meta (version 1.6-1)

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,
        title="", complab="", outclab="",
        byvar, bylab, print.byvar=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.

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.

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,
• byvar, bylab, print.byvar
  As defined above.
• TE, seTE
  Either Fisher's z transformation of correlations (sm="ZCOR") or correlations (sm="COR") for individual studies.
• w.fixed, w.random
  Weight of individual studies (in fixed and random effects model).
• TE.fixed, seTE.fixed
  Estimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (fixed effect model).
• TE.random, seTE.random
  Estimated overall effect (Fisher's z transformation of correlation or correlation) and its standard error (random effects model).
• k
  Number of studies combined in meta-analysis.
• Q
  Heterogeneity statistic Q.
• tau
  Square-root of between-study variance (moment estimator of DerSimonian-Laird).
• method
  A character string indicating method used for pooling: "Inverse"
• call
  Function call.
• version
  Version 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 proportions (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.

References

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

See Also

metacont, metagen, print.meta

Examples

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")