Calculation of common effect and random effects estimates for meta-analyses with correlations; inverse variance weighting is used for pooling.
metacor(
cor,
n,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
cluster = NULL,
sm = gs("smcor"),
level = gs("level"),
common = gs("common"),
random = gs("random") | !is.null(tau.preset),
overall = common | random,
overall.hetstat = common | random,
prediction = gs("prediction") | !missing(method.predict),
method.tau = gs("method.tau"),
method.tau.ci = gs("method.tau.ci"),
tau.preset = NULL,
TE.tau = NULL,
tau.common = gs("tau.common"),
level.ma = gs("level.ma"),
method.random.ci = gs("method.random.ci"),
adhoc.hakn.ci = gs("adhoc.hakn.ci"),
level.predict = gs("level.predict"),
method.predict = gs("method.predict"),
adhoc.hakn.pi = gs("adhoc.hakn.pi"),
null.effect = 0,
method.bias = gs("method.bias"),
backtransf = gs("backtransf"),
text.common = gs("text.common"),
text.random = gs("text.random"),
text.predict = gs("text.predict"),
text.w.common = gs("text.w.common"),
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"),
prediction.subgroup = gs("prediction.subgroup"),
byvar,
adhoc.hakn,
keepdata = gs("keepdata"),
warn.deprecated = gs("warn.deprecated"),
control = NULL,
...
)An object of class c("metacor", "meta") with corresponding
generic functions (see meta-object).
Correlation.
Number of observations.
An optional vector with study labels.
An optional data frame containing the study information, i.e., cor and n.
An optional vector specifying a subset of studies to be used.
An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
An optional vector specifying which estimates come from the same cluster resulting in the use of a three-level meta-analysis model.
A character string indicating which summary measure
("ZCOR" or "COR") is to be used for pooling of
studies.
The level used to calculate confidence intervals for individual studies.
A logical indicating whether a common effect meta-analysis should be conducted.
A logical indicating whether a random effects meta-analysis should be conducted.
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.
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.
A logical indicating whether a prediction interval should be printed.
A character string indicating which method is
used to estimate the between-study variance \(\tau^2\) and its
square root \(\tau\) (see meta-package).
A character string indicating which method is
used to estimate the confidence interval of \(\tau^2\) and
\(\tau\) (see meta-package).
Prespecified value for the square root of the between-study variance \(\tau^2\).
Overall treatment effect used to estimate the between-study variance tau-squared.
A logical indicating whether tau-squared should be the same across subgroups.
The level used to calculate confidence intervals for meta-analysis estimates.
A character string indicating which method
is used to calculate confidence interval and test statistic for
random effects estimate (see meta-package).
A character string indicating whether an
ad hoc variance correction should be applied in the case
of an arbitrarily small Hartung-Knapp variance estimate (see
meta-package).
The level used to calculate prediction interval for a new study.
A character string indicating which method is
used to calculate a prediction interval (see
meta-package).
A character string indicating whether an
ad hoc variance correction should be applied for
prediction interval (see meta-package).
A numeric value specifying the effect under the null hypothesis.
A character string indicating which test is to
be used. Either "Begg", "Egger", or
"Thompson", can be abbreviated. See function
metabias.
A logical indicating whether results for Fisher's
z transformed correlations (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.
A character string used in printouts and forest plot to label the pooled common effect estimate.
A character string used in printouts and forest plot to label the pooled random effects estimate.
A character string used in printouts and forest plot to label the prediction interval.
A character string used to label weights of common effect model.
A character string used to label weights of random effects model.
Title of meta-analysis / systematic review.
Comparison label.
Outcome label.
An optional vector to conduct a meta-analysis with subgroups.
A character string with a name for the subgroup variable.
A logical indicating whether the name of the subgroup variable should be printed in front of the group labels.
A character string defining the separator between name of subgroup variable and subgroup label.
A logical value indicating whether to print results of test for subgroup differences.
A logical indicating whether prediction intervals should be printed for subgroups.
Deprecated argument (replaced by 'subgroup').
Deprecated argument (replaced by 'adhoc.hakn.ci').
A logical indicating whether original data (set) should be kept in meta object.
A logical indicating whether warnings should be printed if deprecated arguments are used.
An optional list to control the iterative process to
estimate the between-study variance \(\tau^2\). This argument
is passed on to rma.uni.
Additional arguments (to catch deprecated arguments).
Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de
Common effect and random effects meta-analysis of correlations based
either on Fisher's z transformation of correlations (sm =
"ZCOR") or direct combination of (untransformed) correlations
(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.
A three-level random effects meta-analysis model (Van den Noortgate
et al., 2013) is utilized if argument cluster is used and at
least one cluster provides more than one estimate. Internally,
rma.mv is called to conduct the analysis and
weights.rma.mv with argument type =
"rowsum" is used to calculate random effects weights.
Default settings are utilised for several arguments (assignments
using gs function). These defaults can be changed for
the current R session using the settings.meta
function.
Furthermore, R function update.meta can be used to
rerun a meta-analysis with different settings.
Argument subgroup can be used to conduct subgroup analysis for
a categorical covariate. The metareg function can be
used instead for more than one categorical covariate or continuous
covariates.
Arguments subset and exclude can be used to exclude
studies from the meta-analysis. Studies are removed completely from
the meta-analysis using argument subset, while excluded
studies are shown in printouts and forest plots using argument
exclude (see Examples in metagen).
Meta-analysis results are the same for both arguments.
Internally, both common effect and random effects models are
calculated regardless of values choosen for arguments
common and random. Accordingly, the estimate
for the random effects model can be extracted from component
TE.random of an object of class "meta" even if
argument random = FALSE. However, all functions in R
package meta will adequately consider the values for
common and random. E.g. functions
print.meta and forest.meta will not
print results for the random effects model if random =
FALSE.
A prediction interval will only be shown if prediction =
TRUE.
Cooper H, Hedges LV, Valentine JC (2009): The Handbook of Research Synthesis and Meta-Analysis, 2nd Edition. New York: Russell Sage Foundation
Van den Noortgate W, López-López JA, Marín-Martínez F, Sánchez-Meca J (2013): Three-level meta-analysis of dependent effect sizes. Behavior Research Methods, 45, 576--94
meta-package, update.meta,
metacont, metagen,
print.meta
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
if (FALSE) {
# Identical forest plots (as back transformation is the identity
# transformation)
forest(m2)
forest(m2, backtransf = FALSE)
}
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