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 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.
Preparing for meta-analysis
The primary studies often use a range of
statistics to present their
Convenience functions to convert these onto a common
metric are presented by:
which converts from
various statistics to
d, g, r, z and the log odds ratio,
which converts to correlation coefficients,
which converts to mean differences,
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).
a range of effect size calculations with partial overlap
but with some extras, noticeably
for converting test statistics, also includes a
convenience function for collating
its output for input to another
or producing a CSV file.
provides functions to read and work
with files output by RevMan 4 and 5.
provides an extensive range of
facilities to support the systematic review process,
ease data extraction, and generate effect sizes.
Fitting the model
Four packages provide the inverse variance weighted,
and Peto methods:
For binary data
the binomial-normal model.
For sparse binary data
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
which provide meta-analysis of correlation
which provides meta-analysis
of mean differences.
a range of graphics.
provides an extensive range of functions
for the meta-analysis of psychometric studies.
Bayesian approaches are contained in various packages.
provides two different models:
a non-parametric and a semi-parametric.
Graphical display of the results is provided.
provides a method
with priors suggested by Higgins.
provides meta-analysis using
beta-binomial prior distributions.
A Bayesian approach is also provided by
provides forest plots via
and diagnostic graphical output.
also provides a Bayesian approach
with forest plots via
and diagnostic graphical output.
Some packages concentrate on providing
a specialised version of the core
meta-analysis function without providing
the range of ancillary
functions. These are:
which subsumes a very wide variety of models under the method
of confidence distributions and
also provides a graphical display,
which uses a more sophisticated approach
to the likelihood,
which as well as the
method of moments provides
two likelihood-based methods, and
another improved method of obtaining confidence intervals.
provides a range of methods for
random effects models and also facilities
for extensive simulation studies of the
properties of those methods.
fits random effects
models relaxing the usual
assumption that the random effects have a normal
distribution by providing t or a mixture
An extensive range of graphical procedures is available.
Forest plots are provided in
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
In addition to the standard funnel plots
an enhanced funnel plot to assess the
impact of extra evidence
is available in
extfunnel, and a funnel plot
for limit meta-analysis in
Radial (Galbraith) plots are provided in
L'Abbe plots are provided in
Baujat plots are provided in
provides a crosshair plot
provides an interactive
visualisation of the results of a meta-analysis.
Confidence intervals for the heterogeneity parameter
are provided in
presents a variety of alternative methods for measuring
and testing heterogeneity with a focus on robustness
to outlying studies.
calculates some extra measures of heterogeneity.
Investigating small study bias
An extensive series of plots of diagnostic statistics is
provides outlier diagnostics.
The issue of whether small studies give different results
from large studies has been addressed by visual
examination of the funnel plots mentioned above.
both the non-parametric method suggested
by Begg and Mazumdar
and a range of regression tests modelled
after the approach of Egger.
provides a method in the context of
An exploratory technique for detecting
an excess of statistically
significant studies is provided by
A recurrent issue in meta-analysis has been
the problem of unobserved studies.
Meta-analysis of significance values
Rosenthal's fail safe n is provided by
provides it as well as two
more recent methods by Orwin and Rosenberg.
Duval's trim and fill method is provided
provides Copas's selection
model and also
the method of limit meta-analysis (a regression based
approach for dealing with small study effects)
due to R??cker et al.
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
performs a sensitivity
the number of unobserved studies is known,
perhaps from a trial registry, but not their outcome.
package allows the inclusion
by multiple imputation
of studies known only to have a non-significant
facilities for using the weight function model
of Vevea and Hedges.
provides some facilities for
meta-analysis of significance values.
Some of these 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 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:
assumes the within study covariances
are known and as well as fixed effects provides a
variety of options for fitting random effects.
provides fixed effects and likelihood
based random effects model fitting procedures.
Both these packages include meta-regression,
also provides for clustered and
provides multivariate meta-analysis
using the method of moments for random effects
although not meta-regression,
(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.
provides various functions for multivariate meta-analysis
and also for detecting publication bias.
concentrates on the situation
where individual studies have information on
the dose-response relationship.
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
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.
provides various descriptive statistics
and univariate methods (diagnostic odds ratio and Lehman
model) as well as the bivariate method due to Reitsma.
In addition meta-regression is provided.
A range of graphical methods is also available.
provides HSROC with estimation
in a Bayesian framework.
Graphical methods are provided.
The case of imperfect reference standards is catered for.
provides a method for
the Reitsma model
incuding the case of an imperfect reference standard
provides the method
of Riley which estimates a common
within and between correlation.
Graphical output is also provided.
provides Bayesian meta-analysis
with a bivariate random effects model
(using JAGS to implement the MCMC method).
Graphical methods are provided.
provides Bayesian inference analysis for bivariate meta-analysis
of diagnostic test studies and an extensive range of
uses a copula based mixed model
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.
provides meta-regression (multiple
moderators are catered for).
Various packages rely on
provide meta-regression (meta,
MAd) and all three of
these provide bubble plots.
also provide meta-regression.
for multivariate meta-analysis
provides for the
meta-regression of diagnostic test studies.
Individual participant data (IPD)
Where all studies can provide individual participant data
then software for analysis of multi--centre trials
or multi-centre cohort studies should prove adequate
and is outside the scope of this task view.
Other packages which provide facilities
related to IPD are:
which uses information on aggregate
summary statistics and a covariate of interest
to assess whether a full IPD analysis
would have more power.
which is designed for ecological studies
enables estimation of an individual level
logistic regression from aggregate data or
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
This is provided in a Bayesian framework by
which acts as a front-end to BUGS
or JAGS, and
which uses JAGS.
works in a frequentist framework.
provide network graphs and
provides a heatmap for
displaying inconsistency and heterogeneity
There are a number of packages specialising
in genetic data:
for startified GWAS meta-analysis
proposes a new statistical method to detect epistasis,
provides meta-analysis of microarray data,
provides meta-analysis of
genome wide SNP association results,
provides microarray meta-analysis
of differentially expressed dene detection,
provides an extensive set of functions for genetic studies,
provides meta-analysis of
p-values or moderated
effect sizes to find differentially expressed genes,
performs meta-analysis for pathway enrichment,
provides meta-analysis in
the dimension reduction of genomic data,
provides objective quality control and
inclusion/exclusion criteria for genomic meta-analysis,
meta-analysis from multiple RNA
of multivariate GWAS
results with graphics, designed to accept GEMMA format,
provides single case meta-analysis.
It is part of a suite of packages
dedicated to single-case designs.
provides facilities for
the meta-analysis of studies of joint time-to-event
and disease progression.
provides meta-analysis 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
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.
provides an interface
via the Rcmdr GUI
to do the heavy lifting,
provides an interface
for network meta-analysis using BUGS code,
provides a shiny