R/meta-package.R

In meta: General Package for Meta-Analysis

#' meta: Brief overview of methods and general hints
#' 
#' @description
#' R package \bold{meta} is a user-friendly general package providing
#' standard methods for meta-analysis and supporting Schwarzer et
#' al. (2015),
#' \url{https://link.springer.com/book/10.1007/978-3-319-21416-0}.
#' 
#' @details
#' R package \bold{meta} (Schwarzer, 2007; Balduzzi et al., 2019)
#' provides the following statistical methods for meta-analysis.
#' \enumerate{
#' \item Common effect (also called fixed effect) and random effects model:
#' \itemize{
#'  \item Meta-analysis of continuous outcome data (\code{\link{metacont}})
#'  \item Meta-analysis of binary outcome data (\code{\link{metabin}})
#'  \item Meta-analysis of incidence rates (\code{\link{metainc}})
#'  \item Generic inverse variance meta-analysis (\code{\link{metagen}})
#'  \item Meta-analysis of single correlations (\code{\link{metacor}})
#'  \item Meta-analysis of single means (\code{\link{metamean}})
#'  \item Meta-analysis of single proportions (\code{\link{metaprop}})
#'  \item Meta-analysis of single incidence rates (\code{\link{metarate}})
#' }
#' \item Several plots for meta-analysis:
#' \itemize{
#'  \item Forest plot (\code{\link{forest.meta}}, \code{\link{forest.metabind}})
#'  \item Funnel plot (\code{\link{funnel.meta}})
#'  \item Galbraith plot / radial plot (\code{\link{radial.meta}})
#'  \item L'Abbe plot for meta-analysis with binary outcome data
#'   (\code{\link{labbe.metabin}}, \code{\link{labbe.default}})
#'  \item Baujat plot to explore heterogeneity in meta-analysis
#'   (\code{\link{baujat.meta}})
#'  \item Bubble plot to display the result of a meta-regression
#'   (\code{\link{bubble.metareg}})
#' }
#' \item Three-level meta-analysis model (Van den Noortgate et al.,
#'   2013)
#' \item Generalised linear mixed models (GLMMs) for binary and count
#'   data (Stijnen et al., 2010) (\code{\link{metabin}},
#'   \code{\link{metainc}}, \code{\link{metaprop}}, and
#'   \code{\link{metarate}})
#' \item Various estimators for the between-study variance
#'  \eqn{\tau^2} in a random effects model (Veroniki et al., 2016);
#'  see description of argument \code{method.tau} below
#' \item Two methods to estimate the I-squared statistic
#'   (Higgins and Thompson, 2002); see description of argument
#'   \code{method.I2} below
#' \item Hartung-Knapp method for random effects meta-analysis
#'  (Hartung & Knapp, 2001a,b), see description of arguments
#'  \code{method.random.ci} and \code{adhoc.hakn.ci} below
#' \item Kenward-Roger method for random effects meta-analysis
#'  (Partlett and Riley, 2017), see description of arguments
#'  \code{method.random.ci} and \code{method.predict} below
#' \item Prediction interval for the treatment effect of a new study
#'  (Veroniki et al., 2019; Higgins et al., 2009; Partlett and Riley, 2017;
#'  Nagashima et al., 2019), see description of argument \code{method.predict}
#'  below
#' \item Statistical tests for funnel plot asymmetry
#'  (\code{\link{metabias.meta}}, \code{\link{metabias.rm5}}) and
#'  trim-and-fill method (\code{\link{trimfill.meta}},
#'  \code{\link{trimfill.default}}) to evaluate bias in meta-analysis
#' \item Meta-regression (\code{\link{metareg}})
#' \item Cumulative meta-analysis (\code{\link{metacum}}) and
#'   leave-one-out meta-analysis (\code{\link{metainf}})
#' \item Import data from RevMan Web (\code{\link{read.cdir}}), RevMan
#'   5 (\code{\link{read.rm5}}), see also \code{\link{metacr}} to
#'   conduct meta-analysis for a single comparison and outcome from a
#'   Cochrane review
#' }
#'
#' R package \bold{meta} provides two vignettes:
#' \itemize{
#'  \item \code{vignette("meta-workflow")} with an overview of main
#'    functions,
#'  \item \code{vignette("meta-tutorial")} with up-to-date commands for
#'    Balduzzi et al. (2019).
#' }
#' 
#' Additional statistical meta-analysis methods are provided by add-on
#' R packages:
#' \itemize{
#' \item Frequentist methods for network meta-analysis (R package
#'   \bold{netmeta})
#' \item Statistical methods for sensitivity analysis in meta-analysis
#'   (R package \bold{metasens})
#' \item Statistical methods for meta-analysis of diagnostic accuracy
#'   studies with several cutpoints (R package \bold{diagmeta})
#' }
#' 
#' In the following, more details on available and default statistical
#' meta-analysis methods are provided and R function
#' \code{\link{settings.meta}} is briefly described which can be used
#' to change the default settings. Additional information on
#' meta-analysis objects and available summary measures can be found
#' on the help pages \code{\link{meta-object}} and
#' \code{\link{meta-sm}}.
#' 
#' \subsection{Estimation of between-study variance}{
#' 
#' The following methods are available in all meta-analysis functions
#' to estimate the between-study variance \eqn{\tau^2}.
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{Method} \cr 
#' \code{method.tau = "REML"}
#'  \tab Restricted maximum-likelihood estimator (Viechtbauer, 2005) \cr
#' \tab (default) \cr
#' \code{method.tau = "PM"}
#'  \tab Paule-Mandel estimator (Paule and Mandel, 1982) \cr
#' \code{method.tau = "DL"}
#'  \tab DerSimonian-Laird estimator (DerSimonian and Laird, 1986) \cr
#' \code{method.tau = "ML"}
#'  \tab Maximum-likelihood estimator (Viechtbauer, 2005) \cr
#' \code{method.tau = "HS"}
#'  \tab Hunter-Schmidt estimator (Hunter and Schmidt, 2015) \cr
#' \code{method.tau = "SJ"}
#'  \tab Sidik-Jonkman estimator (Sidik and Jonkman, 2005) \cr
#' \code{method.tau = "HE"}
#'  \tab Hedges estimator (Hedges and Olkin, 1985) \cr
#' \code{method.tau = "EB"}
#'  \tab Empirical Bayes estimator (Morris, 1983)
#' }
#'
#' For GLMMs, only the maximum-likelihood method is available.
#' 
#' Historically, the DerSimonian-Laird method was the de facto
#' standard to estimate the between-study variance \eqn{\tau^2} and is
#' the default in some software packages including Review Manager 5
#' (RevMan 5) and R package \bold{meta}, version 4 and below. However,
#' its role has been challenged and especially the REML and
#' Paule-Mandel estimators have been recommended (Veroniki et al.,
#' 2016; Langan et al., 2019). Accordingly, the currenct default in R
#' package \bold{meta} is the REML estimator.
#' 
#' The following R command could be used to employ the Paule-Mandel
#' instead of the REML estimator in all meta-analyses of the current R
#' session:
#' \itemize{
#' \item \code{settings.meta(method.tau = "PM")}
#' }
#' 
#' Other estimators for \eqn{\tau^2} could be selected in a similar
#' way.
#'
#' Note, for binary outcomes, two variants of the DerSimonian-Laird
#' estimator are available if the Mantel-Haenszel method is used for
#' pooling. If argument \code{Q.Cochrane = TRUE} (default), the
#' heterogeneity statistic Q is based on the Mantel-Haenszel instead
#' of the inverse variance estimator under the common effect
#' model. This is the estimator for \eqn{\tau^2} implemented in RevMan
#' 5.
#' }
#' 
#' 
#' \subsection{Estimation of I-squared statistic}{
#' 
#' The following methods are available in all meta-analysis functions
#' to estimate the I-squared statistic (Higgins and Thompson, 2002).
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{Method} \cr 
#' \code{method.I2 = "Q"}
#'  \tab Based on heterogeneity statistic Q (default) \cr
#' \code{method.I2 = "tau2"}
#'  \tab Based on between-study variance \eqn{\tau^2}
#' }
#'
#' Using \code{method.I2 = "Q"} (Higgins and Thompson, 2002, section 3.3), the
#' value of I\eqn{^2} does not change if the estimate of \eqn{\tau^2} changes.
#' Furthermore, the value of I\eqn{^2} and the test of heterogeneity based on
#' the Q statistic are in agreement. R package \bold{metafor} uses the second
#' method (\code{method.I2 = "tau2"}) which is described in Higgins and Thompson
#' (2002), section 3.2. This method is more general in the way that the value
#' of I\eqn{^2} changes with the estimate of \eqn{\tau^2}.
#' }
#' 
#' \subsection{Confidence interval for random effects estimate}{
#'
#' The following methods are available in all meta-analysis functions
#' to calculate a confidence interval for the random effects estimate.
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{Method} \cr
#' \code{method.random.ci = "classic"} \tab Based on standard normal
#'   quantile \cr
#' \tab (DerSimonian and Laird, 1986) (default) \cr
#' \code{method.random.ci = "HK"} \tab Method by Hartung and Knapp
#'   (2001a/b) \cr
#' \code{method.random.ci = "KR"} \tab Kenward-Roger method (Partlett and
#'   Riley, 2017)
#' }
#' 
#' DerSimonian and Laird (1986) introduced the classic random effects
#' model using a quantile of the standard normal distribution to
#' calculate a confidence interval for the random effects
#' estimate. This method implicitly assumes that the weights in the
#' random effects meta-analysis are not estimated but
#' given. Particularly, the uncertainty in the estimation of the
#' between-study variance \eqn{\tau^2} is ignored.
#'
#' Hartung and Knapp (2001a,b) proposed an alternative method for
#' random effects meta-analysis based on a refined variance estimator
#' for the treatment estimate and a quantile of a
#' \emph{t}-distribution with \emph{k-1} degrees of freedom where
#' \emph{k} corresponds to the number of studies in the
#' meta-analysis.
#'
#' The Kenward-Roger method is only available for the REML estimator
#' (\code{method.tau = "REML"}) of the between-study variance
#' \eqn{\tau^2} (Partlett and Riley, 2017). This method is based on an
#' adjusted variance estimate for the random effects
#' estimate. Furthermore, a quantile of a \emph{t}-distribution with
#' adequately modified degrees of freedom is used to calculate the
#' confidence interval.
#'
#' For GLMMs and three-level models, the Kenward-Roger method is not
#' available, but a method similar to Knapp and Hartung (2003) is used
#' if \code{method.random.ci = "HK"}. For this method, the variance
#' estimator is not modified, however, a quantile of a
#' \emph{t}-distribution with \emph{k-1} degrees of freedom is used;
#' see description of argument \code{test} in
#' \code{\link[metafor]{rma.glmm}} and \code{\link[metafor]{rma.mv}}.
#' 
#' Simulation studies (Hartung and Knapp, 2001a,b; IntHout et al.,
#' 2014; Langan et al., 2019) show improved coverage probabilities of
#' the Hartung-Knapp method compared to the classic random effects
#' method. However, in rare settings with very homogeneous treatment
#' estimates, the Hartung-Knapp variance estimate can be arbitrarily
#' small resulting in a very narrow confidence interval (Knapp and
#' Hartung, 2003; Wiksten et al., 2016). In such cases, an \emph{ad
#' hoc} variance correction has been proposed by utilising the
#' variance estimate from the classic random effects model with the
#' Hartung-Knapp method (Knapp and Hartung, 2003; IQWiQ, 2022). An
#' alternative \emph{ad hoc} approach is to use the confidence
#' interval of the classic common or random effects meta-analysis if
#' it is wider than the interval from the Hartung-Knapp method
#' (Wiksten et al., 2016; Jackson et al., 2017).
#'
#' Argument \code{adhoc.hakn.ci} can be used to choose the \emph{ad
#' hoc} correction for the Hartung-Knapp (HK) method:
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{\emph{Ad hoc} method} \cr
#' \code{adhoc.hakn.ci = ""} \tab no \emph{ad hoc} correction (default)
#'   \cr
#' \code{adhoc.hakn.ci = "se"} \tab use variance correction if HK standard
#'  error is smaller \cr
#'  \tab than standard error from classic random effects
#'  \cr
#'  \tab meta-analysis (Knapp and Hartung, 2003) \cr
#' \code{adhoc.hakn.ci = "IQWiG6"} \tab use variance correction if HK
#'  confidence interval \cr
#'  \tab is narrower than CI from classic random effects model \cr
#'  \tab with DerSimonian-Laird estimator (IQWiG, 2022) \cr
#' \code{adhoc.hakn.ci = "ci"} \tab use wider confidence interval of
#'  classic random effects \cr
#'  \tab and HK meta-analysis \cr
#'  \tab (Hybrid method 2 in Jackson et al., 2017)
#' }
#' 
#' For GLMMs and three-level models, the \emph{ad hoc} variance
#' corrections are not available.
#' }
#' 
#' \subsection{Prediction interval}{
#'
#' The following methods are available in all meta-analysis functions
#' to calculate a prediction interval for the treatment effect in a
#' single new study.
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{Method} \cr
#' \code{method.predict = "V"} \tab Based on \emph{t}-distribution
#'   with \emph{k-1} degrees of freedom \cr
#'   \tab (Veroniki et al., 2019) (default) \cr
#' \code{method.predict = "HTS"} \tab Based on \emph{t}-distribution
#'   with \emph{k-2} degrees of freedom \cr
#'   \tab (Higgins et al., 2009) \cr
#' \code{method.predict = "HK"} \tab Based on Hartung-Knapp standard error
#'   and \cr
#'   \tab \emph{t}-distribution with \emph{k-1} degrees of freedom \cr
#' \code{method.predict = "HK-PR"} \tab Based on Hartung-Knapp standard error
#'   and \cr
#'   \tab \emph{t}-distribution with \emph{k-2} degrees of freedom \cr
#'   \tab (Partlett and Riley, 2017) \cr
#' \code{method.predict = "KR"} \tab Based on Kenward-Roger standard error
#'   and \cr
#'   \tab \emph{t}-distribution with approximate Kenward-Roger \cr
#'   \tab degrees of freedom \cr
#' \code{method.predict = "KR-PR"} \tab Based on Kenward-Roger standard error
#'   and \cr
#'   \tab \emph{t}-distribution with approximate Kenward-Roger \cr
#'   \tab degrees of freedom minus 1 (Partlett and Riley, 2017) \cr
#' \code{method.predict = "NNF"} \tab Bootstrap approach (Nagashima et
#'   al., 2019) \cr
#' \code{method.predict = "S"} \tab Based on standard normal quantile
#'   (Skipka, 2006)
#' }
#'
#' By default (\code{method.predict = "V"}), the prediction interval
#' is based on a \emph{t}-distribution with \emph{k-1} degrees of
#' freedom where \emph{k} corresponds to the number of studies in the
#' meta-analysis (Veroniki et al., 2019). The method by Higgins et al., (2009),
#' which is based on a \emph{t}-distribution with \emph{k-2} degrees of freedom,
#' has been the default in R package \bold{meta}, version 7.0-0 or lower.
#' 
#' The Hartung-Knapp prediction intervals are also based on a
#' \emph{t}-distribution, however, use a different standard error.
#'
#' The Kenward-Roger method is only available for the REML estimator
#' (\code{method.tau = "REML"}) of the between-study variance
#' \eqn{\tau^2} (Partlett and Riley, 2017). This method is based on an
#' adjusted variance estimate for the random effects
#' estimate. Furthermore, a quantile of a \emph{t}-distribution with
#' adequately modified degrees of freedom is used to calculate the prediction
#' interval.
#'
#' The bootstrap approach is only available if R package \bold{pimeta}
#' is installed (Nagashima et al., 2019). Internally, the
#' \code{\link[pimeta]{pima}} function is called with argument
#' \code{method = "boot"}. Argument \code{seed.predict} can be used to
#' get a reproducible bootstrap prediction interval and argument
#' \code{seed.predict.subgroup} for reproducible bootstrap prediction
#' intervals in subgroups.
#' 
#' The method of Skipka (2006) ignores the uncertainty in the
#' estimation of the between-study variance \eqn{\tau^2} and thus has
#' too narrow limits for meta-analyses with a small number of studies.
#'
#' For GLMMs and three-level models, only the methods by Veroniki et al.
#' (2019), Higgins et al. (2009) and Skipka (2006) are available. Argument
#' \code{method.predict = "V"} in R package \bold{meta} gives the same
#' prediction intervals as R functions \code{\link[metafor]{rma.glmm}} or
#' \code{\link[metafor]{rma.mv}} with argument \code{test = "t"}.
#'
#' Note, in R package \bold{meta}, version 7.0-0 or lower, the methods
#' \code{method.predict = "HK-PR"} and \code{method.predict = "KR-PR"} have
#' been available as \code{method.predict = "HK"} and
#' \code{method.predict = "KR"}.
#'
#' Argument \code{adhoc.hakn.pi} can be used to choose the \emph{ad
#' hoc} correction for the Hartung-Knapp method:
#' 
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{\emph{Ad hoc} method} \cr
#' \code{adhoc.hakn.pi = ""} \tab no \emph{ad hoc} correction (default)
#'   \cr
#' \code{adhoc.hakn.pi = "se"} \tab use variance correction if HK
#'  standard error is smaller
#' }
#' }
#'
#' \subsection{Confidence interval for the between-study variance}{
#'
#' The following methods are available in all meta-analysis functions
#' to calculate a confidence interval for \eqn{\tau^2} and \eqn{\tau}.
#' \tabular{ll}{
#' \bold{Argument} \tab \bold{Method} \cr 
#' \code{method.tau.ci = "J"} \tab Method by Jackson (2013) \cr
#' \code{method.tau.ci = "BJ"} \tab Method by Biggerstaff and Jackson (2008) \cr
#' \code{method.tau.ci = "QP"} \tab Q-Profile method (Viechtbauer, 2007) \cr
#' \code{method.tau.ci = "PL"} \tab Profile-Likelihood method for three-level \cr
#'  \tab meta-analysis model (Van den Noortgate et al., 2013) \cr
#' \code{method.tau.ci = ""} \tab No confidence interval
#' }
#' The first three methods have been recommended by Veroniki et
#' al. (2016). By default, the Jackson method is used for the
#' DerSimonian-Laird estimator of \eqn{\tau^2} and the Q-profile
#' method for all other estimators of \eqn{\tau^2}.
#'
#' The Profile-Likelihood method is the only method available for the
#' three-level meta-analysis model.
#' 
#' For GLMMs, no confidence intervals for \eqn{\tau^2} and \eqn{\tau}
#' are calculated.
#' }
#'
#' \subsection{Change default settings for R session}{
#'
#' R function \code{\link{settings.meta}} can be used to change the
#' previously described and several other default settings for the
#' current R session.
#' 
#' Some pre-defined general settings are available:
#' \itemize{
#' \item \code{settings.meta("RevMan5")}
#' \item \code{settings.meta("JAMA")}
#' \item \code{settings.meta("BMJ")}
#' \item \code{settings.meta("IQWiG5")}
#' \item \code{settings.meta("IQWiG6")}
#' \item \code{settings.meta("geneexpr")}
#' }
#' 
#' The first command can be used to reproduce meta-analyses from
#' Cochrane reviews conducted with \emph{Review Manager 5} (RevMan 5)
#' and specifies to use a RevMan 5 layout in forest plots.
#'
#' The second command can be used to generate forest plots following
#' instructions for authors of the \emph{Journal of the American
#' Medical Association}
#' (\url{https://jamanetwork.com/journals/jama/pages/instructions-for-authors/}). Study
#' labels according to JAMA guidelines can be generated using
#' \code{\link{labels.meta}}.
#'
#' The third command can be used to generate forest plots in the current layout
#' of the \emph{British Medical Journal}.
#'
#' The next two commands implement the recommendations of the
#' Institute for Quality and Efficiency in Health Care (IQWiG),
#' Germany accordinging to General Methods 5 and 6, respectively
#' (\url{https://www.iqwig.de/en/about-us/methods/methods-paper/}).
#'
#' The last setting can be used to print p-values in scientific
#' notation and to suppress the calculation of confidence intervals
#' for the between-study variance.
#'
#' See \code{\link{settings.meta}} for more details on these
#' pre-defined general settings.
#' 
#' In addition, \code{\link{settings.meta}} can be used to define
#' individual settings for the current R session. For example, the
#' following R command specifies the use of Hartung-Knapp and
#' Paule-Mandel method, and the printing of prediction intervals for
#' any meta-analysis generated after execution of this command:
#' \itemize{
#' \item \code{settings.meta(method.random.ci = "HK", method.tau =
#'   "PM", prediction = TRUE)}
#' }
#' }
#'
#' \subsection{Data sets}{
#' The following data sets are available in R package \bold{meta}.
#'
#' \tabular{ll}{
#' \bold{Data set} \tab \bold{Description} \cr
#' \code{\link{Fleiss1993bin}} \tab Aspirin after myocardial infarction \cr
#' \code{\link{Fleiss1993cont}} \tab Mental health treatment on medical utilisation\cr
#' \code{\link{Olkin1995}} \tab Thrombolytic therapy after acute myocardial infarction \cr
#' \code{\link{Pagliaro1992}} \tab Prevention of first bleeding in cirrhosis \cr
#' \code{\link{amlodipine}} \tab Amlodipine for work capacity \cr
#' \code{\link{caffeine}} \tab Caffeine for daytime drowsiness (Cochrane Practice review) \cr
#' \code{\link{cisapride}} \tab Cisapride in non-ulcer dispepsia \cr
#' \code{\link{lungcancer}} \tab Smoking example \cr
#' \code{\link{smoking}} \tab Smoking example \cr
#' \code{\link{woodyplants}} \tab Elevated CO$_2$ and total biomass of woody plants
#' }
#' 
#' \bold{R} package \bold{metadat} has a large collection of meta-analysis data
#' sets.
#' }
#'
#' @note
#' Balduzzi et al. (2019) is the preferred citation in publications
#' for \bold{meta}. Type \code{citation("meta")} for a BibTeX entry of
#' this publication.
#' 
#' Type \code{help(package = "meta")} for a listing of all R functions
#' and datasets available in \bold{meta}. For example, results of
#' several meta-analyses can be combined with \code{\link{metabind}}
#' which is useful to generate a forest plot with results of several
#' subgroup analyses.
#' 
#' R package \bold{meta} imports R functions from \bold{metafor}
#' (Viechtbauer, 2010) to
#' \itemize{
#' \item estimate the between-study variance \eqn{\tau^2},
#' \item conduct meta-regression,
#' \item estimate three-level models,
#' \item estimate generalised linear mixed models.
#' }
#' 
#' To report problems and bugs
#' \itemize{
#' \item type \code{bug.report(package = "meta")} if you do not use
#'   RStudio,
#' \item send an email to Guido Schwarzer
#'   \email{guido.schwarzer@@uniklinik-freiburg.de} if you use RStudio.
#' }
#' 
#' The development version of \bold{meta} is available on GitHub
#' \url{https://github.com/guido-s/meta/}.
#' 
#' @name meta-package
#' 
#' @aliases meta-package meta
#'
#' @author Guido Schwarzer \email{guido.schwarzer@@uniklinik-freiburg.de}
#' 
#' @references
#' Balduzzi S, Rücker G, Schwarzer G (2019):
#' How to perform a meta-analysis with R: a practical tutorial.
#' \emph{Evidence-Based Mental Health},
#' \bold{22}, 153--160
#' 
#' Biggerstaff BJ, Jackson D (2008):
#' The exact distribution of Cochran’s heterogeneity statistic in
#' one-way random effects meta-analysis.
#' \emph{Statistics in Medicine},
#' \bold{27}, 6093--110
#'
#' DerSimonian R & Laird N (1986):
#' Meta-analysis in clinical trials.
#' \emph{Controlled Clinical Trials},
#' \bold{7}, 177--88
#' 
#' Hartung J, Knapp G (2001a):
#' On tests of the overall treatment effect in meta-analysis with
#' normally distributed responses.
#' \emph{Statistics in Medicine},
#' \bold{20}, 1771--82
#' 
#' Hartung J, Knapp G (2001b):
#' A refined method for the meta-analysis of controlled clinical
#' trials with binary outcome.
#' \emph{Statistics in Medicine},
#' \bold{20}, 3875--89
#' 
#' Hedges LV & Olkin I (1985):
#' \emph{Statistical methods for meta-analysis}.
#' San Diego, CA: Academic Press
#' 
#' Higgins JPT & Thompson SG (2002):
#' Quantifying heterogeneity in a meta-analysis.
#' \emph{Statistics in Medicine},
#' \bold{21}, 1539--58
#' 
#' Higgins JPT, Thompson SG, Spiegelhalter DJ (2009):
#' A re-evaluation of random-effects meta-analysis.
#' \emph{Journal of the Royal Statistical Society: Series A},
#' \bold{172}, 137--59
#' 
#' Hunter JE & Schmidt FL (2015):
#' \emph{Methods of Meta-Analysis: Correcting Error and Bias in
#' Research Findings} (Third edition).
#' Thousand Oaks, CA: Sage
#' 
#' IntHout J, Ioannidis JPA, Borm GF (2014):
#' The Hartung-Knapp-Sidik-Jonkman method for random effects
#' meta-analysis is straightforward and considerably outperforms the
#' standard DerSimonian-Laird method.
#' \emph{BMC Medical Research Methodology},
#' \bold{14}, 25
#' 
#' IQWiG (2022):
#' General Methods: Version 6.1.
#' \url{https://www.iqwig.de/en/about-us/methods/methods-paper/}
#'
#' Jackson D (2013):
#' Confidence intervals for the between-study variance in random
#' effects meta-analysis using generalised Cochran heterogeneity
#' statistics.
#' \emph{Research Synthesis Methods},
#' \bold{4}, 220--229
#'
#' Jackson D, Law M, Rücker G, Schwarzer G (2017): 
#' The Hartung-Knapp modification for random-effects meta-analysis: A
#' useful refinement but are there any residual concerns?
#' \emph{Statistics in Medicine},
#' \bold{36}, 3923--34
#' 
#' Knapp G & Hartung J (2003):
#' Improved tests for a random effects meta-regression with a single
#' covariate.
#' \emph{Statistics in Medicine},
#' \bold{22}, 2693--710
#'
#' Langan D, Higgins JPT, Jackson D, Bowden J, Veroniki AA,
#' Kontopantelis E, et al. (2019):
#' A comparison of heterogeneity variance estimators in simulated
#' random-effects meta-analyses.
#' \emph{Research Synthesis Methods},
#' \bold{10}, 83--98
#' 
#' Schwarzer G (2007):
#' meta: An R package for meta-analysis.
#' \emph{R News},
#' \bold{7}, 40--5
#' 
#' Schwarzer G, Carpenter JR and Rücker G (2015):
#' \emph{Meta-Analysis with R (Use-R!)}.
#' Springer International Publishing, Switzerland
#'
#' Skipka G (2006):
#' The inclusion of the estimated inter-study variation into forest
#' plots for random effects meta-analysis - a suggestion for a
#' graphical representation [abstract].
#' \emph{XIV Cochrane Colloquium, Dublin}, 23-26.
#' 
#' Stijnen T, Hamza TH, Ozdemir P (2010):
#' Random effects meta-analysis of event outcome in the framework of
#' the generalized linear mixed model with applications in sparse
#' data.
#' \emph{Statistics in Medicine},
#' \bold{29}, 3046--67
#' 
#' Veroniki AA, Jackson D, Viechtbauer W, Bender R, Bowden J, Knapp G,
#' et al. (2016):
#' Methods to estimate the between-study variance and its uncertainty
#' in meta-analysis.
#' \emph{Research Synthesis Methods},
#' \bold{7}, 55--79 
#' 
#' Veroniki AA, Jackson D, Bender R, Kuss O, Higgins JPT, Knapp G, Salanti G
#' (2019):
#' Methods to calculate uncertainty in the estimated overall effect size from a
#' random-effects meta-analysis.
#' \emph{Research Synthesis Methods},
#' \bold{10}, 23--43
#' 
#' Van den Noortgate W, López-López JA, Marín-Martínez F, Sánchez-Meca J (2013):
#' Three-level meta-analysis of dependent effect sizes.
#' \emph{Behavior Research Methods},
#' \bold{45}, 576--94
#' 
#' Viechtbauer W (2005):
#' Bias and efficiency of meta-analytic variance estimators in the
#' random-effects model.
#' \emph{Journal of Educational and Behavioral Statistics},
#' \bold{30}, 261--93
#' 
#' Viechtbauer W (2007):
#' Confidence intervals for the amount of heterogeneity in
#' meta-analysis.
#' \emph{Statistics in Medicine},
#' \bold{26}, 37--52
#' 
#' Viechtbauer W (2010):
#' Conducting Meta-Analyses in R with the metafor Package.
#' \emph{Journal of Statistical Software},
#' \bold{36}, 1--48
#' 
#' Wiksten A, Rücker G, Schwarzer G (2016):
#' Hartung-Knapp method is not always conservative compared with
#' fixed-effect meta-analysis.
#' \emph{Statistics in Medicine},
#' \bold{35}, 2503--15
#'
#' @keywords package
#' 
#' @seealso \code{\link{meta-object}}, \code{\link{meta-sm}}
#'
#' @import metadat
#'
#' @importFrom dplyr %>% across mutate all_of select rename mutate
#'   if_else
#'
#' @importFrom stringr str_pad
#'
#' @importFrom magrittr %<>%
#'
#' @importFrom purrr compact
#'
#' @importFrom readr read_csv cols
#'
#' @importFrom grid arrow gpar grid.circle grid.draw grid.layout
#'   grid.lines grid.newpage grid.polygon grid.rect grid.text
#'   grid.xaxis textGrob popViewport pushViewport viewport unit unit.c
#'   convertX
#'   grid.get grid.gget
#'
#' @importFrom grDevices gray gray.colors cairo_pdf cairo_ps pdf
#'   postscript svg bmp jpeg png tiff
#'
#' @importFrom graphics abline axis barplot box mtext lines par plot
#'   points polygon text
#' 
#' @importFrom stats as.formula binom.test coef cor lm pchisq pf pnorm
#'   poisson.test pt qlogis qnorm qt runif update var weighted.mean
#'   weights glm binomial vcov fitted residuals
#'
#' @importFrom utils count.fields read.table assignInNamespace
#'   getFromNamespace packageDescription packageVersion head tail find
#'   unzip
#'
#' @importFrom metafor forest funnel funnel.default baujat labbe
#'   radial trimfill rma.uni rma.glmm rma.mv predict.rma
#'   confint.rma.uni confint.rma.mv escalc regtest to.long vcalc blup
#'
#' @importFrom lme4 glmer
#'
#' @importFrom CompQuadForm farebrother
#'
#' @importFrom methods formalArgs
#' 
#' @importFrom xml2 as_xml_document xml_attr xml_find_all xml_text
#' 
#' @export forest funnel baujat labbe radial trimfill blup

"_PACKAGE"

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