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meta (version 3.0-1)

metacor: Meta-analysis of correlations

Description

Calculation of fixed 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,
        sm="ZCOR",
        level=0.95, level.comb=level,
        comb.fixed=TRUE, comb.random=TRUE,
        hakn=FALSE,
        method.tau="DL", tau.preset=NULL, TE.tau=NULL,
        tau.common=FALSE,
        prediction=FALSE, level.predict=level,
        method.bias="linreg",
        title="", complab="", outclab="",
        byvar, bylab, print.byvar=TRUE,
        keepdata=TRUE
        )

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.
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.
level.comb
The level used to calculate confidence intervals for pooled estimates.
comb.fixed
A logical indicating whether a fixed effect meta-analysis should be conducted.
comb.random
A logical indicating whether a random effects meta-analysis should be conducted.
prediction
A logical indicating whether a prediction interval should be printed.
level.predict
The level used to calculate prediction interval for a new study.
hakn
A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.
method.tau
A character string indicating which method is used to estimate the between-study variance tau-squared. Either "DL", "REML", "ML", "HS", "SJ", "HE", or "EB"
tau.preset
Prespecified value for between-study variance tau-squared.
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.bias
A character string indicating which test is to be used. Either "rank", "linreg", or "mm", can be abbreviated.
title
Title of meta-analysis / systematic review.
complab
Comparison label.
outclab
Outcome label.
byvar
An optional vector containing grouping information (must be of same length as event.e).
bylab
A character string with a label for the grouping variable.
print.byvar
A logical indicating whether the name of the grouping variable should be printed in front of the group labels.
keepdata
A logical indicating whether original data (set) should be kept in meta object.

Value

  • An object of class c("metacor", "meta") with corresponding print, summary, plot function. The object is a list containing the following components:
  • cor, n, studlab,
  • sm, level, level.comb,
  • comb.fixed, comb.random,
  • hakn, method.tau, tau.preset, TE.tau, method.bias,
  • tau.common, title, complab, outclab,
  • byvar, bylab, print.byvarAs defined above.
  • TE, seTEEither Fisher's z transformation of correlations (sm="ZCOR") or correlations (sm="COR") for individual studies.
  • w.fixed, w.randomWeight of individual studies (in fixed and random effects model).
  • TE.fixed, seTE.fixedEstimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (fixed effect model).
  • lower.fixed, upper.fixedLower and upper confidence interval limits (fixed effect model).
  • zval.fixed, pval.fixedz-value and p-value for test of overall effect (fixed effect model).
  • TE.random, seTE.randomEstimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (random effects model).
  • lower.random, upper.randomLower and upper confidence interval limits (random effects model).
  • zval.random, pval.randomz-value or t-value and corresponding p-value for test of overall effect (random effects model).
  • prediction, level.predictAs defined above.
  • seTE.predictStandard error utilised for prediction interval.
  • lower.predict, upper.predictLower and upper limits of prediction interval.
  • kNumber of studies combined in meta-analysis.
  • QHeterogeneity statistic Q.
  • tauSquare-root of between-study variance.
  • se.tauStandard error of square-root of between-study variance.
  • CScaling factor utilised internally to calculate common tau-squared across subgroups.
  • methodA character string indicating method used for pooling: "Inverse"
  • df.haknDegrees of freedom for test of treatment effect for Hartung-Knapp method (only if hakn=TRUE).
  • keepdataAs defined above.
  • dataOriginal data (set) used in function call (if keepdata=TRUE).
  • subsetInformation on subset of original data used in meta-analysis (if keepdata=TRUE).
  • callFunction call.
  • versionVersion of R package meta used to create object.

Details

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.

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 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.

If R package metafor (Viechtbauer 2010) is installed, the following statistical methods are also available.

For the random effects model (argument comb.random=TRUE), the method by Hartung and Knapp (Knapp, Hartung 2003) is used to adjust test statistics and confidence intervals if argument hakn=TRUE (internally R function rma.uni of R package metafor is called).

Several methods are available to estimate the between-study variance $\tau^2$ (argument method.tau):

  • DerSimonian-Laird estimator (method.tau="DL") (default)
  • 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 all but the DerSimonian-Laird method the R function rma.uni of R package metafor is called internally. See help page of R function rma.uni for more details on the various methods to estimate between-study variance $\tau^2$.

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.

References

Cooper H, Hedges LV, Valentine JC (2009), The Handbook of Research Synthesis and Meta-Analysis, 2nd Edition. New York: Russell Sage Foundation. 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 .

Viechtbauer W (2010), Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48.

See Also

update.meta, metacont, metagen, print.meta

Examples

Run this code
metacor(c(0.85, 0.7, 0.95), c(20, 40, 10))
forest(metacor(c(0.85, 0.7, 0.95), c(20, 40, 10)))

metacor(c(0.85, 0.7, 0.95), c(20, 40, 10), sm="cor")

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