & Nakagawa, S. (2010). General quantitative genetic methods for comparative biology: Phylogenies, taxonomies and multi-trait models for continuous and categorical characters. Journal of Evolutionary Biology, 23(3), 494–508. ⁠https://doi.org/10.1111/j.1420-9101.2009.01915.x⁠

Nakagawa, S., & Santos, E. S. A. (2012). Methodological issues and advances in biological meta-analysis. Evolutionary Ecology, 26(5), 1253–1274. ⁠https://doi.org/10.1007/s10682-012-9555-5⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.lim2014$o_o_unadj
dat[1:14, -c(2:3)]

## Not run: 
### load metafor package
library(metafor)

### load ape package
library(ape, warn.conflicts=FALSE)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)

### copy tree to 'tree'
tree <- dat.lim2014$o_o_unadj_tree

### compute branch lengths
tree <- compute.brlen(tree)

### compute phylogenetic correlation matrix
A <- vcv(tree, corr=TRUE)

### make copy of the species variable
dat$species.phy <- dat$species

### create effect size id variable
dat$esid <- 1:nrow(dat)

### fit multilevel phylogenetic meta-analytic model
res <- rma.mv(yi, vi,
   random = list(~ 1 | article, ~ 1 | esid, ~ 1 | species, ~ 1 | species.phy),
   R=list(species.phy=A), data=dat)
res

## End(Not run)

Studies on the Effectiveness of St. John's Wort for Treating Depression

Description

Results from 26 studies on the effectiveness of Hypericum perforatum extracts (St. John's wort) for treating depression.

Usage

dat.linde2005

Format

The data frame contains the following columns:

Details

The dataset includes the results from 26 double-blind placebo-controlled trials on the effectiveness of Hypericum perforatum extracts (St. John's wort) for treating depression (note that 2 studies did not provide sufficient response information).

Data were extracted from Table 1 and Figure 3 from Linde et al. (2005). For study duration, the assessment week (instead of the total study duration) was coded for Philipp et al. (1999) and Montgomery et al. (2000). For dosage, the midpoint was coded when a range of values was given.

The definition of what constitutes a response differed across studies and is coded as follows:

1. HRSD score reduction of at least 50% or HRSD score after therapy <10,

2. HRSD reduction of at least 50%,

3. based on HRSD scale but exact definition not reported,

4. global patient assessment of efficacy,

5. at least ‘much improved’ on the Clinical Global Impression sub-scale for global improvement.

The group variable corresponds to the variable used by Linde et al. (2005) to stratify their analyses and is coded as follows:

1. smaller trials restricted to major depression,

2. larger trials restricted to major depression,

3. smaller trials not restricted to major depression,

4. larger trials not restricted to major depression.

Concepts

medicine, psychiatry, risk ratios

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Linde, K., Berner, M., Egger, M., & Mulrow, C. (2005). St John's wort for depression: Meta-analysis of randomised controlled trials. British Journal of Psychiatry, 186(2), 99–107. ⁠https://doi.org/10.1192/bjp.186.2.99⁠

References

Viechtbauer, W. (2007). Accounting for heterogeneity via random-effects models and moderator analyses in meta-analysis. Zeitschrift für Psychologie / Journal of Psychology, 215(2), 104–121. ⁠https://doi.org/10.1027/0044-3409.215.2.104⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.linde2005
head(dat)

## Not run: 
### load metafor package
library(metafor)

### remove studies with no response information and study with no responses in either group
dat <- dat[-c(5,6,26),]

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=ai, ci=ci, n1i=n1i, n2i=n2i, data=dat)
head(dat)

### meta-analysis of the log risk ratios using a random-effects model
res <- rma(yi, vi, data=dat, method="DL")
res

### mixed-effects meta-regression model with stratification variable
res <- rma(yi, vi, mods = ~ 0 + factor(group), data=dat, method="DL")
res

### predicted average risk ratio for each level of the stratification variable
predict(res, newmods=diag(4), transf=exp, digits=2)

## End(Not run)

Studies on Classes of Antidepressants for the Primary Care Setting

Description

Results from 66 trials examining eight classes of antidepressants and placebo for the primary care setting.

Usage

dat.linde2015

Format

The data frame contains the following columns:

Details

This dataset comes from a systematic review of 8 pharmacological treatments of depression and placebo in primary care with 66 studies (8 of which were 3-arm studies) including 14,785 patients.

The primary outcome is early response, defined as at least a 50% score reduction on a depression scale after completion of treatment. Secondary outcomes (also measured as dichotomous) were early remission (defined as having a symptom score below a fixed threshold after completion of treatment), lost to follow-up, lost to follow-up due to adverse events, and any adverse event. The odds ratio was used as effect measure.

This dataset was used as an example in Rücker and Schwarzer (2017) who introduced methods to resolve conflicting rankings of outcomes in network meta-analysis.

Concepts

medicine, psychiatry, odds ratios, network meta-analysis

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Linde, K., Kriston, L., Rücker, G., Jamil, S., Schumann, I., Meissner, K., Sigterman, K., & Schneider, A. (2015). Efficacy and acceptability of pharmacological treatments for depressive disorders in primary care: Systematic review and network meta-analysis. Annals of Family Medicine, 13(1), 69–79. ⁠https://doi.org/10.1370/afm.1687⁠

References

Rücker, G., & Schwarzer, G. (2017). Resolve conflicting rankings of outcomes in network meta-analysis: Partial ordering of treatments. Research Synthesis Methods, 8(4), 526–536. ⁠https://doi.org/10.1002/jrsm.1270⁠

Examples

### Show results from first three studies (including three-arm study
### Lecrubier 1997)
head(dat.linde2015, 3)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Change appearance of confidence intervals
cilayout("(", "-")

### Define order of treatments in printouts
trts <- c("TCA", "SSRI", "SNRI", "NRI", "Low-dose SARI",
 "NaSSa", "rMAO-A", "Hypericum", "Placebo")

### Transform data from wide arm-based format to contrast-based format
### (outcome: early response). Argument 'sm' has to be used for odds
### ratio as summary measure; by default the risk ratio is used in the
### metabin function called internally.
pw1 <- pairwise(list(treatment1, treatment2, treatment3),
  event = list(resp1, resp2, resp3),
  n = list(n1, n2, n3),
  studlab = id, data = dat.linde2015, sm = "OR")

### Conduct random effects network meta-analysis for primary outcome
### (early response); small number of early responses is bad (argument
### small.values)
net1 <- netmeta(pw1, fixed = FALSE, reference = "Placebo", seq = trts,
  small.values = "bad")
net1

### Random effects NMA for early remission
pw2 <- pairwise(treat = list(treatment1, treatment2, treatment3),
  event = list(remi1, remi2, remi3),
  n = list(n1, n2, n3),
  studlab = id, data = dat.linde2015, sm = "OR")
net2 <- netmeta(pw2, fixed = FALSE,
   seq = trts, ref = "Placebo", small.values = "bad")
net2

### Ranking of treatments
nr1 <- netrank(net1)
nr2 <- netrank(net2)
nr1
nr2

### Partial order of treatment rankings (two outcomes)
outcomes <- c("Early response", "Early remission")
po12 <- netposet(nr1, nr2, outcomes = outcomes)
plot(po12)

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on Antidepressants for the Primary Care Setting

Description

Results from 93 trials examining 22 interventions (including placebo and usual care) for the primary care of depression.

Usage

dat.linde2016

Format

The data frame contains the following columns:

Details

This dataset comes from a network meta-analysis of 22 treatments of depression in primary care (Linde et al., 2016), based on 93 trials (79 two-arm trials, 13 three-arm trials, and one four-arm trial). The primary outcome was response after treatment (yes/no), defined as a reduction from baseline by at least 50% on a depression scale. The dataset contains log odds ratios with standard errors for all pairwise comparisons.

The interventions comprised both medical and psychological treatments, also in combination, including placebo and usual care (UC) (Linde et al., 2016). Pharmacological interventions were tricyclic antidepressants (TCA), selective serotonin reuptake inhibitors (SSRI), serotonin-noradrenaline reuptake inhibitors (SNRI), noradrenaline reuptake inhibitors (NRI), low- dose serotonin (5-HT2) antagonists and reuptake inhibitors (low-dose SARI), noradrenergic and specific serotonergic agents (NaSSa), reversible inhibitors of monoaminoxidase A (rMAO-A), hypericum extracts, and an individualized drug. Psychological interventions were cognitive behavioral therapy (CBT; four forms: face-to-face CBT, remote therapist-led CBT, guided self-help CBT, and no or minimal contact CBT), face-to-face problem-solving therapy (PST), face-to-face interpersonal psychotherapy, face-to-face psychodynamic therapy, and “other face-to-face therapy”. Combination therapies were face-to-face CBT + SSRI, face-to-face PST + SSRI, and face-to-face interpersonal psychotherapy + SSRI.

The dataset was used as an example in Rücker et al. (2020) to illustrate component network meta-analysis using frequentist methods.

Concepts

medicine, psychiatry, odds ratios, network meta-analysis, component network meta-analysis

Author(s)

Guido Schwarzer, guido.schwarzer@uniklinik-freiburg.de, https://github.com/guido-s/

Source

Linde, K., Rücker, G., Schneider, A., & Kriston, L. (2016). Questionable assumptions hampered interpretation of a network meta-analysis of primary care depression treatments. Journal of Clinical Epidemiology, 71, 86–96. ⁠https://doi.org/10.1016/j.jclinepi.2015.10.010⁠

References

Rücker, G., Petropoulou, M., & Schwarzer, G. (2020). Network meta-analysis of multicomponent interventions. Biometrical Journal, 62(3), 808–821. ⁠https://doi.org/10.1002/bimj.201800167⁠

Examples

### Show results of first three studies (first study has three treatment
### arms)
head(dat.linde2016, 5)

## Not run: 
### Load netmeta package
suppressPackageStartupMessages(library("netmeta"))

### Print odds ratios and confidence limits with two digits
oldset <- settings.meta(digits = 2)

### Define order of treatments in printouts and forest plots
trts <- c("SSRI",
  "Face-to-face CBT", "Face-to-face interpsy", "Face-to-face PST",
  "Face-to-face CBT + SSRI", "Face-to-face interpsy + SSRI",
  "Face-to-face PST + SSRI",
  "Face-to-face psychodyn", "Other face-to-face",
  "TCA", "SNRI", "NRI", "Low-dose SARI", "NaSSa", "rMAO-A", "Ind drug",
  "Hypericum",
  "Remote CBT", "Self-help CBT", "No contact CBT",
  "UC", "Placebo")

### Conduct random effects network meta-analysis
net <- netmeta(lnOR, selnOR, treat1, treat2, id,
  data = dat.linde2016, reference.group = "placebo",
  seq = trts, sm = "OR", fixed = FALSE)

### Network graph
netgraph(net, seq = "o", number = TRUE)

### Show results
net
forest(net, xlim = c(0.2, 50))

### Additive component network meta-analysis with placebo as inactive
### treatment
nc <- netcomb(net, inactive = "placebo")
nc
forest(nc, xlim = c(0.2, 50))

### Use previous settings
settings.meta(oldset)

## End(Not run)

Studies on the Effectiveness of CBT for Depression

Description

Results from 76 studies examining the effectiveness of cognitive behavioral therapy (CBT) for depression in adults.

Usage

dat.lopez2019

Format

The data frame contains the following columns:

Details

The dataset includes the results from 76 studies examining the effectiveness of cognitive behavioral therapy (CBT) for treating depression in adults. Studies included two or more of the following treatments/conditions:

1. treatment as usual (TAU),

2. no treatment,

3. wait list,

4. psychological or attention placebo,

5. face-to-face CBT,

6. multimedia CBT,

7. hybrid CBT (i.e., multimedia CBT with one or more face-to-face sessions).

Multimedia CBT was defined as CBT delivered via self-help books, audio/video recordings, telephone, computer programs, apps, e-mail, or text messages.

Variable diff is the standardized mean change within each group, with negative values indicating a decrease in depression symptoms.

Concepts

psychiatry, standardized mean changes, network meta-analysis

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Personal communication.

References

López-López, J. A., Davies, S. R., Caldwell, D. M., Churchill, R., Peters, T. J., Tallon, D., Dawson, S., Wu, Q., Li, J., Taylor, A., Lewis, G., Kessler, D. S., Wiles, N., & Welton, N. J. (2019). The process and delivery of CBT for depression in adults: A systematic review and network meta-analysis. Psychological Medicine, 49(12), 1937–1947. ⁠https://doi.org/10.1017/S003329171900120X⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.lopez2019
dat[1:10,1:6]

## Not run: 
### load metafor package
library(metafor)

### create network graph ('igraph' package must be installed)
library(igraph, warn.conflicts=FALSE)
pairs <- data.frame(do.call(rbind,
   sapply(split(dat$treatment, dat$study), function(x) t(combn(x,2)))), stringsAsFactors=FALSE)
pairs$X1 <- factor(pairs$X1, levels=sort(unique(dat$treatment)))
pairs$X2 <- factor(pairs$X2, levels=sort(unique(dat$treatment)))
tab <- table(pairs[,1], pairs[,2])
tab # adjacency matrix
g <- graph_from_adjacency_matrix(tab, mode = "plus", weighted=TRUE, diag=FALSE)
plot(g, edge.curved=FALSE, edge.width=E(g)$weight/2,
     layout=layout_in_circle(g, order=c("Wait list", "No treatment", "TAU", "Multimedia CBT",
                                        "Hybrid CBT", "F2F CBT", "Placebo")),
     vertex.size=45, vertex.color="lightgray", vertex.label.color="black", vertex.label.font=2)

### restructure data into wide format
dat <- to.wide(dat, study="study", grp="treatment", ref="TAU",
               grpvars=c("diff","se","n"), postfix=c("1","2"))

### compute contrasts between treatment pairs and corresponding sampling variances
dat$yi <- with(dat, diff1 - diff2)
dat$vi <- with(dat, se1^2 + se2^2)

### calculate the variance-covariance matrix for multitreatment studies
calc.v <- function(x) {
   v <- matrix(x$se2[1]^2, nrow=nrow(x), ncol=nrow(x))
   diag(v) <- x$vi
   v
}
V <- bldiag(lapply(split(dat, dat$study), calc.v))

### add contrast matrix to the dataset
dat <- contrmat(dat, grp1="treatment1", grp2="treatment2")

### network meta-analysis using a contrast-based random-effects model
### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons
### the treatment left out (TAU) becomes the reference level for the treatment comparisons
res <- rma.mv(yi, V, data=dat,
         mods = ~ 0 + No.treatment + Wait.list + Placebo + F2F.CBT + Hybrid.CBT + Multimedia.CBT,
         random = ~ comp | study, rho=1/2)
res

### forest plot of the contrast estimates (treatments versus TAU)
forest(coef(res), diag(vcov(res)), slab=sub(".", " ", names(coef(res)), fixed=TRUE),
       xlim=c(-5,5), alim=c(-3,3), psize=1, header="Treatment",
       xlab="Difference in Standardized Mean Change (compared to TAU)")

### fit random inconsistency effects model (might have to switch optimizer to get convergence)
res <- rma.mv(yi, V, data=dat,
         mods = ~ 0 + No.treatment + Wait.list + Placebo + F2F.CBT + Hybrid.CBT + Multimedia.CBT,
         random = list(~ comp | study, ~ comp | design), rho=1/2, phi=1/2,
         control=list(optimizer="BFGS"))
res

## End(Not run)

Studies on Temporal Trends in Fish Community Structures in French Rivers

Description

Results from studies examining changes in the abundance of fish species in French rivers.

Usage

dat.maire2019

Format

The object is a list containing a data frame called dat that contains the following columns and distance matrix called dmat:

Details

The dataset includes the results from 35 sampling stations (at 11 sites along various French rivers) examining the abundance of various fish species over time (i.e., over 19-37 years, all until 2015). The temporal trend in these abundance data was quantified in terms of Mann-Kendal trend statistics, with positive values indicating monotonically increasing trends. The corresponding sampling variances were corrected for the temporal autocorrelation in the data (Hamed & Rao, 1998).

The distance matrix dmat indicates the distance of the sampling stations (1-423 river-km). For stations not connected through the river network, a high distance value of 10,000 river-km was set (effectively forcing the spatial correlation to be 0 for such stations).

The dataset can be used to illustrate a meta-analysis allowing for spatial correlation in the outcomes.

Concepts

ecology, climate change, spatial correlation

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Maire, A., Thierry, E., Viechtbauer, W., & Daufresne, M. (2019). Poleward shift in large-river fish communities detected with a novel meta-analysis framework. Freshwater Biology, 64(6), 1143–1156. ⁠https://doi.org/10.1111/fwb.13291⁠

References

Hamed, K. H., & Rao, A. R. (1998). A modified Mann-Kendall trend test for autocorrelated data. Journal of Hydrology, 204(1-4), 182–196. ⁠https://doi.org/10.1016/S0022-1694(97)00125-X⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.maire2019$dat
dat[-10]

### copy distance matrix into 'dmat' and examine first 5 rows/columns
dmat <- dat.maire2019$dmat
dmat[1:5,1:5]

## Not run: 
### load metafor package
library(metafor)

### fit a standard random-effects model ignoring spatial correlation
res1 <- rma.mv(s1, vars1, random = ~ 1 | site_station, data=dat)
res1

### fit model allowing for spatial correlation
res2 <- rma.mv(s1, vars1, random = ~ site_station | const, struct="SPGAU",
               data=dat, dist=list(dmat), control=list(rho.init=10))
res2

### add random effects for sites and stations within sites
res3 <- rma.mv(s1, vars1, random = list(~ 1 | site/station, ~ site_station | const), struct="SPGAU",
               data=dat, dist=list(dmat), control=list(rho.init=10))
res3

### likelihood ratio tests comparing the models
anova(res1, res2)
anova(res2, res3)

### profile likelihood plots for model res2
profile(res2, cline=TRUE)

### effective range (river-km for which the spatial correlation is >= 0.05)
sqrt(3) * res2$rho

### note: it was necessary to adjust the starting value for rho in models
### res2 and res3 so that the optimizer does not get stuck in a local maximum
profile(res2, rho=1, xlim=c(0,200), steps=100)

## End(Not run)

Studies on the Generation Effect

Description

Results from 126 articles that examined the so-called ‘generation effect’.

Usage

dat.mccurdy2020

Format

The data frame contains the following columns:

Details

The generation effect is the memory benefit for self-generated compared with read or experimenter-provided information (Jacoby, 1978; Slamecka & Graf, 1978). In a typical study, participants are presented with a list of stimuli (usually words or word pairs). For half of the stimuli, participants self-generate a target word (e.g., open–cl____), while for the other half, participants simply read an intact target word (e.g., above–below). On a later memory test for the target words, the common finding is that self-generated words are better remembered than read words (i.e., the generation effect).

Although several theories have been proposed to explain the generation effect, there is still some debate on the underlying memory mechanism(s) contributing to this phenomenon. The meta-analysis by McCurdy et al. (2020) translated various theories on the generation effect into hypotheses that could then be tested in moderator analyses based on a dataset containing 126 articles, 310 experiments, and 1653 mean recall estimates collected under various conditions.

Detailed explanations of the various variables coded (and how these can be used to test various hypotheses regarding the generation effect) can be found in the article. The most important variable is condition, which denotes whether a particular row of the dataset corresponds to the results of a ‘read’ or a ‘generate’ condition.

The data structure is quite complex. Articles may have reported the findings from multiple experiments involving one or multiple samples that were examined under various conditions. The pairing variable indicates which rows of the dataset represent a pairing of a read condition with one or multiple corresponding generate conditions within an experiment. A pairing may involve the same sample of subjects (when using a within-subjects design for comparing the conditions) or different samples (when using a between-subjects design).

Concepts

psychology, memory, proportions, raw means, multilevel models, cluster-robust inference

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

McCurdy, M. P., Viechtbauer, W., Sklenar, A. M., Frankenstein, A. N., & Leshikar, E. D. (2020). Theories of the generation effect and the impact of generation constraint: A meta-analytic review. Psychonomic Bulletin & Review, 27(6), 1139–1165. ⁠https://doi.org/10.3758/s13423-020-01762-3⁠

References

Slamecka, N. J., & Graf, P. (1978). The generation effect: Delineation of a phenomenon. Journal of Experimental Psychology: Human Learning and Memory, 4(6), 592–604. ⁠https://doi.org/10.1037/0278-7393.4.6.592⁠

Jacoby, L. L. (1978). On interpreting the effects of repetition: Solving a problem versus remembering a solution. Journal of Verbal Learning and Verbal Behavior, 17(6), 649–668. ⁠https://doi.org/10.1016/S0022-5371(78)90393-6⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.mccurdy2020
head(dat)

## Not run: 
### load metafor package
library(metafor)

### fit multilevel mixed-effects meta-regression model
res <- rma.mv(yi, vi, mods = ~ condition,
              random = list(~ 1 | article/experiment/sample/id, ~ 1 | pairing),
              data=dat, sparse=TRUE, digits=3)
res

### proportion of total amount of heterogeneity due to each component
data.frame(source=res$s.names, sigma2=round(res$sigma2, 3),
   prop=round(res$sigma2 / sum(res$sigma2), 2))

### apply cluster-robust inference methods
sav <- robust(res, cluster=article, clubSandwich=TRUE)
sav

### estimated average recall rate in read and generate conditions
predict(sav, newmods = c(0,1), digits=3)

## End(Not run)

Studies on the Validity of Employment Interviews

Description

Results from 160 studies on the correlation between employment interview assessments and job performance.

Usage

dat.mcdaniel1994

Format

The data frame contains the following columns:

Details

The 160 studies provide data in terms of the correlation between employment interview performance and actual job performance. In addition, the interview type and the interview structure are indicated.

McDaniel et al. (1994) describe the interview type and structure variables as follows. "Questions in situational interviews [...] focus on the individual's ability to project what his or her behavior would be in a given situation. [...] Job-related interviews are those in which the interviewer is a personnel officer or hiring authority and the questions attempt to assess past behaviors and job-related information, but most questions are not considered situational. Psychological interviews are conducted by a psychologist, and the questions are intended to assess personal traits, such as dependability." In structured interviews, "the questions and acceptable responses were specified in advance and the responses were rated for appropriateness of content. [...] Unstructured interviews gather applicant information in a less systematic manner than do structured interviews. Although the questions may be specified in advance, they usually are not, and there is seldom a formalized scoring guide. Also, all persons being interviewed are not typically asked the same questions."

The goal of the meta-analysis was to examine the overall criterion-related validity of employment interviews and to examine whether the validity depends on the type and structure of the interview.

The data in this dataset were obtained from Table A.2 in Rothstein, Sutton, and Borenstein (2005, p. 325-329). Note that the type and struct variables contain some NAs.

Concepts

psychology, correlation coefficients, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Rothstein, H. R., Sutton, A. J., & Borenstein, M. (Eds.). (2005). Publication bias in meta-analysis: Prevention, assessment, and adjustments. Chichester, England: Wiley.

References

McDaniel, M. A., Whetzel, D. L., Schmidt, F. L., & Maurer, S. D. (1994). The validity of employment interviews: A comprehensive review and meta-analysis. Journal of Applied Psychology, 79(4), 599–616. ⁠https://doi.org/10.1037/0021-9010.79.4.599⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.mcdaniel1994
head(dat)

## Not run: 
### load metafor package
library(metafor)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)
head(dat)

### meta-analysis of the transformed correlations using a random-effects model
res <- rma(yi, vi, data=dat)
res

### average correlation with 95% CI
predict(res, transf=transf.ztor, digits=2)

### mixed-effects model with interview type as factor
### note: job-related interviews is the reference level
res <- rma(yi, vi, mods = ~ factor(type), data=dat)
res

### estimated average correlation for each level of interview type
res <- rma(yi, vi, mods = ~ 0 + factor(type), data=dat)
predict(res, newmods=diag(3), transf=transf.ztor, digits=2)

### mixed-effects model with interview structure as factor
### note: structured interviews is the reference level
res <- rma(yi, vi, mods = ~ factor(struct), data=dat)
res

### estimated average correlation for each level of interview structure
res <- rma(yi, vi, mods = ~ 0 + factor(struct), data=dat)
predict(res, newmods=diag(2), transf=transf.ztor, digits=2)

### note: the interpretation of the results is difficult since all
### situational interviews were structured, almost all psychological
### interviews were unstructured, and actually for the majority of
### the psychological interviews it was unknown whether the interview
### was structured or unstructured
table(dat$type, dat$struct, useNA="always")

### meta-analysis of raw correlations using a random-effects model
res <- rma(measure="COR", ri=ri, ni=ni, data=dat.mcdaniel1994)
res

## End(Not run)

The Non-Persuasive Power of a Brain Image

Description

Results from studies exploring how a superfluous fMRI brain image influences the persuasiveness of a scientific claim.

Usage

dat.michael2013

Format

The data frame contains the following columns:

Details

The dataset contains the data from the meta-analysis by Michael et al. (2013) of experiments on the persuasive power of a brain image. The meta-analysis analyzed an original study by McCabe and Castel (2008) as well as 10 replication attempts conducted by the authors of the meta-analysis.

In each study, participants read an article about using brain imaging as a lie detector. The article either included a superfluous fMRI image of a brain (brain) or not (no_brain). After reading the article, all participants responded to the statement “Do you agree or disagree with the conclusion that brain imaging can be used as a lie detector?” on a scale from 1 (strongly disagree) to 4 (strongly agree).

The original study by McCabe and Castel (2008) reported a relatively large increase in agreement due to the presence of brain images. Meta-analysis of the original study with the 10 replications suggests, however, a small, possibly null effect: an estimated average raw mean difference of 0.07 points, 95% CI [-0.00, 0.14], under a random-effects model.

In some studies, the article included a passage critiquing the primary claims made in the article; this is coded in the Included_Critique column for analysis as a possible moderator. Note that Experiment 3 by McCabe and Castel (2008) was a 2x2 between subjects design: brain image presence was manipulated as well as the inclusion of a critique. The two different critique conditions are recorded as separate rows in this dataset. Analysis of this dataset with metafor yields the same results (given rounding) reported in the manuscript.

Concepts

psychology, persuasion, raw mean differences

Author(s)

Robert Calin-Jageman, rcalinjageman@dom.edu, https://calin-jageman.net

Source

Michael, R. B., Newman, E. J., Vuorre, M., Cumming, G., & Garry, M. (2013). On the (non)persuasive power of a brain image. Psychonomic Bulletin & Review, 20(4), 720–-725. ⁠https://doi.org/10.3758/s13423-013-0391-6⁠

References

McCabe, D. P., & Castel, A. D. (2008). Seeing is believing: The effect of brain images on judgments of scientific reasoning. Cognition, 107(1), 343–352. ⁠https://doi.org/10.1016/j.cognition.2007.07.017⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.michael2013
dat

## Not run: 
### load metafor package
library(metafor)

### Data prep
# yi and vi are already provided, but here's how you would use escalc() to obtain
# a raw-mean difference and its variance.
# Note the measure parameter is "MD" for 'raw mean difference'
dat <- metafor::escalc(
  measure = "MD",
  m1i = Brain_m,
  m2i = No_brain_m,
  sd1i = Brain_s,
  sd2i = No_brain_s,
  n1i = Brain_n,
  n2i = No_brain_n,
  data = dat
)

### meta-analysis using a random-effects model of the raw mean differences
res <- rma(yi, vi, data=dat)
print(res, digits=2)

### examine if Included_Critique is a potential moderator
res <- rma(yi, vi, mods = ~ Included_Critique, data=dat)
print(res, digits=2)

## End(Not run)

Studies on the Relationship between Conscientiousness and Medication Adherence

Description

Results from 16 studies on the correlation between conscientiousness and medication adherence.

Usage

dat.molloy2014

Format

The data frame contains the following columns:

Details

Conscientiousness, one of the big-5 personality traits, can be defined as “socially prescribed impulse control that facilitates task- and goal-directed behaviour, such as thinking before acting, delaying gratification, following norms and rules and planning, organising and prioritising tasks” (John & Srivastava, 1999). Conscientiousness has been shown to be related to a number of health-related behaviors (e.g., tobacco/alcohol/drug use, diet and activity patterns, risky behaviors). A recent meta-analysis by Molloy et al. (2014) examined to what extent conscientiousness is related to medication adherence, that is, the extent to which (typically chronically ill) patients follow a prescribed medication regimen (e.g., taking a daily dose of a cholesterol lowering drug in patients with high LDL serum cholesterol levels). The results from the 16 studies included in this meta-analysis are provided in this dataset.

Variable a_measure indicates whether adherence was measured based on self-reports or a more ‘objective’ measure (e.g., electronic monitoring of pill bottle openings, pill counts). Variable c_measure indicates whether conscientiousness was measured with some version of the NEO personality inventory or some other scale. Methodological quality was scored by the authors on a 1 to 4 scale with higher scores indicating higher quality (see article for details on how this score was derived).

Concepts

psychology, medicine, correlation coefficients

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Molloy, G. J., O'Carroll, R. E., & Ferguson, E. (2014). Conscientiousness and medication adherence: A meta-analysis. Annals of Behavioral Medicine, 47(1), 92–101. ⁠https://doi.org/10.1007/s12160-013-9524-4⁠

References

John, O. P., & Srivastava, S. (1999). The Big Five Trait taxonomy: History, measurement, and theoretical perspectives. In L. A. Pervin & O. P. John (Eds.), Handbook of personality: Theory and research (2nd ed., pp. 102-138). New York: Guilford Press.

Examples

### copy data into 'dat' and examine data
dat <- dat.molloy2014
dat[-c(5:6)]

## Not run: 
### load metafor package
library(metafor)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat, slab=paste(authors, year, sep=", "))
dat[-c(5:6)]

### meta-analysis of the transformed correlations using a random-effects model
res <- rma(yi, vi, data=dat)
res

### average correlation with 95% CI
predict(res, digits=3, transf=transf.ztor)

### forest plot
forest(res, addpred=TRUE, xlim=c(-1.6,1.6), atransf=transf.ztor,
       at=transf.rtoz(seq(-0.4, 0.6, by=0.2)), digits=c(2,1), cex=0.9,
       header="Author(s), Year")

### funnel plot
funnel(res)

## End(Not run)

Studies on Assortative Mating

Description

Results from 457 studies on assortative mating in various species.

Usage

dat.moura2021

Format

The object is a list containing a data frame called dat that contains the following columns and a phylogenetic tree called tree:

Details

The 457 studies included in this dataset provide 1828 correlation coefficients describing the similarity in some measure of body size in mating couples in 341 different species.

Concepts

ecology, evolution, correlation coefficients, multivariate models, phylogeny, meta-regression

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Rios Moura, R., Oliveira Gonzaga, M., Silva Pinto, N., Vasconcellos-Neto, J., & Requena, G. S. (2021). Assortative mating in space and time: Patterns and biases. Ecology Letters, 24(5), 1089–1102. ⁠https://doi.org/10.1111/ele.13690⁠

References

Cinar, O., Nakagawa, S., & Viechtbauer, W. (in press). Phylogenetic multilevel meta-analysis: A simulation study on the importance of modelling the phylogeny. Methods in Ecology and Evolution. ⁠https://doi.org/10.1111/2041-210X.13760⁠

Hadfield, J. D., & Nakagawa, S. (2010). General quantitative genetic methods for comparative biology: Phylogenies, taxonomies and multi-trait models for continuous and categorical characters. Journal of Evolutionary Biology, 23(3), 494–508. ⁠https://doi.org/10.1111/j.1420-9101.2009.01915.x⁠

Nakagawa, S., & Santos, E. S. A. (2012). Methodological issues and advances in biological meta-analysis. Evolutionary Ecology, 26(5), 1253–1274. ⁠https://doi.org/10.1007/s10682-012-9555-5⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.moura2021$dat
head(dat)

## Not run: 
### load metafor package
library(metafor)

### load ape package
library(ape, warn.conflicts=FALSE)

### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)

### copy tree to 'tree'
tree <- dat.moura2021$tree

### turn tree into an ultrametric one
tree <- compute.brlen(tree)

### compute phylogenetic correlation matrix
A <- vcv(tree, corr=TRUE)

### make copy of the species.id variable
dat$species.id.phy <- dat$species.id

### fit multilevel phylogenetic meta-analytic model
res <- rma.mv(yi, vi,
   random = list(~ 1 | study.id, ~ 1 | effect.size.id, ~ 1 | species.id, ~ 1 | species.id.phy),
   R=list(species.id.phy=A), data=dat)
res

### examine if spatial and/or temporal pooling of data tends to yield larger correlations
res <- rma.mv(yi, vi,
   mods = ~ spatially.pooled * temporally.pooled,
   random = list(~ 1 | study.id, ~ 1 | effect.size.id, ~ 1 | species.id, ~ 1 | species.id.phy),
   R=list(species.id.phy=A), data=dat)
res

### estimated average correlation without pooling, when pooling spatially,
### when pooling temporally, and when pooling spatially and temporally
predict(res, newmods = rbind(c(0,0,0),c(1,0,0),c(0,1,0),c(1,1,1)), transf=transf.ztor, digits=2)

## End(Not run)

Assessing the Function of House Sparrows' Bib Size Using a Flexible Meta-Analysis Method

Description

A meta-analysis on the association between the size of a male's bib and their social status in house sparrows (Passer domesticus).

Usage

dat.nakagawa2007

Format

The data frame contains the following columns:

Details

Each study measures the association between a sparrows bib size and its social status. Effects are quantified as correlation coefficients.

Concepts

ecology, correlation coefficients

Author(s)

Daniel Noble, daniel.noble@anu.edu.au

Source

Nakagawa, S., Ockendon, N., Gillespie, D. O. S, Hatchwell, B. J., & Burke, T. (2007). Assessing the function of house sparrows' bib size using a flexible meta-analysis method. Behavioral Ecology, 18(5), 831–840. ⁠https://doi.org/10.1093/beheco/arm050⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.nakagawa2007
dat

## Not run: 
### load metafor package
library(metafor)

### calculate Zr
dat <- escalc(measure="ZCOR", ri=Correlation, ni=SampleSize, data=dat)

### fit meta-analytic model
res <- rma.mv(yi, vi, random = ~ 1 | StudyID, data=dat)
res

## End(Not run)

Studies on Anti-Infective-Treated Central Venous Catheters for Prevention of Catheter-Related Bloodstream Infections

Description

Results from 18 studies comparing the risk of catheter-related bloodstream infection when using anti-infective-treated versus standard catheters in the acute care setting.

Usage

dat.nielweise2007

Format

The data frame contains the following columns:

Details

The use of a central venous catheter may lead to a catheter-related bloodstream infection (CRBSI), which in turn increases the risk of morbidity and mortality. Anti-infective-treated catheters have been developed that are meant to reduce the risk of CRBSIs. Niel-Weise et al. (2007) conducted a meta-analysis of studies comparing infection risk when using anti-infective-treated versus standard catheters in the acute care setting. The results from 18 such studies are included in this dataset.

The dataset was used in the article by Stijnen et al. (2010) to illustrate various generalized linear mixed-effects models for the meta-analysis of proportions and odds ratios (see ‘References’).

Concepts

medicine, odds ratios, generalized linear models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

Source

Niel-Weise, B. S., Stijnen, T., & van den Broek, P. J. (2007). Anti-infective-treated central venous catheters: A systematic review of randomized controlled trials. Intensive Care Medicine, 33(12), 2058–2068. ⁠https://doi.org/10.1007/s00134-007-0897-3⁠

References

Stijnen, T., Hamza, T. H., & Ozdemir, P. (2010). Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29(29), 3046–3067. ⁠https://doi.org/10.1002/sim.4040⁠

Examples

### copy data into 'dat' and examine data
dat <- dat.nielweise2007
dat

## Not run: 
### load metafor package
library(metafor)

### standard (inverse-variance) random-effects model
res <- rma(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, drop00=TRUE)
print(res, digits=3)
predict(res, transf=exp, digits=2)

### random-effects conditional logistic model
res <- rma.glmm(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, model="CM.EL")
print(res, digits=3)
predict(res, transf=exp, digits=2)

## End(Not run)

Studies on Anti-Infective-Treated Central Venous Catheters for Prevention of Catheter-Related Bloodstream Infections

Description

Results from 18 studies comparing the risk of catheter-related bloodstream infection when using anti-infective-treated versus standard catheters for total parenteral nutrition or chemotherapy.

Usage

dat.nielweise2008

Format

The data frame contains the following columns:

Details

The use of a central venous catheter may lead to a catheter-related bloodstream infection (CRBSI), which in turn increases the risk of morbidity and mortality. Anti-infective-treated catheters have been developed that are meant to reduce the risk of CRBSIs. Niel-Weise et al. (2008) conducted a meta-analysis of studies comparing infection risk when using anti-infective-treated versus standard catheters for total parenteral nutrition or chemotherapy. The results from 9 such studies are included in this dataset.

The dataset was used in the article by Stijnen et al. (2010) to illustrate various generalized linear mixed-effects models for the meta-analysis of incidence rates and incidence rate ratios (see ‘References’).

Concepts

medicine, incidence rates, generalized linear models

Author(s)

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org