Calculation of fixed 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,
sm=gs("smcor"),
level=gs("level"), level.comb=gs("level.comb"),
comb.fixed=gs("comb.fixed"), comb.random=gs("comb.random"),
hakn=gs("hakn"),
method.tau=gs("method.tau"), tau.preset=NULL, TE.tau=NULL,
tau.common=gs("tau.common"),
prediction=gs("prediction"), level.predict=gs("level.predict"),
null.effect=0,
method.bias=gs("method.bias"),
backtransf=gs("backtransf"),
title=gs("title"), complab=gs("complab"), outclab="",
byvar, bylab, print.byvar=gs("print.byvar"),
byseparator = gs("byseparator"),
keepdata=gs("keepdata")
)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.
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.
The level used to calculate confidence intervals for pooled estimates.
A logical indicating whether a fixed effect meta-analysis should be conducted.
A logical indicating whether a random effects meta-analysis should be conducted.
A logical indicating whether a prediction interval should be printed.
The level used to calculate prediction interval for a new study.
A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.
A character string indicating which method is used
to estimate the between-study variance \(\tau^2\). Either
"DL", "PM", "REML", "ML", "HS",
"SJ", "HE", or "EB", can be abbreviated.
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.
A numeric value specifying the effect under the null hypothesis.
A character string indicating which test is to be
used. Either "rank", "linreg", or "mm", 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.
Title of meta-analysis / systematic review.
Comparison label.
Outcome label.
An optional vector containing grouping information (must
be of same length as event.e).
A character string with a label for the grouping variable.
A logical indicating whether the name of the grouping variable should be printed in front of the group labels.
A character string defining the separator between label and levels of grouping variable.
A logical indicating whether original data (set) should be kept in meta object.
An object of class c("metacor", "meta") with corresponding
print, summary, and forest functions. The
object is a list containing the following components:
As defined above.
Either Fisher's z transformation of correlations
(sm="ZCOR") or correlations (sm="COR") for individual
studies.
Lower and upper confidence interval limits for individual studies.
z-value and p-value for test of treatment effect for individual studies.
Weight of individual studies (in fixed and random effects model).
Estimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (fixed effect model).
Lower and upper confidence interval limits (fixed effect model).
z-value and p-value for test of overall effect (fixed effect model).
Estimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (random effects model).
Lower and upper confidence interval limits (random effects model).
z-value or t-value and corresponding p-value for test of overall effect (random effects model).
As defined above.
Standard error utilised for prediction interval.
Lower and upper limits of prediction interval.
Number of studies combined in meta-analysis.
Heterogeneity statistic Q.
Square-root of between-study variance.
Standard error of square-root of between-study variance.
Scaling factor utilised internally to calculate common tau-squared across subgroups.
A character string indicating method used
for pooling: "Inverse"
Degrees of freedom for test of treatment effect for
Hartung-Knapp method (only if hakn=TRUE).
Levels of grouping variable - if byvar is not
missing.
Estimated treatment effect and
standard error in subgroups (fixed effect model) - if byvar
is not missing.
Lower and upper confidence
interval limits in subgroups (fixed effect model) - if
byvar is not missing.
z-value and p-value for test of
treatment effect in subgroups (fixed effect model) - if
byvar is not missing.
Estimated treatment effect and
standard error in subgroups (random effects model) - if
byvar is not missing.
Lower and upper confidence
interval limits in subgroups (random effects model) - if
byvar is not missing.
z-value or t-value and
corresponding p-value for test of treatment effect in subgroups
(random effects model) - if byvar is not missing.
Weight of subgroups (in fixed and
random effects model) - if byvar is not missing.
Degrees of freedom for test of treatment effect for
Hartung-Knapp method in subgroups - if byvar is not missing
and hakn=TRUE.
Harmonic mean of number of observations in
subgroups (for back transformation of Freeman-Tukey Double arcsine
transformation) - if byvar is not missing.
Number of observations in subgroups - if byvar is
not missing.
Number of studies combined within subgroups - if
byvar is not missing.
Number of all studies in subgroups - if byvar
is not missing.
Heterogeneity statistics within subgroups - if
byvar is not missing.
Overall within subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Overall within subgroups heterogeneity statistic Q
(based on random effects model) - if byvar is not missing
(only calculated if argument tau.common is TRUE).
Degrees of freedom for test of overall within
subgroups heterogeneity - if byvar is not missing.
Overall between subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Overall between subgroups heterogeneity statistic
Q (based on random effects model) - if byvar is not
missing.
Degrees of freedom for test of overall between
subgroups heterogeneity - if byvar is not missing.
Square-root of between-study variance within subgroups
- if byvar is not missing.
Scaling factor utilised internally to calculate common
tau-squared across subgroups - if byvar is not missing.
Heterogeneity statistic H within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic H within subgroups - if byvar is
not missing.
Heterogeneity statistic I2 within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups - if byvar is
not missing.
As defined above.
Original data (set) used in function call (if
keepdata=TRUE).
Information on subset of original data used in
meta-analysis (if keepdata=TRUE).
Function call.
Version of R package meta used to create object.
Fixed effect and random effects meta-analysis of correlations based
either on Fisher's z transformation of correlations
(sm="ZCOR") or direct combination of 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.
For several arguments defaults settings are utilised (assignments
using gs function). These defaults can be changed
using the settings.meta function.
Internally, both fixed effect and random effects models are
calculated regardless of values choosen for arguments
comb.fixed and comb.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 comb.random=FALSE. However, all functions in R
package meta will adequately consider the values for
comb.fixed and comb.random. E.g. function
print.meta will not print results for the random
effects model if comb.random=FALSE.
A prediction interval for treatment effect of a new study is
calculated (Higgins et al., 2009) if arguments prediction and
comb.random are TRUE.
R function update.meta can be used to redo the
meta-analysis of an existing metacor object by only specifying
arguments which should be changed.
For the random effects, the method by Hartung and Knapp (2003) is
used to adjust test statistics and confidence intervals if argument
hakn=TRUE.
The DerSimonian-Laird estimate (1986) is used in the random effects
model if method.tau="DL". The iterative Paule-Mandel method
(1982) to estimate the between-study variance is used if argument
method.tau="PM". Internally, R function paulemandel is
called which is based on R function mpaule.default from R package
metRology from S.L.R. Ellison <s.ellison at lgc.co.uk>.
If R package metafor (Viechtbauer 2010) is installed, the
following methods to estimate the between-study variance
\(\tau^2\) (argument method.tau) are also available:
Restricted maximum-likelihood estimator (method.tau="REML")
Maximum-likelihood estimator (method.tau="ML")
Hunter-Schmidt estimator (method.tau="HS")
Sidik-Jonkman estimator (method.tau="SJ")
Hedges estimator (method.tau="HE")
Empirical Bayes estimator (method.tau="EB").
For these methods the R function rma.uni of R package
metafor is called internally. See help page of R function
rma.uni for more details on these methods to estimate
between-study variance.
Cooper H, Hedges LV, Valentine JC (2009), The Handbook of Research Synthesis and Meta-Analysis, 2nd Edition. New York: Russell Sage Foundation.
DerSimonian R & Laird N (1986), Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--188.
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009), A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A, 172, 137--159.
Knapp G & Hartung J (2003), Improved Tests for a Random Effects Meta-regression with a Single Covariate. Statistics in Medicine, 22, 2693--710, doi: 10.1002/sim.1482 .
Paule RC & Mandel J (1982), Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377--385.
Viechtbauer W (2010), Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48.
# NOT RUN {
m1 <- metacor(c(0.85, 0.7, 0.95), c(20, 40, 10))
#
# Print correlations (back transformed from Fisher's z transformation)
#
m1
#
# Print Fisher's z transformed correlations
#
print(m1, backtransf=FALSE)
#
# Forest plot with back transformed correlations
#
forest(m1)
#
# Forest plot with Fisher's z transformed correlations
#
forest(m1, backtransf=FALSE)
m2 <- update(m1, sm="cor")
m2
# Identical forest plots (as back transformation is the identity transformation)
# forest(m2)
# forest(m2, backtransf=FALSE)
# }
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