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 which can be handled by any of the standard linear modelling functions.

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.

Univariate meta-analysis

Preparing for meta-analysis

• 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, MAc which converts to correlation coefficients, MAd which converts to mean differences, and metafor which converts to effect sizes an extensive set of 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), for non-comparative studies (proportions, incidence rates, and mean change). It also provides for a measure used in psychometrics (Cronbach's alpha).
• meta provides functions to read and work with files output by RevMan 4 and 5.

Fitting the model

• Four packages provide the inverse variance weighted, Mantel-Haenszel, and Peto methods: epiR, meta, metafor, and rmeta. The last three also provide cumulative meta-analysis. The same three provide the usual forest and funnel plots. In addition radial (Galbraith) plots are provided by metafor and L'Abbe plots by meta and metafor.
• For binary data metafor provides the binomial-normal model.
• For sparse binary data exactmeta provides an exact method which does not involve continuity corrections
• Packages which work with specific effect sizes may be more congenial to workers in some areas of science MAc and metacor which provide meta-analysis of correlation coefficients and MAd which provides meta-analysis of mean differences. MAc and MAd provide a range of graphics. psychometric provides an extensive range of functions for the meta-analysis of psychometric studies.
• Bayesian approaches are contained in various packages. bspmma which provides two different models: a non-parametric and a semi-parametric. Graphical display of the results is provided. metamisc provides a method with priors suggested by Higgins. mmeta provides meta-analysis using beta-binomial prior distributions.
• Some packages concentrate on providing a specialised version of the core meta-analysis function without providing the range of ancillary functions. These are: metagen which provides an improved method of obtaining confidence intervals, metaLik which uses a more sophisticated approach to the likelihood, metamisc which as well as the method of moments provides two likelihood-based methods, and metatest which provides another improved method of obtaining confidence intervals.

Investigating heterogeneity

Confidence intervals for the heterogeneity parameter are provided in metafor and metagen.

Investigating small study bias

The issue of whether small studies give different results from large studies has been addressed by visual examination of the funnel plots mentioned above. In addition meta and metafor provide both the non-parametric method suggested by Begg and Mazumdar and a range of regression tests modelled after the approach of Egger. An exploratory technique for detecting an excess of statistically significant studies is provided by PubBias.

Unobserved studies

A recurrent issue in meta-analysis has been the problem of unobserved studies.

• Rosenthal's fail safe n is provided by metafor as well as two more recent methods by Orwin and Rosenberg.
• Duval's trim and fill method is provided by meta and metafor.
• copas provides Copas's selection model.
• selectMeta provides various selection models: the parametric model of Iyengar and Greenhouse, the non-parametric model of Dear and Begg, and proposes a new non-parametric method imposing a monotonicity constraint.
• SAMURAI performs a sensitivity analysis assuming the number of unobserved studies is known, perhaps from a trial registry, but not their outcome.
• extfunnel augments the funnel plot to assess the impact of additional evidence.

Multivariate meta-analysis

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 primary studies may be clustered for instance because they come from the same country or the same research team. In these situations where the outcome is multivariate:

• mvmeta assumes the within study covariances are known and as well as fixed effects provides a variety of options for fitting random effects. metafor provides fixed effects and likelihood based random effects model fitting procedures. Both these packages include meta-regression, metafor also provides for clustered and hierarchical models
• mvtmeta provides multivariate meta-analysis using the method of moments for random effects although not meta-regression,
• metaSEM is available from R-Forge and provides multivariate (and univariate) meta-analysis and meta-regression by embedding it in the structural equation framework and using OpenMx for the structural equation modelling. It can provide a three-level meta-analysis taking account of clustering and allowing for level 2 and level 3 heterogeneity. It also provides via a two-stage approach meta-analysis of correlation or covariance matrices.
• dosresmeta concentrates on the situation where individual studies have information on the dose-response relationship.
• robumeta provides robust variance estimation for clustered and hierarchical estimates.

Meta-analysis of studies of diagnostic tests

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 called Reitsma's method, and the heirarchical summary receiver operating characteristic (HSROC) method. In many situations these are equivalent.

• mada provides various descriptive statistics and univariate methods (diagnostic odds ratio and Lehman model) as well as the bivariate method due to Reitsma. Meta-regression is also provided. A range of graphical methods is also available.
• HSROC provides HSROC with estimation in a Bayesian framework. Graphical methods are provided. The case of imperfect reference standards is catered for.
• Metatron provides a method for the Reitsma model incuding the case of an imperfect reference standard
• metamisc provides the method of Riley which estimates a common within and between correlation. Graphical output is also provided.
• bamdit provides Bayesian meta-analysis with a bivariate random effects model (using JAGS to implement the MCMC method).

Meta-regression

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.

• metafor provides meta-regression (multiple moderators are catered for). A range of model diagnostics is also provided. Various packages rely on metafor to provide meta-regression (meta, MAc, and MAd).
• metagen, metaLik, metaSEM, and metatest also provide meta-regression.
• mvmeta provides meta-regression for multivariate meta-analysis as does metaSEM.
• mada provides for the meta-regression of diagnostic test studies.

Network meta-analysis

Also known as multiple treatment comparison.

This is provided in a Bayesian framework by gemtc, which acts as a front-end to your favourite MCMC package, and pcnetmeta, which uses JAGS. netmeta works in a frequentist framework.

Genetics

There are a number of packages specialising in genetic data: gap combines p-values, MADAM combines p-values using Fisher's method, MAMA provides meta-analysis of microarray data, MetABEL provides meta-analysis of genome wide SNP association results, MetaDE provides microarray meta-analysis of for differentially expressed dene detection, metaMA provides meta-analysis of p-values or moderated effect sizes to find differentially expressed genes, MetaPCA provides meta-analysis in the dimension reduction of genomic data, MetaQC provides objective quality control and inclusion/exclusion criteria for genomic meta-analysis, MetaSKAT, seqMeta, and skatMeta provide meta-analysis for the SKAT test.

Others

SCMA provides single case meta-analysis. It is part of a suite of packages dedicated to single-case designs.

CRTSize provides meta-analysis as part of a package primarily dedicated to the determination of sample size in cluster randomised trials.

CAMAN offers the possibility of using finite semiparametric mixtures as an alternative to the random effects model where there is heterogeneity. Covariates can be included to provide meta-regression.

RcmdrPlugin.MA provides an interface to the Rcmdr GUI.