|Maintainer:||Michael Dewey, Wolfgang Viechtbauer|
|Contact:||lists at dewey.myzen.co.uk|
|Contributions:||Suggestions and improvements for this task view are very welcome and can be made through issues or pull requests on GitHub or via e-mail to the maintainer address. For further details see the Contributing guide.|
|Citation:||Michael Dewey, Wolfgang Viechtbauer (2023). CRAN Task View: Meta-Analysis. Version 2023-03-09. URL https://CRAN.R-project.org/view=MetaAnalysis.|
|Installation:||The packages from this task view can be installed automatically using the ctv package. For example, |
This task view covers packages which include facilities for meta-analysis of summary statistics from primary studies. The task view does not consider the meta-analysis of individual participant data (IPD) which can be handled by any of the standard linear modelling functions but it does include some packages which offer special facilities for IPD.
The standard meta-analysis model is a form of weighted least squares and so any of the wide range of R packages providing weighted least squares would in principle be able to fit the model. The advantage of using a specialised package is that (a) it takes care of the small tweaks necessary (b) it provides a range of ancillary functions for displaying and investigating the model. Where the model is referred to below, it is this model which is meant.
Where summary statistics are not available, a meta-analysis of significance levels is possible. This is not completely unconnected with the problem of adjustment for multiple comparisons but the packages below which offer this, chiefly in the context of genetic data, also offer additional functionality.
The primary studies often use a range of statistics to present their results. Convenience functions to convert these onto a common metric are presented by: compute.es which converts from various statistics to d, g, r, z, and the log odds ratio, MAd which converts to mean differences, and metafor which converts to an extensive set of effect size measures for comparative studies (such as binary data, person years, mean differences and ratios, and so on), for studies of association (a wide range of correlation types), and for non-comparative studies (proportions, incidence rates, and mean change). It also provides for a measure used in psychometrics (Cronbach’s alpha). esc provides a range of effect size calculations with partial overlap with metafor but with some extras, noticeably for converting test statistics, and also includes a convenience function for collating its output for input to another package like metafor or producing a CSV file. estimraw estimates the cell frequencies from odds ratios, risk ratios, or risk differences. effsize contains functions to compute mean difference effect sizes (Cohen’s d and Hedges’ g) and measures of dominance (Cliff’s delta) and stochastic superiority (Vargha-Delaney A). effectsize provides a large number of different effect sizes and converts between them. psychmeta provides extensive facilities for converting effect sizes and correcting for various restrictions and measurement artifacts. metansue provides some methods for converting to effect sizes, while es.dif computes Cohen’s d, Hedges’ g, biased/unbiased c (an effect size between a mean and a constant), and e (an effect size between means without assuming variance equality) from raw data. MOTE provides a variety of conversions based on Cohen’s d. estmeansd converts between quantiles and means and standard deviations. metaBLUE estimates means and standard deviations from various order statistics. SingleCaseES provides basic effect sizes for single-case designs including parametric and non-overlap measures. smd computes standardised mean differences. CohensdpLibrary provides Cohen’s d from a variety of designs.
meta provides functions to read and work with files output by RevMan 4 and 5.
metagear provides many tools for the systematic review process including screening articles, downloading the articles, generating a PRISMA diagram, and some tools for effect sizes. revtools provides tools for downloading from bibliographic databases and uses machine learning methods to process them. citationchaser assists in the process of chasing citations.
metavcov computes the variance-covariance matrix for multivariate meta-analysis when correlations between outcomes can be provided but not between treatment effects.
clubSandwich and metafor provide functions to impute variance-covariance matrix for multivariate meta-analysis.
metafuse uses a fused lasso to merge covariate estimates across a number of independent datasets.
metapower provides power analysis for meta-analysis and meta-regression. POMADE does the same for the overall average effect size in a meta-analysis of dependent effect sizes.
PRISMA2020 produces an interactive flow diagram that conforms to PRISMA 2020 version, PRISMAstatement also generates flowcharts conforming to the PRISMA statement.
Several packages provide assistance in digitising data from published figures: metaDigitise and juicr provide graphical interfaces and accept various input formats. digitize has a more limited range of facilities. #### Fitting the model
Four packages provide the inverse variance weighted, Mantel-Haenszel, and Peto methods: epiR, meta, metafor, and rmeta.
For binary and time-to-event data, metafor provides binomial-normal and the Poisson-normal models.
Packages which work with specific effect sizes may be more congenial to workers in some areas of science and include metacor which provides meta-analysis of correlation coefficients and MAd which provides meta-analysis of mean differences. MAd provides a range of graphics. mixmeta provides an integrated interface to standard meta-analysis and extensions like multivariate and dose-response.
psychmeta implements the Hunter-Schmidt method including corrections for reliability.
clubSandwich and metafor provide cluster-robust variance estimates.
wildmeta conducts single coefficient tests and multiple-contrast hypothesis tests of meta-regression models using cluster wild bootstrapping.
Bayesian approaches are contained in various packages. bspmma provides two different models: a non-parametric and a semi-parametric. Graphical display of the results is provided. bayesmeta includes shrinkage estimates, meta-regression, posterior predictive p-values, and forest plots via either metafor or forestplot. Diagnostic graphical output is available. metaBMA provides a Bayesian approach using model averaging; a variety of priors are provided and it is possible for the user to define new ones. MetaStan includes binomial-normal hierarchical models and can use weakly informative priors for the heterogeneity and treatment effect parameters. baggr provides facilities using Stan for hierarchical Bayesian models; graphical facilities are provided. brms can also fit Bayesian meta-analytic models using Stan as the backend. BayesCombo provides facilities using a Bayesian approach and has graphical facilities. RBesT uses Bayesian synthesis to generate priors from various sources. metamisc provides a method with priors suggested by Higgins. RoBMA provides a framework for estimating ensembles of meta-analytic models and using Bayesian model averaging to combine them. ra4bayesmeta provides principled reference analysis within the Bayesian normal-normal model. metabup provides a Bayesian approach using basic uncertainty pooling. mmeta provides a Bayesian approach to possibly dependent 2 by 2 tables.
Some packages concentrate on providing a specialised version of the core meta-analysis function without providing a full range of ancillary functions. These are: metaLik which uses a more sophisticated approach to the likelihood, metatest which provides another improved method of obtaining confidence intervals, gmeta which subsumes a very wide variety of models under the method of confidence distributions and also provides a graphical display, and CoTiMA which performs meta-analyses of correlation matrices of repeatedly measured variables for studies with different time lags using a SEM framework with OpenMx as the engine.
metaplus fits random effects models relaxing the usual assumption that the random effects have a normal distribution by providing t or a mixture of normals.
ratesci fits random effects models to binary data using a variety of methods for confidence intervals.
RandMeta estimates exact confidence intervals in random effects models using an efficient algorithm.
rma.exact estimates exact confidence intervals in random effects normal-normal models and also provides plots of them.
pimeta provides a range of methods for prediction interval estimation from random effects models and has graphical facilities.
metamedian implements several methods to meta-analyze one-group or two-group studies that report the median of the outcome. These methods estimate the pooled median in the one-group context and the pooled raw difference of medians across groups in the two-group context. meta also provides methods for medians.
MetaUtility proposes a metric for estimating the proportion of effects above a cut-off of scientific importance.
metasens provides imputation methods for missing binary data.
metagam provides a framework for meta-analysis of generalised additive models including the case where individual participant data cannot be shared across locations.
metawho implements a method for combining within study interactions.
metarep provides replicability analyses after a conventional analysis.
rema uses a permutation approach to handle meta-analyses of rare event data.
meta.shrinkage uses shrinkage methods to provide better estimates of individual means in meta-analysis.
metaumbrella provides facilities for umbrella reviews.
vcmeta provides functions for varying-coefficient meta-analysis as an alternative to the usual fixed or random effect methods.
robustmeta provides methods for meta-analysis for cases where primary studies may have influential outlying values.
coefa provides a method for conducting a meta-analysis of factor analyses based on co-occurrence matrices.
An extensive range of graphical procedures is available.
The issue of whether small studies give different results from large studies can be addressed by visual examination of the funnel plots mentioned above. In addition:
A related issue in meta-analysis is the problem of unobserved studies and publication bias.
In all cases poolr considers correlated p-values in addition to independent. The others above do not.
Some methods are also provided in some of the genetics packages mentioned below.
Standard methods outlined above assume that the effect sizes are independent. This assumption may be violated in a number of ways: within each primary study multiple treatments may be compared to the same control, each primary study may report multiple endpoints or multiple assessments, or primary studies may be clustered for instance because they come from the same country or the same research team.
A special case of multivariate meta-analysis is the case of summarising studies of diagnostic tests. This gives rise to a bivariate, binary meta-analysis with the within-study correlation assumed zero although the between-study correlation is estimated. This is an active area of research and a variety of methods are available including what is referred to here as Reitsma’s method and the hierarchical summary receiver operating characteristic (HSROC) method. In many situations these are equivalent.
Where suitable moderator variables are available they may be included using meta-regression. All these packages are mentioned above, this just draws that information together.
Where all studies provide individual participant data, software for the analysis of multi-centre trials or multi-centre cohort studies should prove adequate but is outside the scope of this task view (see the MixedModels task view for relevant packages). Other packages which provide facilities related to IPD are:
Also known as multiple treatment comparison, this is a very active area of research and development. Note that some of the packages mentioned above under multivariate meta-analysis can also be used for network meta-analysis with appropriate setup.
There are a number of packages specialising in genetic data: catmap combines case-control and family study data, graphical facilities are provided, CPBayes uses a Bayesian approach to study cross-phenotype genetic associations, etma proposes a new statistical method to detect epistasis, gap combines p-values, getmstatistic quantifies systematic heterogeneity, getspres uses standardised predictive random effects to explore heterogeneity in genetic association meta-analyses, GMCM uses a Gaussian mixture copula model for high-throughput experiments, MendelianRandomization provides several methods for performing Mendelian randomisation analyses with summarised data, metaGE provides meta-analysis of genome-wide association studies for studying Genotype x Environment interactions. MetaIntegrator provides meta-analysis of gene expression data, metaMA provides meta-analysis of p-values or moderated effect sizes to find differentially expressed genes, metaRNASeq does meta-analysis from multiple RNA sequencing experiments, MetaSubtract uses leave-one-out methods to validate meta-GWAS results, ofGEM provides a method for identifying gene-environment interactions using meta-filtering, RobustRankAggreg provides methods for aggregating lists of genes, SPAtest combines association results, MetaSKAT provides for meta-analysis of the SKAT, and metaGE provides functions for a meta-analysis of genome-wide association studies for studying genotype x environment interactions.
|Regular:||aggregation, altmeta, amanida, baggr, bamdit, BayesCombo, bayesmeta, BayesMultMeta, bipd, bnma, boot.heterogeneity, boutliers, brms, bspmma, CAMAN, catmap, CIAAWconsensus, citationchaser, clubSandwich, coefa, CohensdpLibrary, compute.es, CoTiMA, CPBayes, dfmeta, diagmeta, digitize, dosresmeta, DTAplots, ecoreg, effectsize, effsize, epiR, es.dif, esc, estimraw, estmeansd, etma, EValue, forestmodel, forestplot, forestploter, forplo, fsn, gap, gemtc, GENMETA, getmstatistic, getspres, GMCM, gmeta, harmonicmeanp, jarbes, joint.Cox, juicr, KenSyn, MAd, mada, MBNMAdose, mc.heterogeneity, MendelianRandomization, meta.shrinkage, meta4diag, MetaAnalyser, metaBLUE, metaBMA, metabolic, metabup, metacart, metaconfoundr, metacor, metadat, metaDigitise, metaforest, metafuse, metagam, metaGE, metagear, MetaIntegration, MetaIntegrator, metaLik, metaMA, metamedian, metamicrobiomeR, metamisc, metansue, metap, metapack, metaplus, metapower, metarep, metaRMST, metaRNASeq, metaSEM, metasens, MetaSKAT, MetaStan, MetaSubtract, metaSurvival, metatest, metaumbrella, MetaUtility, metavcov, metaviz, metawho, mixmeta, mmeta, MOTE, multibiasmeta, multinma, mvmeta, mvtmeta, netmeta, nmadb, NMADiagT, nmaINLA, NMAoutlier, nmaplateplot, nmarank, nmathresh, ofGEM, OssaNMA, pcnetmeta, pema, phacking, pimeta, POMADE, poolr, PRISMA2020, PRISMAstatement, psychmeta, psymetadata, PublicationBias, publipha, puniform, ra4bayesmeta, RandMeta, ratesci, RBesT, RcmdrPlugin.EZR, RcmdrPlugin.MA, RcmdrPlugin.RMTCJags, rema, remaCor, revtools, rma.exact, rmeta, rnmamod, RoBMA, robumeta, RobustBayesianCopas, robustmeta, RobustRankAggreg, SCMA, selectMeta, SingleCaseES, smd, SPAtest, TFisher, vcmeta, viscomp, weightr, wildmeta.|