#' Meta-analysis of correlations
#'
#' @description
#' Calculation of fixed effect / common effect and random effects
#' estimates for meta-analyses with correlations; inverse variance
#' weighting is used for pooling.
#'
#' @param cor Correlation.
#' @param n Number of observations.
#' @param studlab An optional vector with study labels.
#' @param data An optional data frame containing the study
#' information, i.e., cor and n.
#' @param subset An optional vector specifying a subset of studies to
#' be used.
#' @param exclude An optional vector specifying studies to exclude
#' from meta-analysis, however, to include in printouts and forest
#' plots.
#' @param sm A character string indicating which summary measure
#' (\code{"ZCOR"} or \code{"COR"}) is to be used for pooling of
#' studies.
#' @param level The level used to calculate confidence intervals for
#' individual studies.
#' @param level.ma The level used to calculate confidence intervals
#' for meta-analysis estimates.
#' @param fixed A logical indicating whether a fixed effect / common
#' effect meta-analysis should be conducted.
#' @param random A logical indicating whether a random effects
#' meta-analysis should be conducted.
#' @param overall A logical indicating whether overall summaries
#' should be reported. This argument is useful in a meta-analysis
#' with subgroups if overall results should not be reported.
#' @param overall.hetstat A logical value indicating whether to print
#' heterogeneity measures for overall treatment comparisons. This
#' argument is useful in a meta-analysis with subgroups if
#' heterogeneity statistics should only be printed on subgroup
#' level.
#' @param prediction A logical indicating whether a prediction
#' interval should be printed.
#' @param level.predict The level used to calculate prediction
#' interval for a new study.
#' @param hakn A logical indicating whether the method by Hartung and
#' Knapp should be used to adjust test statistics and confidence
#' intervals.
#' @param adhoc.hakn A character string indicating whether an \emph{ad
#' hoc} variance correction should be applied in the case of an
#' arbitrarily small Hartung-Knapp variance estimate, see Details.
#' @param method.tau A character string indicating which method is
#' used to estimate the between-study variance \eqn{\tau^2} and its
#' square root \eqn{\tau}. Either \code{"DL"}, \code{"PM"},
#' \code{"REML"}, \code{"ML"}, \code{"HS"}, \code{"SJ"},
#' \code{"HE"}, or \code{"EB"}, can be abbreviated.
#' @param method.tau.ci A character string indicating which method is
#' used to estimate the confidence interval of \eqn{\tau^2} and
#' \eqn{\tau}. Either \code{"QP"}, \code{"BJ"}, or \code{"J"}, or
#' \code{""}, can be abbreviated.
#' @param tau.preset Prespecified value for the square root of the
#' between-study variance \eqn{\tau^2}.
#' @param TE.tau Overall effect used to estimate the between-study
#' variance tau-squared.
#' @param tau.common A logical indicating whether tau-squared should
#' be the same across subgroups.
#' @param null.effect A numeric value specifying the effect under the
#' null hypothesis.
#' @param method.bias A character string indicating which test is to
#' be used. Either \code{"Begg"}, \code{"Egger"}, or
#' \code{"Thompson"}, can be abbreviated. See function
#' \code{\link{metabias}}.
#' @param backtransf A logical indicating whether results for Fisher's
#' z transformed correlations (\code{sm = "ZCOR"}) should be back
#' transformed in printouts and plots. If TRUE (default), results
#' will be presented as correlations; otherwise Fisher's z
#' transformed correlations will be shown.
#' @param text.fixed A character string used in printouts and forest
#' plot to label the pooled fixed effect estimate.
#' @param text.random A character string used in printouts and forest
#' plot to label the pooled random effects estimate.
#' @param text.predict A character string used in printouts and forest
#' plot to label the prediction interval.
#' @param text.w.fixed A character string used to label weights of
#' fixed effect model.
#' @param text.w.random A character string used to label weights of
#' random effects model.
#' @param title Title of meta-analysis / systematic review.
#' @param complab Comparison label.
#' @param outclab Outcome label.
#' @param subgroup An optional vector to conduct a meta-analysis with
#' subgroups.
#' @param subgroup.name A character string with a name for the
#' subgroup variable.
#' @param print.subgroup.name A logical indicating whether the name of
#' the subgroup variable should be printed in front of the group
#' labels.
#' @param sep.subgroup A character string defining the separator
#' between name of subgroup variable and subgroup label.
#' @param test.subgroup A logical value indicating whether to print
#' results of test for subgroup differences.
#' @param byvar Deprecated argument (replaced by 'subgroup').
#' @param keepdata A logical indicating whether original data (set)
#' should be kept in meta object.
#' @param warn.deprecated A logical indicating whether warnings should
#' be printed if deprecated arguments are used.
#' @param control An optional list to control the iterative process to
#' estimate the between-study variance \eqn{\tau^2}. This argument
#' is passed on to \code{\link[metafor]{rma.uni}}.
#' @param \dots Additional arguments (to catch deprecated arguments).
#'
#' @details
#' Fixed effect and random effects meta-analysis of correlations based
#' either on Fisher's z transformation of correlations (\code{sm =
#' "ZCOR"}) or direct combination of (untransformed) correlations
#' (\code{sm = "COR"}) (see Cooper et al., p264-5 and p273-4). Only
#' few statisticians would advocate the use of untransformed
#' correlations unless sample sizes are very large (see Cooper et al.,
#' p265). The artificial example given below shows that the smallest
#' study gets the largest weight if correlations are combined directly
#' because the correlation is closest to 1.
#'
#' Default settings are utilised for several arguments (assignments
#' using \code{\link{gs}} function). These defaults can be changed for
#' the current R session using the \code{\link{settings.meta}}
#' function.
#'
#' Furthermore, R function \code{\link{update.meta}} can be used to
#' rerun a meta-analysis with different settings.
#'
#' \subsection{Estimation of between-study variance}{
#'
#' The following methods to estimate the between-study variance
#' \eqn{\tau^2} are available:
#' \itemize{
#' \item DerSimonian-Laird estimator (\code{method.tau = "DL"})
#' \item Paule-Mandel estimator (\code{method.tau = "PM"})
#' \item Restricted maximum-likelihood estimator (\code{method.tau =
#' "REML"})
#' \item Maximum-likelihood estimator (\code{method.tau = "ML"})
#' \item Hunter-Schmidt estimator (\code{method.tau = "HS"})
#' \item Sidik-Jonkman estimator (\code{method.tau = "SJ"})
#' \item Hedges estimator (\code{method.tau = "HE"})
#' \item Empirical Bayes estimator (\code{method.tau = "EB"})
#' }
#' See \code{\link{metagen}} for more information on these
#' estimators.
#' }
#'
#' \subsection{Confidence interval for the between-study variance}{
#'
#' The following methods to calculate a confidence interval for
#' \eqn{\tau^2} and \eqn{\tau} are available.
#' \tabular{ll}{
#' \bold{Argument}\tab \bold{Method} \cr
#' \code{method.tau.ci = "J"}\tab Method by Jackson \cr
#' \code{method.tau.ci = "BJ"}\tab Method by Biggerstaff and Jackson \cr
#' \code{method.tau.ci = "QP"}\tab Q-Profile method
#' }
#' See \code{\link{metagen}} for more information on these methods. No
#' confidence intervals for \eqn{\tau^2} and \eqn{\tau} are calculated
#' if \code{method.tau.ci = ""}.
#' }
#'
#' \subsection{Hartung-Knapp method}{
#'
#' Hartung and Knapp (2001) and Knapp and Hartung (2003) proposed an
#' alternative method for random effects meta-analysis based on a
#' refined variance estimator for the treatment estimate. Simulation
#' studies (Hartung and Knapp, 2001; IntHout et al., 2014; Langan et
#' al., 2019) show improved coverage probabilities compared to the
#' classic random effects method.
#'
#' 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 HK method (Knapp and Hartung, 2003; IQWiQ, 2020). An
#' alternative approach is to use the wider confidence interval of
#' classic fixed or random effects meta-analysis and the HK method
#' (Wiksten et al., 2016; Jackson et al., 2017).
#'
#' Argument \code{adhoc.hakn} can be used to choose the \emph{ad hoc}
#' method:
#' \tabular{ll}{
#' \bold{Argument}\tab \bold{\emph{Ad hoc} method} \cr
#' \code{adhoc.hakn = ""}\tab not used \cr
#' \code{adhoc.hakn = "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 = "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, 2020) \cr
#' \code{adhoc.hakn = "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)
#' }
#' }
#'
#' \subsection{Prediction interval}{
#'
#' A prediction interval for the proportion in a new study (Higgins et
#' al., 2009) is calculated if arguments \code{prediction} and
#' \code{random} are \code{TRUE}. Note, the definition of
#' prediction intervals varies in the literature. This function
#' implements equation (12) of Higgins et al., (2009) which proposed a
#' \emph{t} distribution with \emph{K-2} degrees of freedom where
#' \emph{K} corresponds to the number of studies in the meta-analysis.
#' }
#'
#' \subsection{Subgroup analysis}{
#'
#' Argument \code{subgroup} can be used to conduct subgroup analysis for
#' a categorical covariate. The \code{\link{metareg}} function can be
#' used instead for more than one categorical covariate or continuous
#' covariates.
#' }
#'
#' \subsection{Exclusion of studies from meta-analysis}{
#'
#' Arguments \code{subset} and \code{exclude} can be used to exclude
#' studies from the meta-analysis. Studies are removed completely from
#' the meta-analysis using argument \code{subset}, while excluded
#' studies are shown in printouts and forest plots using argument
#' \code{exclude} (see Examples in \code{\link{metagen}}).
#' Meta-analysis results are the same for both arguments.
#' }
#'
#' \subsection{Presentation of meta-analysis results}{
#'
#' Internally, both fixed effect and random effects models are
#' calculated regardless of values choosen for arguments
#' \code{fixed} and \code{random}. Accordingly, the estimate
#' for the random effects model can be extracted from component
#' \code{TE.random} of an object of class \code{"meta"} even if
#' argument \code{random = FALSE}. However, all functions in R
#' package \bold{meta} will adequately consider the values for
#' \code{fixed} and \code{random}. E.g. functions
#' \code{\link{print.meta}} and \code{\link{forest.meta}} will not
#' print results for the random effects model if \code{random =
#' FALSE}.
#' }
#'
#' @note
#' The function \code{\link{metagen}} is called internally to
#' calculate individual and overall treatment estimates and standard
#' errors.
#'
#' @return
#' An object of class \code{c("metacor", "meta")} with corresponding
#' \code{print}, \code{summary}, and \code{forest} functions. The
#' object is a list containing the following components:
#' \item{cor, n, studlab, exclude,}{As defined above.}
#' \item{sm, level, level.ma,}{As defined above.}
#' \item{fixed, random,}{As defined above.}
#' \item{hakn, adhoc.hakn, method.tau, method.tau.ci,}{As defined above.}
#' \item{tau.preset, TE.tau, method.bias,}{As defined above.}
#' \item{method.bias, tau.common, title, complab, outclab,}{As defined
#' above.}
#' \item{subgroup, subgroup.name, print.subgroup.name, sep.subgroup}{As defined above.}
#' \item{TE, seTE}{Either Fisher's z transformation of correlations
#' (\code{sm = "ZCOR"}) or correlations (\code{sm="COR"}) for
#' individual studies.}
#' \item{lower, upper}{Lower and upper confidence interval limits for
#' individual studies.}
#' \item{zval, pval}{z-value and p-value for test of effect in
#' individual studies.}
#' \item{w.fixed, w.random}{Weight of individual studies (in fixed and
#' random effects model).}
#' \item{TE.fixed, seTE.fixed}{Estimated overall effect (Fisher's z
#' transformation of correlation or correlation) and standard error
#' (fixed effect model).}
#' \item{lower.fixed, upper.fixed}{Lower and upper confidence interval
#' limits (fixed effect model).}
#' \item{statistic.fixed, pval.fixed}{z-value and p-value for test of
#' overall effect (fixed effect model).}
#' \item{TE.random, seTE.random}{Estimated overall effect (Fisher's z
#' transformation of correlation or correlation) and standard error
#' (random effects model).}
#' \item{lower.random, upper.random}{Lower and upper confidence
#' interval limits (random effects model).}
#' \item{statistic.random, pval.random}{z-value or t-value and
#' corresponding p-value for test of overall effect (random effects
#' model).}
#' \item{prediction, level.predict}{As defined above.}
#' \item{seTE.predict}{Standard error utilised for prediction
#' interval.}
#' \item{lower.predict, upper.predict}{Lower and upper limits of
#' prediction interval.}
#' \item{k}{Number of studies combined in meta-analysis.}
#' \item{Q}{Heterogeneity statistic Q.}
#' \item{df.Q}{Degrees of freedom for heterogeneity statistic.}
#' \item{pval.Q}{P-value of heterogeneity test.}
#' \item{tau2}{Between-study variance \eqn{\tau^2}.}
#' \item{se.tau2}{Standard error of \eqn{\tau^2}.}
#' \item{lower.tau2, upper.tau2}{Lower and upper limit of confidence
#' interval for \eqn{\tau^2}.}
#' \item{tau}{Square-root of between-study variance \eqn{\tau}.}
#' \item{lower.tau, upper.tau}{Lower and upper limit of confidence
#' interval for \eqn{\tau}.}
#' \item{H}{Heterogeneity statistic H.}
#' \item{lower.H, upper.H}{Lower and upper confidence limit for
#' heterogeneity statistic H.}
#' \item{I2}{Heterogeneity statistic I\eqn{^2}.}
#' \item{lower.I2, upper.I2}{Lower and upper confidence limit for
#' heterogeneity statistic I\eqn{^2}.}
#' \item{Rb}{Heterogeneity statistic R\eqn{_b}.}
#' \item{lower.Rb, upper.Rb}{Lower and upper confidence limit for
#' heterogeneity statistic R\eqn{_b}.}
#' \item{df.hakn}{Degrees of freedom for test of effect for
#' Hartung-Knapp method (only if \code{hakn = TRUE}).}
#' \item{method}{Pooling method: \code{"Inverse"}.}
#' \item{bylevs}{Levels of grouping variable - if \code{subgroup} is not
#' missing.}
#' \item{TE.fixed.w, seTE.fixed.w}{Estimated effect and
#' standard error in subgroups (fixed effect model) - if
#' \code{subgroup} is not missing.}
#' \item{lower.fixed.w, upper.fixed.w}{Lower and upper confidence
#' interval limits in subgroups (fixed effect model) - if
#' \code{subgroup} is not missing.}
#' \item{statistic.fixed.w, pval.fixed.w}{z-value and p-value for test
#' of effect in subgroups (fixed effect model) - if \code{subgroup} is
#' not missing.}
#' \item{TE.random.w, seTE.random.w}{Estimated effect and standard
#' error in subgroups (random effects model) - if \code{subgroup} is
#' not missing.}
#' \item{lower.random.w, upper.random.w}{Lower and upper confidence
#' interval limits in subgroups (random effects model) - if
#' \code{subgroup} is not missing.}
#' \item{statistic.random.w, pval.random.w}{z-value or t-value and
#' corresponding p-value for test of effect in subgroups (random
#' effects model) - if \code{subgroup} is not missing.}
#' \item{w.fixed.w, w.random.w}{Weight of subgroups (in fixed and
#' random effects model) - if \code{subgroup} is not missing.}
#' \item{df.hakn.w}{Degrees of freedom for test of effect for
#' Hartung-Knapp method in subgroups - if \code{subgroup} is not
#' missing and \code{hakn = TRUE}.}
#' \item{n.e.w}{Number of observations in experimental group in
#' subgroups - if \code{subgroup} is not missing.}
#' \item{n.c.w}{Number of observations in control group in subgroups -
#' if \code{subgroup} is not missing.}
#' \item{k.w}{Number of studies combined within subgroups - if
#' \code{subgroup} is not missing.}
#' \item{k.all.w}{Number of all studies in subgroups - if \code{subgroup}
#' is not missing.}
#' \item{Q.w.fixed}{Overall within subgroups heterogeneity statistic Q
#' (based on fixed effect model) - if \code{subgroup} is not missing.}
#' \item{Q.w.random}{Overall within subgroups heterogeneity statistic
#' Q (based on random effects model) - if \code{subgroup} is not
#' missing (only calculated if argument \code{tau.common} is TRUE).}
#' \item{df.Q.w}{Degrees of freedom for test of overall within
#' subgroups heterogeneity - if \code{subgroup} is not missing.}
#' \item{pval.Q.w.fixed}{P-value of within subgroups heterogeneity
#' statistic Q (based on fixed effect model) - if \code{subgroup} is
#' not missing.}
#' \item{pval.Q.w.random}{P-value of within subgroups heterogeneity
#' statistic Q (based on random effects model) - if \code{subgroup} is
#' not missing.}
#' \item{Q.b.fixed}{Overall between subgroups heterogeneity statistic
#' Q (based on fixed effect model) - if \code{subgroup} is not
#' missing.}
#' \item{Q.b.random}{Overall between subgroups heterogeneity statistic
#' Q (based on random effects model) - if \code{subgroup} is not
#' missing.}
#' \item{df.Q.b}{Degrees of freedom for test of overall between
#' subgroups heterogeneity - if \code{subgroup} is not missing.}
#' \item{pval.Q.b.fixed}{P-value of between subgroups heterogeneity
#' statistic Q (based on fixed effect model) - if \code{subgroup} is
#' not missing.}
#' \item{pval.Q.b.random}{P-value of between subgroups heterogeneity
#' statistic Q (based on random effects model) - if \code{subgroup} is
#' not missing.}
#' \item{tau.w}{Square-root of between-study variance within subgroups
#' - if \code{subgroup} is not missing.}
#' \item{H.w}{Heterogeneity statistic H within subgroups - if
#' \code{subgroup} is not missing.}
#' \item{lower.H.w, upper.H.w}{Lower and upper confidence limit for
#' heterogeneity statistic H within subgroups - if \code{subgroup} is
#' not missing.}
#' \item{I2.w}{Heterogeneity statistic I\eqn{^2} within subgroups - if
#' \code{subgroup} is not missing.}
#' \item{lower.I2.w, upper.I2.w}{Lower and upper confidence limit for
#' heterogeneity statistic I\eqn{^2} within subgroups - if \code{subgroup} is
#' not missing.}
#' \item{keepdata}{As defined above.}
#' \item{data}{Original data (set) used in function call (if
#' \code{keepdata = TRUE}).}
#' \item{subset}{Information on subset of original data used in
#' meta-analysis (if \code{keepdata = TRUE}).}
#' \item{call}{Function call.}
#' \item{version}{Version of R package \bold{meta} used to create
#' object.}
#'
#' @author Guido Schwarzer \email{sc@@imbi.uni-freiburg.de}
#'
#' @seealso \code{\link{update.meta}}, \code{\link{metacont}},
#' \code{\link{metagen}}, \code{\link{print.meta}}
#'
#' @references
#' Cooper H, Hedges LV, Valentine JC (2009):
#' \emph{The Handbook of Research Synthesis and Meta-Analysis},
#' 2nd Edition.
#' New York: Russell Sage Foundation
#'
#' DerSimonian R & Laird N (1986):
#' Meta-analysis in clinical trials.
#' \emph{Controlled Clinical Trials},
#' \bold{7}, 177--88
#'
#' Hartung J & Knapp G (2001):
#' On tests of the overall treatment effect in meta-analysis with
#' normally distributed responses.
#' \emph{Statistics in Medicine},
#' \bold{20}, 1771--82
#'
#' 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
#'
#' 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 (2020):
#' General Methods: Version 6.0.
#' \url{https://www.iqwig.de/en/about-us/methods/methods-paper/}
#'
#' 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
#'
#' 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
#'
#' @examples
#' m1 <- metacor(c(0.85, 0.7, 0.95), c(20, 40, 10))
#'
#' # Print correlations (back transformed from Fisher's z
#' # transformation)
#' #
#' m1
#'
#' # Print Fisher's z transformed correlations
#' #
#' print(m1, backtransf = FALSE)
#'
#' # Forest plot with back transformed correlations
#' #
#' forest(m1)
#'
#' # Forest plot with Fisher's z transformed correlations
#' #
#' forest(m1, backtransf = FALSE)
#'
#' m2 <- update(m1, sm = "cor")
#' m2
#'
#' # Identical forest plots (as back transformation is the identity
#' # transformation)
#' # forest(m2)
#' # forest(m2, backtransf = FALSE)
#'
#' @export metacor
metacor <- function(cor, n, studlab,
##
data = NULL, subset = NULL, exclude = NULL,
##
sm = gs("smcor"),
##
level = gs("level"), level.ma = gs("level.ma"),
fixed = gs("fixed"),
random = gs("random") | !is.null(tau.preset),
overall = fixed | random,
overall.hetstat = fixed | random,
##
hakn = gs("hakn"), adhoc.hakn = gs("adhoc.hakn"),
method.tau = gs("method.tau"),
method.tau.ci = gs("method.tau.ci"),
tau.preset = NULL, TE.tau = NULL,
tau.common = gs("tau.common"),
##
prediction = gs("prediction"),
level.predict = gs("level.predict"),
##
null.effect = 0,
##
method.bias = gs("method.bias"),
##
backtransf = gs("backtransf"),
##
text.fixed = gs("text.fixed"),
text.random = gs("text.random"),
text.predict = gs("text.predict"),
text.w.fixed = gs("text.w.fixed"),
text.w.random = gs("text.w.random"),
##
title = gs("title"), complab = gs("complab"),
outclab = "",
##
subgroup, subgroup.name = NULL,
print.subgroup.name = gs("print.subgroup.name"),
sep.subgroup = gs("sep.subgroup"),
test.subgroup = gs("test.subgroup"),
byvar,
##
keepdata = gs("keepdata"),
warn.deprecated = gs("warn.deprecated"),
##
control = NULL,
...) {
##
##
## (1) Check arguments
##
##
chknull(sm)
chklevel(level)
##
chklogical(hakn)
adhoc.hakn <- setchar(adhoc.hakn, .settings$adhoc4hakn)
method.tau <- setchar(method.tau, .settings$meth4tau)
if (is.null(method.tau.ci))
method.tau.ci <- if (method.tau == "DL") "J" else "QP"
method.tau.ci <- setchar(method.tau.ci, .settings$meth4tau.ci)
chklogical(tau.common)
##
chklogical(prediction)
chklevel(level.predict)
##
chknumeric(null.effect, length = 1)
##
method.bias <- setmethodbias(method.bias)
##
chklogical(backtransf)
##
if (!is.null(text.fixed))
chkchar(text.fixed, length = 1)
if (!is.null(text.random))
chkchar(text.random, length = 1)
if (!is.null(text.predict))
chkchar(text.predict, length = 1)
if (!is.null(text.w.fixed))
chkchar(text.w.fixed, length = 1)
if (!is.null(text.w.random))
chkchar(text.w.random, length = 1)
##
chklogical(keepdata)
##
## Check for deprecated arguments in '...'
##
args <- list(...)
chklogical(warn.deprecated)
##
level.ma <- deprecated(level.ma, missing(level.ma), args, "level.comb",
warn.deprecated)
chklevel(level.ma)
##
fixed <- deprecated(fixed, missing(fixed), args, "comb.fixed",
warn.deprecated)
chklogical(fixed)
##
random <- deprecated(random, missing(random), args, "comb.random",
warn.deprecated)
chklogical(random)
##
missing.subgroup.name <- missing(subgroup.name)
subgroup.name <-
deprecated(subgroup.name, missing.subgroup.name, args, "bylab",
warn.deprecated)
##
print.subgroup.name <-
deprecated(print.subgroup.name, missing(print.subgroup.name),
args, "print.byvar", warn.deprecated)
print.subgroup.name <- replaceNULL(print.subgroup.name, FALSE)
chklogical(print.subgroup.name)
##
sep.subgroup <-
deprecated(sep.subgroup, missing(sep.subgroup), args, "byseparator",
warn.deprecated)
if (!is.null(sep.subgroup))
chkchar(sep.subgroup, length = 1)
##
## Some more checks
##
chklogical(overall)
chklogical(overall.hetstat)
##
## Additional arguments / checks for metacor objects
##
fun <- "metacor"
sm <- setchar(sm, .settings$sm4cor)
##
##
## (2) Read data
##
##
nulldata <- is.null(data)
##
if (nulldata)
data <- sys.frame(sys.parent())
##
mf <- match.call()
##
## Catch 'cor' and 'n' from data:
##
cor <- eval(mf[[match("cor", names(mf))]],
data, enclos = sys.frame(sys.parent()))
chknull(cor)
k.All <- length(cor)
##
n <- eval(mf[[match("n", names(mf))]],
data, enclos = sys.frame(sys.parent()))
chknull(n)
##
## Catch 'studlab', 'subgroup', 'subset' and 'exclude' from data:
##
studlab <- eval(mf[[match("studlab", names(mf))]],
data, enclos = sys.frame(sys.parent()))
studlab <- setstudlab(studlab, k.All)
##
missing.subgroup <- missing(subgroup)
subgroup <- eval(mf[[match("subgroup", names(mf))]],
data, enclos = sys.frame(sys.parent()))
missing.byvar <- missing(byvar)
byvar <- eval(mf[[match("byvar", names(mf))]],
data, enclos = sys.frame(sys.parent()))
subgroup <- deprecated2(subgroup, missing.subgroup, byvar, missing.byvar)
by <- !is.null(subgroup)
##
subset <- eval(mf[[match("subset", names(mf))]],
data, enclos = sys.frame(sys.parent()))
missing.subset <- is.null(subset)
##
exclude <- eval(mf[[match("exclude", names(mf))]],
data, enclos = sys.frame(sys.parent()))
missing.exclude <- is.null(exclude)
##
## Additional checks
##
if (!by & tau.common) {
warning("Value for argument 'tau.common' set to FALSE as ",
"argument 'subgroup' is missing.")
tau.common <- FALSE
}
if (by & !tau.common & !is.null(tau.preset)) {
warning("Argument 'tau.common' set to TRUE as ",
"argument tau.preset is not NULL.")
tau.common <- TRUE
}
##
##
## (3) Check length of essential variables
##
##
chklength(n, k.All, fun)
chklength(studlab, k.All, fun)
##
if (by) {
chklength(subgroup, k.All, fun)
chklogical(test.subgroup)
}
##
##
## (4) Subset, exclude studies, and subgroups
##
##
if (!missing.subset)
if ((is.logical(subset) & (sum(subset) > k.All)) ||
(length(subset) > k.All))
stop("Length of subset is larger than number of studies.")
##
if (!missing.exclude) {
if ((is.logical(exclude) & (sum(exclude) > k.All)) ||
(length(exclude) > k.All))
stop("Length of argument 'exclude' is larger than number of studies.")
##
exclude2 <- rep(FALSE, k.All)
exclude2[exclude] <- TRUE
exclude <- exclude2
}
else
exclude <- rep(FALSE, k.All)
##
##
## (5) Store complete dataset in list object data
## (if argument keepdata is TRUE)
##
##
if (keepdata) {
if (nulldata)
data <- data.frame(.cor = cor)
else
data$.cor <- cor
##
data$.n <- n
data$.studlab <- studlab
##
if (by)
data$.subgroup <- subgroup
##
if (!missing.subset) {
if (length(subset) == dim(data)[1])
data$.subset <- subset
else {
data$.subset <- FALSE
data$.subset[subset] <- TRUE
}
}
##
if (!missing.exclude)
data$.exclude <- exclude
}
##
##
## (6) Use subset for analysis
##
##
if (!missing.subset) {
cor <- cor[subset]
n <- n[subset]
studlab <- studlab[subset]
##
exclude <- exclude[subset]
##
if (by)
subgroup <- subgroup[subset]
}
##
## Determine total number of studies
##
k.all <- length(cor)
##
if (k.all == 0)
stop("No studies to combine in meta-analysis.")
##
## No meta-analysis for a single study
##
if (k.all == 1) {
fixed <- FALSE
random <- FALSE
prediction <- FALSE
overall <- FALSE
overall.hetstat <- FALSE
}
##
## Check variable values
##
chknumeric(cor, -1, 1)
chknumeric(n, 0, zero = TRUE)
##
if (by) {
chkmiss(subgroup)
##
if (missing.subgroup.name & is.null(subgroup.name)) {
if (!missing.subgroup)
subgroup.name <- byvarname(mf[[match("subgroup", names(mf))]])
else if (!missing.byvar)
subgroup.name <- byvarname(mf[[match("byvar", names(mf))]])
}
}
##
if (!is.null(subgroup.name))
chkchar(subgroup.name, length = 1)
##
##
## (7) Calculate results for individual studies
##
##
if (sm == "ZCOR") {
TE <- 0.5 * log((1 + cor) / (1 - cor))
seTE <- sqrt(1 / (n - 3))
transf.null.effect <- 0.5 * log((1 + null.effect) / (1 - null.effect))
}
if (sm == "COR") {
TE <- cor
seTE <- sqrt((1 - cor^2)^2 / (n - 1))
transf.null.effect <- null.effect
}
##
##
## (8) Do meta-analysis
##
##
m <- metagen(TE, seTE, studlab,
exclude = if (missing.exclude) NULL else exclude,
##
sm = sm,
level = level,
level.ma = level.ma,
fixed = fixed,
random = random,
overall = overall,
overall.hetstat = overall.hetstat,
##
hakn = hakn, adhoc.hakn = adhoc.hakn,
method.tau = method.tau, method.tau.ci = method.tau.ci,
tau.preset = tau.preset,
TE.tau = TE.tau,
tau.common = FALSE,
##
prediction = prediction,
level.predict = level.predict,
##
null.effect = transf.null.effect,
##
method.bias = method.bias,
##
backtransf = backtransf,
##
text.fixed = text.fixed, text.random = text.random,
text.predict = text.predict,
text.w.fixed = text.w.fixed, text.w.random = text.w.random,
##
title = title, complab = complab, outclab = outclab,
##
keepdata = FALSE,
warn = FALSE,
##
control = control)
##
if (by & tau.common) {
## Estimate common tau-squared across subgroups
hcc <- hetcalc(TE, seTE, method.tau, "",
TE.tau, level.ma, subgroup, control)
}
##
##
## (9) Generate R object
##
##
res <- list(cor = cor, n = n)
##
## Add meta-analysis results
## (after removing unneeded list elements)
##
m$n.e <- NULL
m$n.c <- NULL
m$label.e <- ""
m$label.c <- ""
m$label.left <- ""
m$label.right <- ""
m$warn <- NULL
##
res <- c(res, m)
res$null.effect <- null.effect
##
## Add data
##
res$call <- match.call()
##
if (keepdata) {
res$data <- data
if (!missing.subset)
res$subset <- subset
}
##
class(res) <- c(fun, "meta")
##
## Add results from subgroup analysis
##
if (by) {
res$subgroup <- subgroup
res$subgroup.name <- subgroup.name
res$print.subgroup.name <- print.subgroup.name
res$sep.subgroup <- sep.subgroup
res$test.subgroup <- test.subgroup
res$tau.common <- tau.common
##
if (!tau.common)
res <- c(res, subgroup(res))
else if (!is.null(tau.preset))
res <- c(res, subgroup(res, tau.preset))
else
res <- c(res, subgroup(res, hcc$tau.resid))
##
if (!tau.common || !is.null(tau.preset)) {
res$tau2.resid <- res$lower.tau2.resid <- res$upper.tau2.resid <- NA
res$tau.resid <- res$lower.tau.resid <- res$upper.tau.resid <- NA
##
res$Q.resid <- res$df.Q.resid <- res$pval.Q.resid <- NA
res$H.resid <- res$lower.H.resid <- res$upper.H.resid <- NA
res$I2.resid <- res$lower.I2.resid <- res$upper.I2.resid <- NA
}
else {
res$Q.w.random <- hcc$Q.resid
res$df.Q.w.random <- hcc$df.Q.resid
res$pval.Q.w.random <- hcc$pval.Q.resid
##
res$tau2.resid <- hcc$tau2.resid
res$lower.tau2.resid <- hcc$lower.tau2.resid
res$upper.tau2.resid <- hcc$upper.tau2.resid
##
res$tau.resid <- hcc$tau.resid
res$lower.tau.resid <- hcc$lower.tau.resid
res$upper.tau.resid <- hcc$upper.tau.resid
res$sign.lower.tau.resid <- hcc$sign.lower.tau.resid
res$sign.upper.tau.resid <- hcc$sign.upper.tau.resid
##
res$Q.resid <- hcc$Q.resid
res$df.Q.resid <- hcc$df.Q.resid
res$pval.Q.resid <- hcc$pval.Q.resid
##
res$H.resid <- hcc$H.resid
res$lower.H.resid <- hcc$lower.H.resid
res$upper.H.resid <- hcc$upper.H.resid
##
res$I2.resid <- hcc$I2.resid
res$lower.I2.resid <- hcc$lower.I2.resid
res$upper.I2.resid <- hcc$upper.I2.resid
}
##
res$event.e.w <- NULL
res$event.c.w <- NULL
res$event.w <- NULL
res$n.e.w <- NULL
res$n.c.w <- NULL
res$time.e.w <- NULL
res$time.c.w <- NULL
}
##
## Backward compatibility
##
res$comb.fixed <- fixed
res$comb.random <- random
res$level.comb <- level.ma
##
if (by) {
res$byvar <- subgroup
res$bylab <- subgroup.name
res$print.byvar <- print.subgroup.name
res$byseparator <- sep.subgroup
}
##
class(res) <- c(fun, "meta")
res
}
