This task view covers packages which include
facilities for metaanalysis
of summary statistics from primary studies.
The task view does not consider
the metaanalysis of individual participant data (IPD)
which can be handled by
any of the standard linear modelling functions
but does include some
packages which offer special facilities for IPD.
The standard metaanalysis 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 metaanalysis 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 metaanalysis
Preparing for metaanalysis
 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 noncomparative
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, also includes a
convenience function for collating
its output for input to another
package like metafor
or producing a CSV file.
effsize
contains functions to compute effect sizes mean difference (Cohen's
d and Hedges g), dominance matrices (Cliff's Delta)
and stochastic superiority (VarghaDelaney A).
psychmeta provides extensive facilties for
converting effect sizes and for correcting for a variety
of restrictions and measurement errors.

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.

metavcov computes the variancecovariance
matrix for multivariate metaanalysis
when correlations between outcomes can be
provided but not between treatment effects, and
clubSandwich
imputes
variancecovariance matrix for multivariate metaanalysis

metafuse uses a fused lasso to merge
covariate estimates across a number of independent datasets.
Fitting the model

Four packages provide the inverse variance weighted,
MantelHaenszel,
and Peto methods: epiR,
meta, metafor, and rmeta.

For binary data metafor provides
the binomialnormal 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 and include
MAc and
metacor
which provide metaanalysis of correlation
coefficients and
MAd which provides metaanalysis
of mean differences.
MAc and MAd provide
a range of graphics.
psychometric
provides an extensive range of functions
for the metaanalysis of psychometric studies.

psychmeta implements the HunterSchmidt method
including corrections for reliability and rangerestriction issues

Bayesian approaches are contained in various packages.
bspmma which
provides two different models:
a nonparametric and a semiparametric.
Graphical display of the results is provided.
metamisc provides a method
with priors suggested by Higgins.
mmeta provides metaanalysis using
betabinomial prior distributions.
A Bayesian approach is also provided by bmeta which
provides forest plots via
forestplot
and diagnostic graphical output.
bayesmeta also provides a Bayesian approach
with forest plots via metafor
and diagnostic graphical output.

Some packages concentrate on providing
a specialised version of the core
metaanalysis function without providing
the range of ancillary
functions. These are:
gmeta
which subsumes a very wide variety of models under the method
of confidence distributions and
also provides a graphical display,
metaLik
which uses a more sophisticated approach
to the likelihood,
metamisc which as well as the
method of moments provides
two likelihoodbased methods, and
metatest which provides
another improved method of obtaining confidence intervals,
metaBMA has a
Bayesian approach using model averaging, a variety of priors
are provided and it is possible for the user to define
new ones.
 metagen provides a range of methods for
random effects models and also facilities
for extensive simulation studies of the
properties of those methods.

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
normalnormal models and also provides plots of them.

clubSandwich
gives clusterrobust variance estimates.
Graphical methods
An extensive range of graphical procedures is available.

Forest plots are provided in forestmodel
(using ggplot2), forestplot,
meta, metafor,
psychmeta, and rmeta.
Although the most basic plot can be produced
by any of them
they each provide their own choice of enhancements.

Funnel plots are provided in
meta, metafor, psychometric
and rmeta.
In addition to the standard funnel plots
an enhanced funnel plot to assess the
impact of extra evidence
is available in extfunnel, a funnel plot
for limit metaanalysis in
metasens, and metaviz provides
funnel plots in the context of visual inference.

Radial (Galbraith) plots are provided in
meta and metafor.

L'Abbe plots are provided in
meta and metafor.

Baujat plots are provided in
meta and metafor.

metaplotr
provides a crosshair plot

MetaAnalyser provides an interactive
visualisation of the results of a metaanalysis.

metaviz provides rainforestplots, an
enhanced version of forest plots. It accepts
input from metafor.
Investigating heterogeneity

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

altmeta
presents a variety of alternative methods for measuring
and testing heterogeneity with a focus on robustness
to outlying studies.

hetmeta
calculates some extra measures of heterogeneity.

metaforest investigates heterogeneity using random forests.
Note that it has nothing to do with forest plots.
Model criticism

An extensive series of plots of diagnostic statistics is
provided in metafor.

metaplus provides outlier diagnostics.

psychmeta provides leaveoneout methods.

ConfoundedMeta conducts a sensitivity analysis
to estimate the proportion of studies with
true effect sizes above a threshold.
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 nonparametric method suggested
by Begg and Mazumdar
and a range of regression tests modelled
after the approach of Egger.

xmeta provides a method in the context of
multivariate metaanalysis.

An exploratory technique for detecting
an excess of statistically
significant studies is provided by PubBias.
Unobserved studies
A recurrent issue in metaanalysis has been
the problem of unobserved studies.

Rosenthal's fail safe n is provided by
MAc and MAd.
metafor provides it as well as two
more recent methods by Orwin and Rosenberg.

Duval's trim and fill method is provided
by meta and metafor.

metasens provides Copas's selection
model and also
the method of limit metaanalysis (a regression based
approach for dealing with small study effects)
due to Rücker et al.

selectMeta provides various selection models:
the parametric model of Iyengar and Greenhouse,
the nonparametric model of Dear and Begg, and
proposes a new nonparametric 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.

The metansue package allows the inclusion
by multiple imputation
of studies known only to have a nonsignificant
result.

weightr
provides
facilities for using the weight function model
of Vevea and Hedges.
Other study designs

SCMA provides single case metaanalysis.
It is part of a suite of packages
dedicated to singlecase designs.

joint.Cox provides facilities for
the metaanalysis of studies of joint timetoevent
and disease progression.

metamisc provides for metaanalysis of prognostic studies
using the c statistic or the O/E ratio. Some plots are provided.
Metaanalysis of significance values

metap provides some facilities for
metaanalysis of significance values.

TFisher provides Fisher's method using thresholding for
the pvalues.
Some methods are also provided in some
of the genetics packages mentioned below.
Multivariate metaanalysis
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 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 metaregression,
metafor also provides for clustered and
hierarchical models.

mvtmeta provides multivariate metaanalysis
using the method of moments for random effects
although not metaregression,

metaSEM provides multivariate
(and univariate) metaanalysis and
metaregression by embedding it in the
structural equation framework
and using OpenMx for the structural equation modelling.
It can provide a threelevel metaanalysis
taking account of clustering and allowing for
level 2 and level 3 heterogeneity.
It also provides via a twostage approach
metaanalysis of correlation or covariance matrices.

xmeta
provides various functions for multivariate metaanalysis
and also for detecting publication bias.

dosresmeta concentrates on the situation
where individual studies have information on
the doseresponse relationship.

robumeta provides robust variance
estimation for clustered and hierarchical estimates.

CIAAWconsensus
has a function for multivariate ma in the context
of atomic weights and estimating
isotope ratios.
Metaanalysis of studies of diagnostic tests
A special case of multivariate metaanalysis
is the case of summarising
studies of diagnostic tests.
This gives rise to a bivariate, binary
metaanalysis with the withinstudy correlation
assumed zero
although the betweenstudy 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.

mada provides various descriptive statistics
and univariate methods (diagnostic odds ratio and Lehman
model) as well as the bivariate method due to Reitsma.
In addition metaregression is provided.
A range of graphical methods is also available.

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 metaanalysis
with a bivariate random effects model
(using JAGS to implement the MCMC method).
Graphical methods are provided.

meta4diag
provides Bayesian inference analysis for bivariate metaanalysis
of diagnostic test studies and an extensive range of
graphical methods.

CopulaREMADA uses a copula based mixed model
Metaregression
Where suitable moderator variables are
available they may be included using metaregression.
All these packages are mentioned above, this
just draws that information together.

metafor provides metaregression (multiple
moderators are catered for).
Various packages rely on metafor to
provide metaregression (meta, MAc,
and MAd) and all three of
these provide bubble plots.
psychmeta also uses metafor.

bmeta, metagen,
metaLik, metaSEM, and
metatest also provide metaregression.

mvmeta provides metaregression
for multivariate metaanalysis
as do metafor and metaSEM.

metacart integrates regression and classification trees
into the metaanalysis framework for moderator selection.

mada provides for the
metaregression of diagnostic test studies.
Individual participant data (IPD)
Where all studies can provide individual participant data
then software for analysis of multicentre trials
or multicentre cohort studies should prove adequate
and is outside the scope of this task view.
Other packages which provide facilities
related to IPD are:

ipdmeta which uses information on aggregate
summary statistics and a covariate of interest
to assess whether a full IPD analysis
would have more power.

ecoreg which is designed for ecological studies
enables estimation of an individual level
logistic regression from aggregate data or
individual data.

surrosurv evaluates failure time surrogates
in the context of IPD metaanalysis
Network metaanalysis
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 metaanalysis can also be
used for network metaanalysis with
appropriate setup.
This is provided in a Bayesian framework by
gemtc,
which acts as a frontend to BUGS
or JAGS, and pcnetmeta,
which uses JAGS.
nmaINLA uses integrated nested Laplace approximations
as an alternative to MCMC.
It provides a number of datasets.
netmeta works in a frequentist framework.
Both pcnetmeta and netmeta
provide network graphs and
netmeta provides a heatmap for
displaying inconsistency and heterogeneity.
Genetics
There are a number of packages specialising
in genetic data:
CPBayes
uses a Bayesian approach to study crossphenotype genetic
associations,
EasyStrata for stratified GWAS metaanalysis
with graphics,
etma
proposes a new statistical method to detect epistasis,
gap combines pvalues,
getmstatistic quantifies systematic heterogeneity,
MetABEL provides metaanalysis of
genome wide SNP association results,
MetaDE provides microarray metaanalysis
of differentially expressed gene detection,
MetaIntegrator
provides an extensive set of functions for genetic studies,
metaMA provides metaanalysis of
pvalues or moderated
effect sizes to find differentially expressed genes,
MetaPath
performs metaanalysis for pathway enrichment,
MetaPCA provides metaanalysis in
the dimension reduction of genomic data,
MetaQC provides objective quality control and
inclusion/exclusion criteria for genomic metaanalysis,
metaRNASeq metaanalysis from multiple RNA
sequencing experiments,
MetaSubtract uses leaveoneout methods to
validate metaGWAS results,
MultiMeta for metaanalysis
of multivariate GWAS
results with graphics, designed to accept GEMMA format,
MetaSKAT, seqMeta,
provide metaanalysis
for the SKAT test.
Others
CRTSize
provides metaanalysis as part of a package
primarily dedicated to the determination
of sample size in cluster randomised trials in
particular by simulating adding a new study to the
metaanalysis.
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 metaregression.
RcmdrPlugin.EZR provides an interface
via the Rcmdr GUI
using meta and metatest
to do the heavy lifting,
RcmdrPlugin.RMTCJags provides an interface
for network metaanalysis using BUGS code,
and MAVIS provides a Shiny
interface using metafor, MAc,
MAd, and weightr.