metagen.R
#' Generic inverse variance meta-analysis
#'
#' @description
#'
#' Fixed effect and random effects meta-analysis based on estimates
#' (e.g. log hazard ratios) and their standard errors. The inverse
#' variance method is used for pooling.
#'
#' Three-level random effects meta-analysis (Van den Noortgate et al.,
#' 2013) is available by internally calling
#' \code{\link[metafor]{rma.mv}} function from R package
#' \bold{metafor} (Viechtbauer, 2010).
#'
#' @param TE Estimate of treatment effect, e.g., log hazard ratio or
#' risk difference.
#' @param seTE Standard error of treatment estimate.
#' @param studlab An optional vector with study labels.
#' @param data An optional data frame containing the study
#' information.
#' @param subset An optional vector specifying a subset of studies to
#' be used (see Details).
#' @param exclude An optional vector specifying studies to exclude
#' from meta-analysis, however, to include in printouts and forest
#' plots (see Details).
#' @param id An optional vector specifying which estimates come from
#' the same study resulting in the use of a three-level
#' meta-analysis model.
#' @param sm A character string indicating underlying summary measure,
#' e.g., \code{"RD"}, \code{"RR"}, \code{"OR"}, \code{"ASD"},
#' \code{"HR"}, \code{"MD"}, \code{"SMD"}, or \code{"ROM"}.
#' @param method.ci A character string indicating which method is used
#' to calculate confidence intervals for individual studies, see
#' Details.
#' @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 null.effect A numeric value specifying the effect under the
#' null hypothesis.
#' @param n.e Number of observations in experimental group (or total
#' sample size in study).
#' @param n.c Number of observations in control group.
#' @param pval P-value (used to estimate the standard error).
#' @param df Degrees of freedom (used in test or to construct
#' confidence interval).
#' @param lower Lower limit of confidence interval (used to estimate
#' the standard error).
#' @param upper Upper limit of confidence interval (used to estimate
#' the standard error).
#' @param level.ci Level of confidence interval.
#' @param median Median (used to estimate the treatment effect and
#' standard error).
#' @param q1 First quartile (used to estimate the treatment effect and
#' standard error).
#' @param q3 Third quartile (used to estimate the treatment effect and
#' standard error).
#' @param min Minimum (used to estimate the treatment effect and
#' standard error).
#' @param max Maximum (used to estimate the treatment effect and
#' standard error).
#' @param method.mean A character string indicating which method to
#' use to approximate the mean from the median and other statistics
#' (see Details).
#' @param method.sd A character string indicating which method to use
#' to approximate the standard deviation from sample size, median,
#' interquartile range and range (see Details).
#' @param approx.TE Approximation method to estimate treatment
#' estimate (see Details).
#' @param approx.seTE Approximation method to estimate standard error
#' (see Details).
#' @param hakn A logical indicating whether 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. Either
#' \code{""}, \code{"se"}, \code{"ci"}, or \code{"iqwig6"} (see
#' Details), can be abbreviated.
#' @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"}, \code{"J"},
#' \code{"PL"}, 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 treatment 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 detail.tau Detail on between-study variance estimate.
#' @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 should be
#' back transformed in printouts and plots. If \code{backtransf =
#' TRUE} (default), results for \code{sm = "OR"} are printed as odds
#' ratios rather than log odds ratios and results for \code{sm =
#' "ZCOR"} are printed as correlations rather than Fisher's z
#' transformed correlations, for example.
#' @param pscale A numeric giving scaling factor for printing of
#' single event probabilities or risk differences, i.e. if argument
#' \code{sm} is equal to \code{"PLOGIT"}, \code{"PLN"},
#' \code{"PRAW"}, \code{"PAS"}, \code{"PFT"}, or \code{"RD"}.
#' @param irscale A numeric defining a scaling factor for printing of
#' single incidence rates or incidence rate differences, i.e. if
#' argument \code{sm} is equal to \code{"IR"}, \code{"IRLN"},
#' \code{"IRS"}, \code{"IRFT"}, or \code{"IRD"}.
#' @param irunit A character specifying the time unit used to
#' calculate rates, e.g. person-years.
#' @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 label.e Label for experimental group.
#' @param label.c Label for control group.
#' @param label.left Graph label on left side of forest plot.
#' @param label.right Graph label on right side of forest plot.
#' @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 A logical indicating whether warnings should be printed
#' (e.g., if studies are excluded from meta-analysis due to zero
#' standard errors).
#' @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}} or
#' \code{\link[metafor]{rma.mv}}.
#' @param \dots Additional arguments (to catch deprecated arguments).
#'
#' @details
#' This function provides the \emph{generic inverse variance method}
#' for meta-analysis which requires treatment estimates and their
#' standard errors (Borenstein et al., 2010). The method is useful,
#' e.g., for pooling of survival data (using log hazard ratio and
#' standard errors as input). Arguments \code{TE} and \code{seTE} can
#' be used to provide treatment estimates and standard errors
#' directly. However, it is possible to derive these quantities from
#' other information.
#'
#' 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{Three-level random effects meta-analysis}{
#'
#' A three-level random effects meta-analysis model (Van den Noortgate
#' et al., 2013) is utilized if argument \code{id} is used and at
#' least one study provides more than one estimate. Internally,
#' \code{\link[metafor]{rma.mv}} is called to conduct the analysis and
#' \code{\link[metafor]{weights.rma.mv}} with argument \code{type =
#' "rowsum"} is used to calculate random effects weights.
#' }
#'
#' \subsection{Approximate treatment estimates}{
#'
#' Missing treatment estimates can be derived from
#' \enumerate{
#' \item confidence limits provided by arguments \code{lower} and
#' \code{upper};
#' \item median, interquartile range and range (arguments
#' \code{median}, \code{q1}, \code{q3}, \code{min}, and \code{max});
#' \item median and interquartile range (arguments \code{median},
#' \code{q1} and \code{q3});
#' \item median and range (arguments \code{median}, \code{min} and
#' \code{max}).
#' }
#' For confidence limits, the treatment estimate is defined as the
#' center of the confidence interval (on the log scale for relative
#' effect measures like the odds ratio or hazard ratio).
#'
#' If the treatment effect is a mean it can be approximated from
#' sample size, median, interquartile range and range. By default,
#' methods described in Luo et al. (2018) are utilized (argument
#' \code{method.mean = "Luo"}):
#' \itemize{
#' \item equation (7) if sample size, median and range are available,
#' \item equation (11) if sample size, median and interquartile range
#' are available,
#' \item equation (15) if sample size, median, range and interquartile
#' range are available.
#' }
#'
#' Instead the methods described in Wan et al. (2014) are used if
#' argument \code{method.mean = "Wan"}):
#' \itemize{
#' \item equation (2) if sample size, median and range are available,
#' \item equation (14) if sample size, median and interquartile range
#' are available,
#' \item equation (10) if sample size, median, range and interquartile
#' range are available.
#' }
#'
#' By default, missing treatment estimates are replaced successively
#' using these method, i.e., confidence limits are utilised before
#' interquartile ranges. Argument \code{approx.TE} can be used to
#' overwrite this default for each individual study:
#' \itemize{
#' \item Use treatment estimate directly (entry \code{""} in argument
#' \code{approx.TE});
#' \item confidence limits (\code{"ci"} in argument \code{approx.TE});
#' \item median, interquartile range and range (\code{"iqr.range"});
#' \item median and interquartile range (\code{"iqr"});
#' \item median and range (\code{"range"}).
#' }
#' }
#'
#' \subsection{Approximate standard errors}{
#'
#' Missing standard errors can be derived from
#' \enumerate{
#' \item p-value provided by arguments \code{pval} and (optional)
#' \code{df};
#' \item confidence limits (arguments \code{lower}, \code{upper}, and
#' (optional) \code{df});
#' \item sample size, median, interquartile range and range (arguments
#' \code{n.e} and / or \code{n.c}, \code{median}, \code{q1},
#' \code{q3}, \code{min}, and \code{max});
#' \item sample size, median and interquartile range (arguments
#' \code{n.e} and / or \code{n.c}, \code{median}, \code{q1} and
#' \code{q3});
#' \item sample size, median and range (arguments \code{n.e} and / or
#' \code{n.c}, \code{median}, \code{min} and \code{max}).
#' }
#' For p-values and confidence limits, calculations are either based
#' on the standard normal or \emph{t} distribution if argument
#' \code{df} is provided. Furthermore, argument \code{level.ci} can be
#' used to provide the level of the confidence interval.
#'
#' Wan et al. (2014) describe methods to estimate the standard
#' deviation (and thus the standard error by deviding the standard
#' deviation with the square root of the sample size) from the sample
#' size, median and additional statistics. Shi et al. (2020) provide
#' an improved estimate of the standard deviation if the interquartile
#' range and range are available in addition to the sample size and
#' median. Accordingly, equation (11) in Shi et al. (2020) is the
#' default (argument \code{method.sd = "Shi"}), if the median,
#' interquartile range and range are provided (arguments
#' \code{median}, \code{q1}, \code{q3}, \code{min} and
#' \code{max}). The method by Wan et al. (2014) is used if argument
#' \code{method.sd = "Wan"} and, depending on the sample size, either
#' equation (12) or (13) is used. If only the interquartile range or
#' range is available, equations (15) / (16) and (7) / (9) in Wan et
#' al. (2014) are used, respectively. The sample size of individual
#' studies must be provided with arguments \code{n.e} and / or
#' \code{n.c}. The total sample size is calculated as \code{n.e} +
#' \code{n.c} if both arguments are provided.
#'
#' By default, missing standard errors are replaced successively using
#' these method, e.g., p-value before confidence limits before
#' interquartile range and range. Argument \code{approx.seTE} can be
#' used to overwrite this default for each individual study:
#'
#' \itemize{
#' \item Use standard error directly (entry \code{""} in argument
#' \code{approx.seTE});
#' \item p-value (\code{"pval"} in argument \code{approx.seTE});
#' \item confidence limits (\code{"ci"});
#' \item median, interquartile range and range (\code{"iqr.range"});
#' \item median and interquartile range (\code{"iqr"});
#' \item median and range (\code{"range"}).
#' }
#' }
#'
#' \subsection{Confidence intervals for individual studies}{
#'
#' For the mean difference (argument \code{sm = "MD"}), the confidence
#' interval for individual studies can be based on the
#' \itemize{
#' \item standard normal distribution (\code{method.ci = "z"}), or
#' \item t-distribution (\code{method.ci = "t"}).
#' }
#'
#' By default, the first method is used if argument \code{df} is
#' missing and the second method otherwise.
#'
#' Note, this choice does not affect the results of the fixed effect
#' and random effects meta-analysis.
#' }
#'
#' \subsection{Estimation of between-study variance}{
#'
#' The following methods are available to estimate the between-study
#' variance \eqn{\tau^2}.
#' \tabular{ll}{
#' \bold{Argument}\tab \bold{Method} \cr
#' \code{method.tau = "DL"}
#' \tab DerSimonian-Laird estimator (DerSimonian and Laird, 1986) \cr
#' \code{method.tau = "PM"}
#' \tab Paule-Mandel estimator (Paule and Mandel, 1982) \cr
#' \code{method.tau = "REML"}
#' \tab Restricted maximum-likelihood estimator (Viechtbauer, 2005) \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)
#' }
#'
#' Historically, the DerSimonian-Laird method was the de facto
#' standard to estimate the between-study variance \eqn{\tau^2} and is
#' still the default in many software packages including Review
#' Manager 5 (RevMan 5) and R package \pkg{meta}. However, its role
#' has been challenged and especially the Paule-Mandel and REML
#' estimators have been recommended (Veroniki et al.,
#' 2016). Accordingly, the following R command can be used to use the
#' Paule-Mandel estimator in all meta-analyses of the R session:
#' \code{settings.meta(method.tau = "PM")}
#' }
#'
#' \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 (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 meta-analysis model \cr
#' \tab (Van den Noortgate et al., 2013)
#' }
#' 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. No confidence intervals for
#' \eqn{\tau^2} and \eqn{\tau} are calculated if \code{method.tau.ci =
#' ""}.
#' }
#'
#' \subsection{Hartung-Knapp method}{
#'
#' Hartung and Knapp (2001a,b) proposed an alternative method for
#' random effects meta-analysis based on a refined variance estimator
#' for the treatment estimate. Simulation studies (Hartung and Knapp,
#' 2001a,b; IntHout et al., 2014; Langan et al., 2019) show improved
#' coverage probabilities compared to the classic random effects
#' method. However, in rare settings with very homogeneous treatment
#' estimates, the Hartung-Knapp (HK) 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 treatment effect of 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{Specify the null hypothesis of test for an overall effect}{
#'
#' Argument \code{null.effect} can be used to specify the (treatment)
#' effect under the null hypothesis in a test for an overall
#' effect.
#'
#' By default (\code{null.effect = 0}), the null hypothesis
#' corresponds to "no difference" (which is obvious for absolute
#' effect measures like the mean difference (\code{sm = "MD"}) or
#' standardised mean difference (\code{sm = "SMD"})). For relative
#' effect measures, e.g., risk ratio (\code{sm = "RR"}) or odds ratio
#' (\code{sm = "OR"}), the null effect is defined on the log scale,
#' i.e., \emph{ln}(RR) = 0 or \emph{ln}(OR) = 0 which is equivalent to
#' testing RR = 1 or OR = 1.
#'
#' Use of argument \code{null.effect} is especially useful for summary
#' measures without a "natural" null effect, i.e., in situations
#' without a second (treatment) group. For example, an overall
#' proportion of 50\% could be tested in the meta-analysis of single
#' proportions with argument \code{null.effect = 0.5}.
#'
#' Note, all tests for an overall effect are two-sided with the
#' alternative hypothesis that the effect is unequal to
#' \code{null.effect}.
#' }
#'
#' \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).
#' 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}. For example, functions
#' \code{\link{print.meta}} and \code{\link{forest.meta}} will not
#' show results for the random effects model if \code{random =
#' FALSE}.
#'
#' Argument \code{pscale} can be used to rescale single proportions or
#' risk differences, e.g. \code{pscale = 1000} means that proportions
#' are expressed as events per 1000 observations. This is useful in
#' situations with (very) low event probabilities.
#'
#' Argument \code{irscale} can be used to rescale single rates or rate
#' differences, e.g. \code{irscale = 1000} means that rates are
#' expressed as events per 1000 time units, e.g. person-years. This is
#' useful in situations with (very) low rates. Argument \code{irunit}
#' can be used to specify the time unit used in individual studies
#' (default: "person-years"). This information is printed in summaries
#' and forest plots if argument \code{irscale} is not equal to 1.
#'
#' Default settings for \code{fixed}, \code{random},
#' \code{pscale}, \code{irscale}, \code{irunit} and several other
#' arguments can be set for the whole R session using
#' \code{\link{settings.meta}}.
#' }
#'
#' @note
#' R function \code{\link[metafor]{rma.uni}} from R package
#' \pkg{metafor} (Viechtbauer 2010) is called internally to estimate
#' the between-study variance \eqn{\tau^2}.
#'
#'
#' @return
#' An object of class \code{c("metagen", "meta")} with corresponding
#' \code{print}, \code{summary}, and \code{forest} functions. The
#' object is a list containing the following components:
#' \item{TE, seTE, studlab, exclude, n.e, n.c}{As defined above.}
#' \item{id, sm, method.ci, level, level.ma,}{As defined above.}
#' \item{fixed, random,}{As defined above.}
#' \item{overall, overall.hetstat,}{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{tau.common, title, complab, outclab,}{As defined above.}
#' \item{label.e, label.c, label.left, label.right,}{As defined
#' above.}
#' \item{subgroup, subgroup.name,}{As defined above.}
#' \item{print.subgroup.name, sep.subgroup, warn,}{As defined above.}
#' \item{lower, upper}{Lower and upper confidence interval limits for
#' individual studies.}
#' \item{statistic, pval}{Statistic and p-value for test of treatment
#' effect for individual studies.}
#' \item{w.fixed, w.random}{Weight of individual studies (in fixed and
#' random effects model).}
#' \item{TE.fixed, seTE.fixed}{Estimated overall treatment effect 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}{Statistic and p-value for test of
#' overall treatment effect (fixed effect model).}
#' \item{TE.random, seTE.random}{Estimated overall treatment effect
#' 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}{Statistic and p-value for test
#' of overall treatment 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{null.effect}{As defined above.}
#' \item{k}{Number of studies combined in meta-analysis.}
#' \item{Q}{Heterogeneity statistic.}
#' \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{approx.TE, approx.seTE}{As defined above.}
#' \item{method}{Pooling method: \code{"Inverse"}.}
#' \item{df.hakn}{Degrees of freedom for test of treatment effect for
#' Hartung-Knapp method (only if \code{hakn = TRUE}).}
#' \item{bylevs}{Levels of grouping variable - if \code{subgroup} is not
#' missing.}
#' \item{TE.fixed.w, seTE.fixed.w}{Estimated treatment 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}{Statistics and p-values for
#' test of treatment effect in subgroups (fixed effect model) - if
#' \code{subgroup} is not missing.}
#' \item{TE.random.w, seTE.random.w}{Estimated treatment 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}{Statistics and p-values
#' for test of treatment 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 treatment effect
#' for Hartung-Knapp method in subgroups - if \code{subgroup} is not
#' missing and \code{hakn = TRUE}.}
#' \item{n.harmonic.mean.w}{Harmonic mean of number of observations in
#' subgroups (for back transformation of Freeman-Tukey Double
#' arcsine transformation) - if \code{subgroup} is not missing.}
#' \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{metabin}},
#' \code{\link{metacont}}, \code{\link{print.meta}},
#' \code{\link{settings.meta}}
#'
#' @references
#' 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
#'
#' Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010):
#' A basic introduction to fixed-effect and random-effects models for
#' meta-analysis.
#' \emph{Research Synthesis Methods},
#' \bold{1}, 97--111
#'
#' Cooper H & Hedges LV (1994):
#' \emph{The Handbook of Research Synthesis}.
#' Newbury Park, CA: Russell Sage Foundation
#'
#' DerSimonian R & Laird N (1986):
#' Meta-analysis in clinical trials.
#' \emph{Controlled Clinical Trials},
#' \bold{7}, 177--88
#'
#' Hedges LV & Olkin I (1985):
#' \emph{Statistical methods for meta-analysis}.
#' San Diego, CA: Academic Press
#'
#' 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
#'
#' 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
#'
#' 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 (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
#'
#' Luo D, Wan X, Liu J, Tong T (2018):
#' Optimally estimating the sample mean from the sample size, median,
#' mid-range, and/or mid-quartile range.
#' \emph{Statistical Methods in Medical Research},
#' \bold{27}, 1785--805
#'
#' Morris CN (1983):
#' Parametric empirical Bayes inference: Theory and applications (with
#' discussion).
#' \emph{Journal of the American Statistical Association}
#' \bold{78}, 47--65
#'
#' Paule RC & Mandel J (1982):
#' Consensus values and weighting factors.
#' \emph{Journal of Research of the National Bureau of Standards},
#' \bold{87}, 377--85
#'
#' \emph{Review Manager (RevMan)} [Computer program]. Version 5.4.
#' The Cochrane Collaboration, 2020
#'
#' Shi J, Luo D, Weng H, Zeng X-T, Lin L, Chu H, et al. (2020):
#' Optimally estimating the sample standard deviation from the
#' five-number summary.
#' \emph{Research Synthesis Methods}.
#'
#' Sidik K & Jonkman JN (2005):
#' Simple heterogeneity variance estimation for meta-analysis.
#' \emph{Journal of the Royal Statistical Society: Series C (Applied Statistics)},
#' \bold{54}, 367--84
#'
#' 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
#'
#' 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
#'
#' 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
#'
#' Wan X, Wang W, Liu J, Tong T (2014):
#' Estimating the sample mean and standard deviation from the sample
#' size, median, range and/or interquartile range.
#' \emph{BMC Medical Research Methodology},
#' \bold{14}, 135
#'
#' 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
#' data(Fleiss1993bin)
#' m1 <- metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I")
#' m1
#'
#' # Identical results using the generic inverse variance method with
#' # log risk ratio and its standard error:
#' # Note, argument 'n.e' in metagen() is used to provide the total
#' # sample size which is calculated from the group sample sizes n.e
#' # and n.c in meta-analysis m1.
#' m1.gen <- metagen(TE, seTE, studlab, n.e = n.e + n.c, data = m1, sm = "RR")
#' m1.gen
#' forest(m1.gen, leftcols = c("studlab", "n.e", "TE", "seTE"))
#'
#'
#' # Meta-analysis with prespecified between-study variance
#' #
#' metagen(m1$TE, m1$seTE, sm = "RR", tau.preset = sqrt(0.1))
#'
#'
#' # Meta-analysis of survival data:
#' #
#' logHR <- log(c(0.95, 1.5))
#' selogHR <- c(0.25, 0.35)
#' metagen(logHR, selogHR, sm = "HR")
#'
#'
#' # Paule-Mandel method to estimate between-study variance for data
#' # from Paule & Mandel (1982)
#' #
#' average <- c(27.044, 26.022, 26.340, 26.787, 26.796)
#' variance <- c(0.003, 0.076, 0.464, 0.003, 0.014)
#' #
#' metagen(average, sqrt(variance), sm = "MD", method.tau = "PM")
#'
#'
#' # Conduct meta-analysis using hazard ratios and 95% confidence intervals
#' #
#' # Data from Steurer et al. (2006), Analysis 1.1 Overall survival
#' # https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD004270.pub2/abstract
#' #
#' study <- c("FCG on CLL 1996", "Leporrier 2001", "Rai 2000", "Robak 2000")
#' HR <- c(0.55, 0.92, 0.79, 1.18)
#' lower.HR <- c(0.28, 0.79, 0.59, 0.64)
#' upper.HR <- c(1.09, 1.08, 1.05, 2.17)
#' #
#' # Input must be log hazard ratios, not hazard ratios
#' #
#' metagen(log(HR), lower = log(lower.HR), upper = log(upper.HR),
#' studlab = study, sm = "HR")
#'
#'
#' # Exclude MRC-1 and MRC-2 studies from meta-analysis, however,
#' # show them in printouts and forest plots
#' #
#' metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I",
#' exclude = study %in% c("MRC-1", "MRC-2"))
#' #
#' # Exclude MRC-1 and MRC-2 studies completely from meta-analysis
#' #
#' metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I",
#' subset = !(study %in% c("MRC-1", "MRC-2")))
#'
#'
#' # Exclude studies with total sample size above 1500
#' #
#' metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I",
#' exclude = (n.asp + n.plac) > 1500)
#'
#' # Exclude studies containing "MRC" in study name
#' #
#' metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I",
#' exclude = grep("MRC", study))
#'
#' # Use both arguments 'subset' and 'exclude'
#' #
#' metabin(d.asp, n.asp, d.plac, n.plac, study,
#' data = Fleiss1993bin, sm = "RR", method = "I",
#' subset = (n.asp + n.plac) > 1500,
#' exclude = grep("MRC", study))
#'
#' @export metagen
metagen <- function(TE, seTE, studlab,
##
data = NULL, subset = NULL, exclude = NULL, id = NULL,
##
sm = "",
##
method.ci = if (missing(df)) "z" else "t",
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"),
detail.tau = "",
##
prediction = gs("prediction"),
level.predict = gs("level.predict"),
##
null.effect = 0,
##
method.bias = gs("method.bias"),
##
n.e = NULL, n.c = NULL,
##
pval, df, lower, upper, level.ci = 0.95,
median, q1, q3, min, max,
method.mean = "Luo",
method.sd = "Shi",
##
approx.TE, approx.seTE,
##
backtransf = gs("backtransf"),
pscale = 1,
irscale = 1, irunit = "person-years",
##
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 = "",
label.e = gs("label.e"), label.c = gs("label.c"),
label.left = gs("label.left"),
label.right = gs("label.right"),
##
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 = gs("warn"), warn.deprecated = gs("warn.deprecated"),
##
control = NULL,
...) {
##
##
## (1) Check arguments
##
##
chknull(sm)
##
method.ci <- setchar(method.ci, .settings$ci4cont)
##
method.mean <- setchar(method.mean, c("Luo", "Wan"))
method.sd <- setchar(method.sd, c("Shi", "Wan"))
##
chklevel(level)
##
chklogical(hakn)
adhoc.hakn <- setchar(adhoc.hakn, .settings$adhoc4hakn)
missing.method.tau <- missing(method.tau)
method.tau <- setchar(method.tau, .settings$meth4tau)
##
missing.id <- missing(id)
##
missing.method.tau.ci <- missing(method.tau.ci)
if (is.null(method.tau.ci))
if (method.tau == "DL")
method.tau.ci <- "J"
else if (!missing.id)
method.tau.ci <- "PL"
else
method.tau.ci <- "QP"
method.tau.ci <- setchar(method.tau.ci, .settings$meth4tau.ci)
##
chklogical(tau.common)
##
chklogical(prediction)
chklevel(level.predict)
##
chknumeric(null.effect, length = 1)
##
method.bias <- setmethodbias(method.bias)
##
chklogical(backtransf)
if (!is.prop(sm))
pscale <- 1
chknumeric(pscale, length = 1)
if (!backtransf & pscale != 1) {
warning("Argument 'pscale' set to 1 as argument 'backtransf' is FALSE.")
pscale <- 1
}
if (!is.rate(sm))
irscale <- 1
chknumeric(irscale, length = 1)
if (!backtransf & irscale != 1) {
warning("Argument 'irscale' set to 1 as argument 'backtransf' is FALSE.")
irscale <- 1
}
##
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)
##
## Additional arguments / checks
##
fun <- "metagen"
chklogical(warn)
##
## 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)
##
missing.fixed <- missing(fixed)
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)
##
##
## (2) Read data
##
##
nulldata <- is.null(data)
##
if (nulldata)
data <- sys.frame(sys.parent())
##
mf <- match.call()
##
## Catch 'TE', 'seTE', 'median', 'lower', 'upper', 'n.e', 'n.c', and
## 'id' from data:
##
missing.TE <- missing(TE)
missing.seTE <- missing(seTE)
missing.median <- missing(median)
missing.lower <- missing(lower)
missing.upper <- missing(upper)
##
if (missing.TE & missing.median & (missing.lower | missing.upper))
stop("Treatment estimates missing. ",
"Provide either argument 'TE' or 'median', ",
"or arguments 'lower' and 'upper'.",
call. = FALSE)
##
TE <- eval(mf[[match("TE", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
seTE <- eval(mf[[match("seTE", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
median <- eval(mf[[match("median", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
lower <- eval(mf[[match("lower", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
upper <- eval(mf[[match("upper", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
id <- eval(mf[[match("id", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
if (!missing.id & is.null(id))
missing.id <- TRUE
##
k.All <- if (!missing.TE)
length(TE)
else if (!missing.median)
length(median)
else if (!missing.lower)
length(lower)
else
length(upper)
##
if (!missing.TE)
chknull(TE)
else
TE <- rep_len(NA, k.All)
##
if (!missing.seTE)
chknull(seTE)
else
seTE <- rep_len(NA, k.All)
##
if (!missing.median)
chknull(median)
##
n.e <- eval(mf[[match("n.e", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
n.c <- eval(mf[[match("n.c", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
## 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,
warn.deprecated)
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)
##
## Catch 'pval', 'df', 'level.ci', 'q1', 'q3', 'min', 'max',
## 'approx.TE' and 'approx.seTE', from data:
##
missing.pval <- missing(pval)
pval <- eval(mf[[match("pval", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.df <- missing(df)
df <- eval(mf[[match("df", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
if (!missing(level.ci))
level.ci <- eval(mf[[match("level.ci", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.q1 <- missing(q1)
q1 <- eval(mf[[match("q1", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.q3 <- missing(q3)
q3 <- eval(mf[[match("q3", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.min <- missing(min)
min <- eval(mf[[match("min", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.max <- missing(max)
max <- eval(mf[[match("max", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.approx.TE <- missing(approx.TE)
approx.TE <- eval(mf[[match("approx.TE", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
missing.approx.seTE <- missing(approx.seTE)
approx.seTE <- eval(mf[[match("approx.seTE", names(mf))]],
data, enclos = sys.frame(sys.parent()))
##
##
## (3) Check length of essential variables
##
##
arg <- if (!missing.TE) "TE" else "median"
chklength(seTE, k.All, arg)
chklength(studlab, k.All, arg)
##
if (by) {
chklength(subgroup, k.All, arg)
chklogical(test.subgroup)
}
##
## Additional checks
##
if (!by & tau.common) {
warning("Value for argument 'tau.common' set to FALSE as ",
"argument 'subgroup' is missing.",
call. = FALSE)
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.",
call. = FALSE)
tau.common <- TRUE
}
if (!is.null(n.e))
chklength(n.e, k.All, arg)
if (!is.null(n.c))
chklength(n.c, k.All, arg)
if (!missing.id)
chklength(id, k.All, arg)
##
if (!missing.approx.TE) {
if (length(approx.TE) == 1)
rep_len(approx.TE, k.All)
else
chklength(approx.TE, k.All, arg)
##
approx.TE <- setchar(approx.TE, c("", "ci", "iqr.range", "iqr", "range"))
}
##
if (!missing.approx.seTE) {
if (length(approx.seTE) == 1)
rep_len(approx.seTE, k.All)
else
chklength(approx.seTE, k.All, arg)
##
approx.seTE <- setchar(approx.seTE,
c("", "pval", "ci", "iqr.range", "iqr", "range"))
}
##
if (!missing.pval)
chklength(pval, k.All, arg)
if (!missing.df)
chklength(df, k.All, arg)
if (!missing.lower)
chklength(lower, k.All, arg)
if (!missing.upper)
chklength(upper, k.All, arg)
if (length(level.ci) == 1)
level.ci <- rep_len(level.ci, k.All)
else
chklength(level.ci, k.All, arg)
if (!missing.median)
chklength(median, k.All, arg)
if (!missing.q1)
chklength(q1, k.All, arg)
if (!missing.q3)
chklength(q3, k.All, arg)
if (!missing.min)
chklength(min, k.All, arg)
if (!missing.max)
chklength(max, k.All, arg)
##
##
## (4) Subset, exclude studies, and subgroups
##
##
if (!missing.subset)
if ((is.logical(subset) & (sum(subset) > k.All)) ||
(length(subset) > k.All))
stop("Length of argument '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 (inherits(data, "meta")) {
data <- data$data
if (isCol(data, ".subset"))
data <- data[data$.subset, ]
}
##
if (nulldata)
data <- data.frame(.TE = TE)
else
data$.TE <- TE
##
data$.seTE <- seTE
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
##
if (!missing.id) {
data$.id <- id
idx <- seq_along(id)
data$.idx <- idx
}
##
if (!missing.pval)
data$.pval <- pval
if (!missing.df)
data$.df <- df
if (!missing.lower)
data$.lower <- lower
if (!missing.upper)
data$.upper <- upper
if (!missing.lower | !missing.upper)
data$.level.ci <- level.ci
if (!missing.median)
data$.median <- median
if (!missing.q1)
data$.q1 <- q1
if (!missing.q3)
data$.q3 <- q3
if (!missing.min)
data$.min <- min
if (!missing.max)
data$.max <- max
if (!missing.approx.TE)
data$.approx.TE <- approx.TE
if (!missing.approx.seTE)
data$.approx.seTE <- approx.seTE
}
##
##
## (6) Use subset for analysis
##
##
if (!missing.subset) {
TE <- TE[subset]
seTE <- seTE[subset]
studlab <- studlab[subset]
##
exclude <- exclude[subset]
##
if (by)
subgroup <- subgroup[subset]
##
if (!is.null(n.e))
n.e <- n.e[subset]
if (!is.null(n.c))
n.c <- n.c[subset]
##
if (!missing.id) {
id <- id[subset]
idx <- idx[subset]
}
##
if (!missing.pval)
pval <- pval[subset]
if (!missing.df)
df <- df[subset]
if (!missing.lower)
lower <- lower[subset]
if (!missing.upper)
upper <- upper[subset]
level.ci <- level.ci[subset]
if (!missing.median)
median <- median[subset]
if (!missing.q1)
q1 <- q1[subset]
if (!missing.q3)
q3 <- q3[subset]
if (!missing.min)
min <- min[subset]
if (!missing.max)
max <- max[subset]
if (!missing.approx.TE)
approx.TE <- approx.TE[subset]
if (!missing.approx.seTE)
approx.seTE <- approx.seTE[subset]
}
##
## Determine total number of studies
##
k.all <- length(TE)
##
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(TE)
chknumeric(seTE, 0)
##
## No three-level meta-analysis conducted if variable 'id' contains
## different values for each estimate
##
three.level <- FALSE
##
sel.ni <- !is.infinite(TE) & !is.infinite(seTE)
if (!missing.id && length(unique(id[sel.ni])) != length(id[sel.ni]))
three.level <- TRUE
##
if (!three.level & method.tau.ci == "PL") {
if (method.tau == "DL")
method.tau.ci <- "J"
else
method.tau.ci <- "QP"
}
##
if (three.level) {
if (!(method.tau %in% c("REML", "ML"))) {
if (!missing.method.tau)
warning("For three-level model, argument 'method.tau' set to \"REML\".",
call. = FALSE)
method.tau <- "REML"
}
}
##
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 standard error from other information
##
##
if (missing.approx.seTE) {
approx.seTE <- rep_len("", length(TE))
##
## Use confidence limits
##
sel.NA <- is.na(seTE)
if (any(sel.NA) & !missing.lower & !missing.upper) {
j <- sel.NA & !is.na(lower) & !is.na(upper)
approx.seTE[j] <- "ci"
if (missing.df)
seTE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j])$seTE
else
seTE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j], df[j])$seTE
}
##
## Use p-values
##
sel.NA <- is.na(seTE)
if (any(sel.NA) & !missing.pval) {
j <- sel.NA & !is.na(TE) & !is.na(pval)
approx.seTE[j] <- "pval"
if (missing.df)
seTE[j] <- seTE.pval(TE[j], pval[j])$seTE
else
seTE[j] <- seTE.pval(TE[j], pval[j], df[j])$seTE
}
##
## Use IQR and range
##
sel.NA <- is.na(seTE)
if (any(sel.NA) & !missing.median &
!missing.q1 & !missing.q3 &
!missing.min & !missing.max &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(q1) & !is.na(q3) &
!is.na(min) & !is.na(max)
approx.seTE[j] <- "iqr.range"
if (is.null(n.c))
seTE[j] <- mean.sd.iqr.range(n.e[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
else if (is.null(n.e))
seTE[j] <- mean.sd.iqr.range(n.c[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
else
seTE[j] <- mean.sd.iqr.range(n.e[j] + n.c[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
}
##
## Use IQR
##
sel.NA <- is.na(seTE)
if (any(sel.NA) & !missing.median &
!missing.q1 & !missing.q3 &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(q1) & !is.na(q3)
approx.seTE[j] <- "iqr"
if (is.null(n.c))
seTE[j] <- mean.sd.iqr(n.e[j], median[j], q1[j], q3[j])$se
else if (is.null(n.e))
seTE[j] <- mean.sd.iqr(n.c[j], median[j], q1[j], q3[j])$se
else
seTE[j] <- mean.sd.iqr(n.e[j] + n.c[j], median[j], q1[j], q3[j])$se
}
##
## Use range
##
sel.NA <- is.na(seTE)
if (any(sel.NA) & !missing.median &
!missing.min & !missing.max &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(min) & !is.na(max)
approx.seTE[j] <- "range"
if (is.null(n.c))
seTE[j] <- mean.sd.range(n.e[j], median[j], min[j], max[j])$se
else if (is.null(n.e))
seTE[j] <- mean.sd.range(n.c[j], median[j], min[j], max[j])$se
else
seTE[j] <- mean.sd.range(n.e[j] + n.c[j], median[j],
min[j], max[j])$se
}
}
else {
j <- 0
for (i in approx.seTE) {
j <- j + 1
##
if (i == "ci") {
if (missing.df)
seTE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j])$seTE
else
seTE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j], df[j])$seTE
}
else if (i == "pval") {
if (missing.df)
seTE[j] <- seTE.pval(TE[j], pval[j])$seTE
else
seTE[j] <- seTE.pval(TE[j], pval[j], df[j])$seTE
}
else if (i == "iqr.range") {
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.seTE' = \"iqr\".",
call. = FALSE)
else if (is.null(n.c))
seTE[j] <- mean.sd.iqr.range(n.e[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
else if (is.null(n.e))
seTE[j] <- mean.sd.iqr.range(n.c[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
else
seTE[j] <- mean.sd.iqr.range(n.e[j] + n.c[j], median[j], q1[j], q3[j],
min[j], max[j],
method.sd = method.sd)$se
}
else if (i == "iqr") {
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.seTE' = \"iqr\".",
call. = FALSE)
else if (is.null(n.c))
seTE[j] <- mean.sd.iqr(n.e[j], median[j], q1[j], q3[j])$se
else if (is.null(n.e))
seTE[j] <- mean.sd.iqr(n.c[j], median[j], q1[j], q3[j])$se
else
seTE[j] <- mean.sd.iqr(n.e[j] + n.c[j], median[j], q1[j], q3[j])$se
}
else if (i == "range") {
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.seTE' = \"range\".",
call. = FALSE)
else if (is.null(n.c))
seTE[j] <- mean.sd.range(n.e[j], median[j], min[j], max[j])$se
else if (is.null(n.e))
seTE[j] <- mean.sd.range(n.c[j], median[j], min[j], max[j])$se
else
seTE[j] <- mean.sd.range(n.e[j] + n.c[j], median[j],
min[j], max[j])$se
}
}
}
##
##
## (8) Calculate treatment estimate from other information
##
##
if (missing.approx.TE) {
approx.TE <- rep_len("", length(TE))
##
## Use confidence limits
##
sel.NA <- is.na(TE)
if (any(sel.NA) & !missing.lower & !missing.upper) {
j <- sel.NA & !is.na(lower) & !is.na(upper)
approx.TE[j] <- "ci"
TE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j])$TE
}
##
## Use IQR and range
##
sel.NA <- is.na(TE)
if (any(sel.NA) & !missing.median &
!missing.q1 & !missing.q3 &
!missing.min & !missing.max &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(q1) & !is.na(q3) &
!is.na(min) & !is.na(max)
approx.TE[j] <- "iqr.range"
if (is.null(n.c))
TE[j] <- mean.sd.iqr.range(n.e[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.iqr.range(n.c[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
else
TE[j] <- mean.sd.iqr.range(n.e[j] + n.c[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
}
##
## Use IQR
##
sel.NA <- is.na(TE)
if (any(sel.NA) & !missing.median &
!missing.q1 & !missing.q3 &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(q1) & !is.na(q3)
approx.TE[j] <- "iqr"
if (is.null(n.c))
TE[j] <- mean.sd.iqr(n.e[j], median[j], q1[j], q3[j], method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.iqr(n.c[j], median[j], q1[j], q3[j], method.mean)$mean
else
TE[j] <- mean.sd.iqr(n.e[j] + n.c[j], median[j], q1[j], q3[j],
method.mean)$mean
}
##
## Use range
##
sel.NA <- is.na(TE)
if (any(sel.NA) & !missing.median &
!missing.min & !missing.max &
!(is.null(n.e) & is.null(n.c))) {
j <- sel.NA & !is.na(median) & !is.na(min) & !is.na(max)
approx.TE[j] <- "range"
if (is.null(n.c))
TE[j] <- mean.sd.range(n.e[j], median[j], min[j], max[j],
method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.range(n.c[j], median[j], min[j], max[j],
method.mean)$mean
else
TE[j] <- mean.sd.range(n.e[j] + n.c[j], median[j], min[j], max[j],
method.mean)$mean
}
}
else {
j <- 0
for (i in approx.TE) {
j <- j + 1
##
if (i == "ci")
TE[j] <- TE.seTE.ci(lower[j], upper[j], level.ci[j])$TE
else if (i == "iqr.range")
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.TE' = \"iqr.range\".",
call. = FALSE)
else if (is.null(n.c))
TE[j] <- mean.sd.iqr.range(n.e[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.iqr.range(n.c[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
else
TE[j] <- mean.sd.iqr.range(n.e[j] + n.c[j], median[j], q1[j], q3[j],
min[j], max[j], method.mean)$mean
else if (i == "iqr") {
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.TE' = \"iqr\".",
call. = FALSE)
else if (is.null(n.c))
TE[j] <- mean.sd.iqr(n.e[j], median[j], q1[j], q3[j], method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.iqr(n.c[j], median[j], q1[j], q3[j], method.mean)$mean
else
TE[j] <- mean.sd.iqr(n.e[j] + n.c[j], median[j], q1[j], q3[j],
method.mean)$mean
}
else if (i == "range") {
cat(paste0("Use 'range' for study", j, "\n"))
if (is.null(n.e) & is.null(n.c))
stop("Sample size needed if argument 'approx.TE' = \"range\".",
call. = FALSE)
else if (is.null(n.c))
TE[j] <- mean.sd.range(n.e[j], median[j], min[j], max[j],
method.mean)$mean
else if (is.null(n.e))
TE[j] <- mean.sd.range(n.c[j], median[j], min[j], max[j],
method.mean)$mean
else
TE[j] <- mean.sd.range(n.e[j] + n.c[j], median[j], min[j], max[j],
method.mean)$mean
}
}
}
##
if (keepdata) {
if (!isCol(data, ".subset")) {
data$.TE <- TE
data$.seTE <- seTE
}
else {
data$.TE[data$.subset] <- TE
data$.seTE[data$.subset] <- seTE
}
}
##
##
## (9) Check standard errors
##
##
TE <- int2num(TE)
seTE <- int2num(seTE)
##
if (any(seTE[!is.na(seTE)] <= 0)) {
if (warn)
warning("Zero values in seTE replaced by NAs.")
seTE[!is.na(seTE) & seTE == 0] <- NA
}
##
tau2.calc <- NA
##
##
## (10) Do meta-analysis
##
##
k <- sum(!is.na(seTE[!exclude]))
##
if (!missing.id) {
id.incl <- id[!exclude]
k.study <- length(unique(id.incl[!is.na(seTE[!exclude])]))
}
else
k.study <- k
##
seTE.random.hakn.orig <- NULL
##
if (k == 0) {
TE.fixed <- NA
seTE.fixed <- NA
statistic.fixed <- NA
pval.fixed <- NA
lower.fixed <- NA
upper.fixed <- NA
w.fixed <- rep(0, k.all)
##
TE.random <- NA
seTE.random <- NA
statistic.random <- NA
pval.random <- NA
lower.random <- NA
upper.random <- NA
w.random <- rep(0, k.all)
if (hakn)
df.hakn <- NA
##
hc <- list(tau2 = NA, se.tau2 = NA, lower.tau2 = NA, upper.tau2 = NA,
tau = NA, lower.tau = NA, upper.tau = NA,
method.tau.ci = "", sign.lower.tau = "", sign.upper.tau = "",
##
Q = NA, df.Q = NA, pval.Q = NA,
H = NA, lower.H = NA, upper.H = NA,
I2 = NA, lower.I2 = NA, upper.I2 = NA,
##
Q.resid = NA, df.Q.resid = NA, pval.Q.resid = NA,
H.resid = NA, lower.H.resid = NA, upper.H.resid = NA,
I2.resid = NA, lower.I2.resid = NA, upper.I2.resid = NA)
}
else {
## At least two studies to perform Hartung-Knapp method
if (k == 1 & hakn)
hakn <- FALSE
##
## Estimate tau-squared
##
hc <- hetcalc(TE[!exclude], seTE[!exclude],
method.tau, method.tau.ci,
TE.tau, level.ma,
control = control, id = id)
##
if (by & tau.common) {
## Estimate common tau-squared across subgroups
hcc <- hetcalc(TE[!exclude], seTE[!exclude],
method.tau, method.tau.ci,
TE.tau, level.ma,
subgroup = subgroup,
control = control, id = id)
}
##
## Different calculations for three-level models
##
if (!three.level) {
##
## Classic meta-analysis
##
if (is.null(tau.preset))
tau2.calc <- if (is.na(sum(hc$tau2))) 0 else sum(hc$tau2)
else {
tau2.calc <- tau.preset^2
##
hc$tau2 <- tau.preset^2
hc$se.tau2 <- hc$lower.tau2 <- hc$upper.tau2 <- NA
hc$tau <- tau.preset
hc$lower.tau <- hc$upper.tau <- NA
hc$method.tau.ci <- ""
hc$sign.lower.tau <- ""
hc$sign.upper.tau <- ""
}
##
## Fixed effect estimate (Cooper & Hedges, 1994, p. 265-6)
##
w.fixed <- 1 / seTE^2
w.fixed[is.na(w.fixed) | is.na(TE) | exclude] <- 0
##
TE.fixed <- weighted.mean(TE, w.fixed, na.rm = TRUE)
seTE.fixed <- sqrt(1 / sum(w.fixed, na.rm = TRUE))
##
ci.f <- ci(TE.fixed, seTE.fixed, level = level.ma,
null.effect = null.effect)
statistic.fixed <- ci.f$statistic
pval.fixed <- ci.f$p
lower.fixed <- ci.f$lower
upper.fixed <- ci.f$upper
##
## Random effects estimate (Cooper & Hedges, 1994, p. 265, 274-5
##
w.random <- 1 / (seTE^2 + sum(tau2.calc, na.rm = TRUE))
w.random[is.na(w.random) | is.na(TE) | exclude] <- 0
##
TE.random <- weighted.mean(TE, w.random, na.rm = TRUE)
seTE.random <- sqrt(1 / sum(w.random, na.rm = TRUE))
}
else {
##
## Three-level meta-analysis
##
## No fixed effect method for three-level model
##
if (fixed) {
if (!missing.fixed)
warning("Fixed effect model not calculated for three-level model.",
call. = FALSE)
fixed <- FALSE
}
##
w.fixed <- rep_len(NA, length(seTE))
##
TE.fixed <- seTE.fixed <- lower.fixed <- upper.fixed <-
statistic.fixed <- pval.fixed <- NA
##
## Conduct three-level meta-analysis
##
sel.4 <- !is.na(TE) & !is.na(seTE)
TE.4 <- TE[sel.4]
seTE.4 <- seTE[sel.4]
id.4 <- id[sel.4]
idx.4 <- idx[sel.4]
##
m4 <- rma.mv(TE.4, seTE.4^2,
method = method.tau, test = ifelse(hakn, "t", "z"),
random = ~ 1 | id.4 / idx.4,
control = control)
##
w.random <- rep_len(NA, length(TE))
w.random[sel.4] <- weights(m4, type = "rowsum")
w.random[is.na(w.random)] <- 0
##
TE.random <- m4$b
seTE.random <- m4$se
##
tau2.calc <- sum(m4$tau2)
##
## Confidence interval for three-level model
##
ci.r <- list(statistic = m4$zval, p = m4$pval,
lower = m4$ci.lb, upper = m4$ci.ub)
df.hakn <- k - 1
##
## No adhoc method for three-level models
##
if (!missing(adhoc.hakn) && adhoc.hakn != "") {
warning("Ad hoc variance correction not implemented ",
"for three-level model.",
call. = FALSE)
adhoc.hakn <- ""
}
}
##
## Hartung-Knapp adjustment (not three-level model)
##
if (hakn & !three.level) {
## alpha <- (1 - level.ma) / 2
df.hakn <- k - 1
q <- 1 / (k - 1) * sum(w.random * (TE - TE.random)^2, na.rm = TRUE)
##
seTE.random.classic <- seTE.random
seTE.random <- sqrt(q / sum(w.random))
##
if (adhoc.hakn == "se") {
##
## Variance correction if SE_HK < SE_notHK (Knapp and Hartung, 2003),
## i.e., if q < 1
##
if (q < 1) {
seTE.random.hakn.orig <- seTE.random
seTE.random <- seTE.random.classic
}
}
else if (adhoc.hakn == "ci") {
##
## Use wider confidence interval, i.e., confidence interval
## from classic random effects meta-analysis if CI_HK is
## smaller
## (Wiksten et al., 2016; Jackson et al., 2017, hybrid 2)
##
ci.hk <- ci(TE.random, seTE.random, level = level.ma, df = df.hakn)
ci.re <- ci(TE.random, seTE.random.classic, level = level.ma)
##
width.hk <- ci.hk$upper - ci.hk$lower
width.re <- ci.re$upper - ci.re$lower
##
if (width.hk < width.re) {
seTE.random.hakn.orig <- seTE.random
seTE.random <- seTE.random.classic
df.hakn <- NA
}
}
else if (adhoc.hakn == "iqwig6") {
##
## Variance correction if CI_HK < CI_DL (IQWiG, 2020)
##
ci.hk <- ci(TE.random, seTE.random, level = level.ma, df = df.hakn)
##
m.dl <- metagen(TE, seTE, method.tau = "DL", method.tau.ci = "",
hakn = FALSE)
ci.dl <- ci(m.dl$TE.random, m.dl$seTE.random, level = level.ma)
##
width.hk <- ci.hk$upper - ci.hk$lower
width.dl <- ci.dl$upper - ci.dl$lower
##
if (width.hk < width.dl) {
seTE.random.hakn.orig <- seTE.random
seTE.random <- seTE.random.classic
}
}
##
ci.r <- ci(TE.random, seTE.random, level = level.ma, df = df.hakn,
null.effect = null.effect)
}
else if (!three.level)
ci.r <- ci(TE.random, seTE.random, level = level.ma,
null.effect = null.effect)
##
statistic.random <- ci.r$statistic
pval.random <- ci.r$p
lower.random <- ci.r$lower
upper.random <- ci.r$upper
}
##
## Individual study results
##
ci.study <- ci(TE, seTE, level = level,
df = if (method.ci == "t") df else NULL,
null.effect = null.effect)
##
## Prediction interval
##
if (k >= 3) {
seTE.predict <- sqrt(seTE.random^2 + tau2.calc)
ci.p <- ci(TE.random, seTE.predict, level.predict, k - 2)
p.lower <- ci.p$lower
p.upper <- ci.p$upper
}
else {
seTE.predict <- NA
p.lower <- NA
p.upper <- NA
}
##
## Calculate Rb (but not for three-level model)
##
if (length(tau2.calc) == 1)
Rbres <- Rb(seTE[!is.na(seTE)], seTE.random,
tau2.calc, hc$Q, hc$df.Q, level.ma)
else
Rbres <- list(TE = NA, lower = NA, upper = NA)
##
##
## (11) Generate R object
##
##
if (missing(detail.tau) && k != k.study)
detail.tau <- c("level 2", "level 1")
##
res <- list(studlab = studlab,
##
TE = TE, seTE = seTE,
lower = ci.study$lower, upper = ci.study$upper,
zval = ci.study$statistic,
statistic = ci.study$statistic,
pval = ci.study$p,
df = if (method.ci == "t") df else rep_len(NA, length(TE)),
w.fixed = w.fixed, w.random = w.random,
id = id,
##
TE.fixed = TE.fixed, seTE.fixed = seTE.fixed,
lower.fixed = lower.fixed, upper.fixed = upper.fixed,
zval.fixed = statistic.fixed,
statistic.fixed = statistic.fixed, pval.fixed = pval.fixed,
##
TE.random = TE.random, seTE.random = seTE.random,
lower.random = lower.random, upper.random = upper.random,
zval.random = statistic.random,
statistic.random = statistic.random, pval.random = pval.random,
##
null.effect = null.effect,
##
seTE.predict = seTE.predict,
lower.predict = p.lower, upper.predict = p.upper,
level.predict = level.predict,
##
k = k, k.study = k.study, k.all = k.all,
Q = hc$Q, df.Q = hc$df.Q, pval.Q = hc$pval.Q,
tau2 = hc$tau2, se.tau2 = hc$se.tau2,
lower.tau2 = hc$lower.tau2, upper.tau2 = hc$upper.tau2,
tau = hc$tau, lower.tau = hc$lower.tau, upper.tau = hc$upper.tau,
method.tau.ci = hc$method.tau.ci,
sign.lower.tau = hc$sign.lower.tau,
sign.upper.tau = hc$sign.upper.tau,
##
H = hc$H, lower.H = hc$lower.H, upper.H = hc$upper.H,
##
I2 = hc$I2, lower.I2 = hc$lower.I2, upper.I2 = hc$upper.I2,
##
Rb = Rbres$TE, lower.Rb = Rbres$lower, upper.Rb = Rbres$upper,
##
method.mean = method.mean,
approx.TE = approx.TE,
approx.seTE = approx.seTE,
##
sm = sm, method = "Inverse",
level = level,
level.ma = level.ma,
fixed = fixed,
random = random,
overall = overall,
overall.hetstat = overall.hetstat,
hakn = hakn, adhoc.hakn = adhoc.hakn,
df.hakn = if (hakn) df.hakn else NA,
seTE.random.hakn.orig = seTE.random.hakn.orig,
method.tau = method.tau, method.tau.ci = hc$method.tau.ci,
tau.preset = tau.preset,
TE.tau =
if (!missing(TE.tau) & method.tau == "DL") TE.tau else NULL,
tau.common = tau.common,
detail.tau = detail.tau,
prediction = prediction,
method.bias = method.bias,
n.e = n.e,
n.c = n.c,
##
text.fixed = text.fixed, text.random = text.random,
text.predict = text.predict,
text.w.fixed = text.w.fixed, text.w.random = text.w.random,
##
title = title, complab = complab, outclab = outclab,
label.e = label.e,
label.c = label.c,
label.left = label.left,
label.right = label.right,
##
data = if (keepdata) data else NULL,
subset = if (keepdata) subset else NULL,
exclude = if (!missing.exclude) exclude else NULL,
##
print.subgroup.name = print.subgroup.name,
sep.subgroup = sep.subgroup,
test.subgroup = test.subgroup,
##
three.level = three.level,
##
warn = warn,
call = match.call(),
backtransf = backtransf,
pscale = pscale,
irscale = irscale, irunit = irunit,
control = control,
version = packageDescription("meta")$Version)
##
class(res) <- c(fun, "meta")
##
## Add results from subgroup analysis
##
if (by) {
res$subgroup <- subgroup
res$subgroup.name <- subgroup.name
##
if (!tau.common) {
res <- c(res, subgroup(res))
if (three.level) {
res$Q.b.random <- NA
res$df.Q.b <- NA
res$pval.Q.b.random <- NA
}
}
else if (!is.null(tau.preset))
res <- c(res, subgroup(res, tau.preset))
else {
if (three.level)
res <- c(res, subgroup(res, NULL,
factor(res$subgroup, bylevs(res$subgroup))))
else
res <- c(res, subgroup(res, hcc$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$sign.lower.tau
res$sign.upper.tau.resid <- hcc$sign.upper.tau
##
res$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$n.w <- NULL
res$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
}
