Package 'metadat'

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, [email protected]
Daniel Noble, [email protected]
Alistair Senior, [email protected]
W. Kyle Hamilton, [email protected]
Wolfgang Viechtbauer, [email protected]

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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 [email protected] 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)

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, [email protected], [email protected]
Laura Marusich, [email protected], [email protected]

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 = ~ SA.measure.type - 1,
                  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)

### 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 = 1.5)

### 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)

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, [email protected], 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

See Also

pairwise, metabin, netmeta, netcomb, netmetabin

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)

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, [email protected], 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)

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, [email protected], 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, header=TRUE, refline=0.5, xlim=c(0.38,0.72), digits=c(3,2))

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

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected]

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)

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, [email protected], 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, header=TRUE, top=2, 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)

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, [email protected], 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)

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. 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 inventory 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

Author(s)

Wolfgang Viechtbauer, [email protected], 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)

## End(Not run)

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, [email protected], 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,.8), atransf=exp, at=log(c(2/3, 1, 3/2)),
       header=TRUE, top=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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected]

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, header=TRUE, xlim=c(-12,-5))

## End(Not run)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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, [email protected], 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)

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: