metacor: Meta-analysis of correlations

In meta: General Package for Meta-Analysis

Meta-analysis of correlations

Description

Calculation of common effect and random effects estimates for meta-analyses with correlations; inverse variance weighting is used for pooling.

Usage

metacor(
  cor,
  n,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  cluster = NULL,
  rho = 0,
  sm = gs("smcor"),
  level = gs("level"),
  common = gs("common"),
  random = gs("random") | !is.null(tau.preset),
  overall = common | random,
  overall.hetstat = if (is.null(gs("overall.hetstat"))) common | random else
    gs("overall.hetstat"),
  prediction = gs("prediction") | !missing(method.predict),
  method.tau = gs("method.tau"),
  method.tau.ci = gs("method.tau.ci"),
  level.hetstat = gs("level.hetstat"),
  tau.preset = NULL,
  TE.tau = NULL,
  tau.common = gs("tau.common"),
  method.I2 = gs("method.I2"),
  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"),
  seed.predict = NULL,
  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 = "",
  label.left = gs("label.left"),
  label.right = gs("label.right"),
  col.label.left = gs("col.label.left"),
  col.label.right = gs("col.label.right"),
  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"),
  seed.predict.subgroup = NULL,
  byvar,
  adhoc.hakn,
  keepdata = gs("keepdata"),
  warn.deprecated = gs("warn.deprecated"),
  control = NULL,
  ...
)

Arguments

cor	Correlation.
n	Number of observations.
studlab	An optional vector with study labels.
data	An optional data frame containing the study information, i.e., cor and n.
subset	An optional vector specifying a subset of studies to be used.
exclude	An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
cluster	An optional vector specifying which estimates come from the same cluster resulting in the use of a three-level meta-analysis model.
rho	Assumed correlation of estimates within a cluster.
sm	A character string indicating which summary measure ("ZCOR" or "COR") is to be used for pooling of studies.
level	The level used to calculate confidence intervals for individual studies.
common	A logical indicating whether a common effect meta-analysis should be conducted.
random	A logical indicating whether a random effects meta-analysis should be conducted.
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.
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.
prediction	A logical indicating whether a prediction interval should be printed.
method.tau	A character string indicating which method is used to estimate the between-study variance \tau^2 and its square root \tau (see meta-package).
method.tau.ci	A character string indicating which method is used to estimate the confidence interval of \tau^2 and \tau (see meta-package).
level.hetstat	The level used to calculate confidence intervals for heterogeneity statistics.
tau.preset	Prespecified value for the square root of the between-study variance \tau^2.
TE.tau	Overall treatment effect used to estimate the between-study variance tau-squared.
tau.common	A logical indicating whether tau-squared should be the same across subgroups.
method.I2	A character string indicating which method is used to estimate the heterogeneity statistic I^2. Either "Q" or "tau2", can be abbreviated (see meta-package).
level.ma	The level used to calculate confidence intervals for meta-analysis estimates.
method.random.ci	A character string indicating which method is used to calculate confidence interval and test statistic for random effects estimate (see meta-package).
adhoc.hakn.ci	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).
level.predict	The level used to calculate prediction interval for a new study.
method.predict	A character string indicating which method is used to calculate a prediction interval (see meta-package).
adhoc.hakn.pi	A character string indicating whether an ad hoc variance correction should be applied for prediction interval (see meta-package).
seed.predict	A numeric value used as seed to calculate bootstrap prediction interval (see meta-package).
null.effect	A numeric value specifying the effect under the null hypothesis.
method.bias	A character string indicating which test is to be used. Either "Begg", "Egger", or "Thompson", can be abbreviated. See function metabias.
backtransf	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.
text.common	A character string used in printouts and forest plot to label the pooled common effect estimate.
text.random	A character string used in printouts and forest plot to label the pooled random effects estimate.
text.predict	A character string used in printouts and forest plot to label the prediction interval.
text.w.common	A character string used to label weights of common effect model.
text.w.random	A character string used to label weights of random effects model.
title	Title of meta-analysis / systematic review.
complab	Comparison label.
outclab	Outcome label.
label.left	Graph label on left side of null effect in forest plot.
label.right	Graph label on right side of null effect in forest plot.
col.label.left	The colour of the graph label on the left side of the null effect.
col.label.right	The colour of the graph label on the right side of the null effect.
subgroup	An optional vector to conduct a meta-analysis with subgroups.
subgroup.name	A character string with a name for the subgroup variable.
print.subgroup.name	A logical indicating whether the name of the subgroup variable should be printed in front of the group labels.
sep.subgroup	A character string defining the separator between name of subgroup variable and subgroup label.
test.subgroup	A logical value indicating whether to print results of test for subgroup differences.
prediction.subgroup	A logical indicating whether prediction intervals should be printed for subgroups.
seed.predict.subgroup	A numeric vector providing seeds to calculate bootstrap prediction intervals within subgroups. Must be of same length as the number of subgroups.
byvar	Deprecated argument (replaced by 'subgroup').
adhoc.hakn	Deprecated argument (replaced by 'adhoc.hakn.ci').
keepdata	A logical indicating whether original data (set) should be kept in meta object.
warn.deprecated	A logical indicating whether warnings should be printed if deprecated arguments are used.
control	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).

Details

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., 2009, 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., 2009, 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 utilised 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.

Subgroup analysis

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.

Exclusion of studies from meta-analysis

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.

Presentation of meta-analysis results

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.

Value

An object of class c("metacor", "meta") with corresponding generic functions (see meta-object).

Note

The function metagen is called internally to calculate individual and overall treatment estimates and standard errors.

Author(s)

Guido Schwarzer [e-mail]

References

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

See Also

meta-package, update.meta, metacont, metagen, print.meta

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

## Not run: 
# Identical forest plots (as back transformation is the identity
# transformation)
forest(m2)
forest(m2, backtransf = FALSE)

## End(Not run)

meta documentation built on Oct. 31, 2024, 5:07 p.m.