metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, studlab, data=NULL, subset=NULL, sm=.settings$smcont, pooledvar=.settings$pooledvar,
method.smd=.settings$method.smd, sd.glass=.settings$sd.glass,
exact.smd=.settings$exact.smd, level=.settings$level, level.comb=.settings$level.comb, comb.fixed=.settings$comb.fixed, comb.random=.settings$comb.random, hakn=.settings$hakn, method.tau=.settings$method.tau, tau.preset=NULL, TE.tau=NULL, tau.common=.settings$tau.common, prediction=.settings$prediction, level.predict=.settings$level.predict, method.bias=.settings$method.bias, backtransf=.settings$backtransf, title=.settings$title, complab=.settings$complab, outclab="", label.e=.settings$label.e, label.c=.settings$label.c, label.left=.settings$label.left, label.right=.settings$label.right, byvar, bylab, print.byvar=.settings$print.byvar,
byseparator=.settings$byseparator, keepdata=.settings$keepdata, warn=.settings$warn)"DL", "PM", "REML", "ML", "HS",
"SJ", "HE", or "EB", can be abbreviated."rank", "linreg", or "mm", can
be abbreviated. See function metabiassm="ROM") should be back transformed in printouts
and plots. If TRUE (default), results will be presented as ratio
of means; otherwise log ratio of means will be shown."MD", "SMD", or "ROM") is to be used for
pooling of studies.sm="MD").sm="SMD"). Either "Hedges" for Hedges' g (default),
"Cohen" for Cohen's d, or "Glass" for Glass' delta,
can be abbreviated."control" using
the standard deviation in the control group (sd.c) or
"experimental" using the standard deviation in the
experimental group (sd.e), can be abbreviated.n.e).c("metacont", "meta") with corresponding
print, summary, plot function. The object is a
list containing the following components:Three different types of summary measures are available for continuous outcomes:
sm="MD")
sm="SMD")
sm="ROM")
Meta-analysis of ratio of means -- also called response ratios -- is described in Hedges et al. (1999) and Friedrich et al. (2008). For the standardised mean difference three methods are implemented:
method.smd="Hedges") - see Hedges (1981)
method.smd="Cohen") - see Cohen (1988)
method.smd="Glass") - see Glass (1976)
Hedges (1981) calculated the exact bias in Cohen's d which is a
ratio of gamma distributions with the degrees of freedom, i.e. total
sample size minus two, as argument. By default (argument
exact.smd=FALSE), an accurate approximation of this bias
provided in Hedges (1981) is utilised for Hedges' g as well as its
standard error; these approximations are also used in RevMan
5. Following Borenstein et al. (2009) these approximations are not
used in the estimation of Cohen's d. White and Thomas (2005) argued
that approximations are unnecessary with modern software and
accordingly promote to use the exact formulae; this is possible
using argument exact.smd=TRUE. For Hedges' g the exact
formulae are used to calculate the standardised mean difference as
well as the standard error; for Cohen's d the exact formula is only
used to calculate the standard error. In typical applications (with
sample sizes above 10), the differences between using the exact
formulae and the approximation will be minimal.
For Glass' delta, by default (argument sd.glass="control"),
the standard deviation in the control group (sd.c) is used in
the denominator of the standard mean difference. The standard
deviation in the experimental group (sd.e) can be used by
specifying sd.glass="experimental".
Calculations are conducted on the log scale for ratio of means
(sm="ROM"). Accordingly, list elements TE,
TE.fixed, and TE.random contain the logarithm of ratio
of means. In printouts and plots these values are back transformed
if argument backtransf=TRUE.
For several arguments defaults settings are utilised (assignments
with .settings$). 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.
The function metagen is called internally to calculate
individual and overall treatment estimates and standard errors.
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 metacont 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 method.tau) are also available:
method.tau="REML")
method.tau="ML")
method.tau="HS")
method.tau="SJ")
method.tau="HE")
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.
Cohen J (1988), Statistical Power Analysis for the Behavioral Sciences (second ed.), Lawrence Erlbaum Associates.
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation.
DerSimonian R & Laird N (1986), Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--88.
Friedrich JO, Adhikari NK, Beyene J (2008), The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: A simulation study. BMC Med Res Methodol, 8, 32.
Glass G (1976), Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3--8.
Hartung J & Knapp G (2001), On tests of the overall treatment effect in meta-analysis with normally distributed responses. Statistics in Medicine, 20, 1771--82. doi: 10.1002/sim.791 . Hedges LV (1981), Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107--28.
Hedges LV, Gurevitch J, Curtis PS (1999), The meta-analysis of response ratios in experimental ecology. Ecology, 80, 1150--6.
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--59.
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--85. Review Manager (RevMan) [Computer program]. Version 5.3. Copenhagen: The Nordic Cochrane Centre, The Cochrane Collaboration, 2014.
Viechtbauer W (2010), Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48.
White IR, Thomas J (2005), Standardized mean differences in individually-randomized and cluster-randomized trials, with applications to meta-analysis. Clinical Trials, 2, 141--51.
update.meta, metabin, metagendata(Fleiss93cont)
meta1 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont, sm="SMD")
meta1
forest(meta1)
meta2 <- metacont(Fleiss93cont$n.e, Fleiss93cont$mean.e,
Fleiss93cont$sd.e,
Fleiss93cont$n.c, Fleiss93cont$mean.c,
Fleiss93cont$sd.c,
sm="SMD")
meta2
data(amlodipine)
meta3 <- metacont(n.amlo, mean.amlo, sqrt(var.amlo),
n.plac, mean.plac, sqrt(var.plac),
data=amlodipine, studlab=study)
summary(meta3)
# Use pooled variance
#
meta4 <- metacont(n.amlo, mean.amlo, sqrt(var.amlo),
n.plac, mean.plac, sqrt(var.plac),
data=amlodipine, studlab=study,
pooledvar=TRUE)
summary(meta4)
# Use Cohen's d instead of Hedges' g as effect measure
#
meta5 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont,
sm="SMD", method.smd="Cohen")
meta5
# Use Glass' delta instead of Hedges' g as effect measure
#
meta6 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont,
sm="SMD", method.smd="Glass")
meta6
# Use Glass' delta based on the standard deviation in the experimental group
#
meta7 <- metacont(n.e, mean.e, sd.e, n.c, mean.c, sd.c, data=Fleiss93cont,
sm="SMD", method.smd="Glass", sd.glass="experimental")
meta7
# Calculate Hedges' g based on exact formulae
#
update(meta1, exact.smd=TRUE)
#
# Meta-analysis of response ratios (Hedges et al., 1999)
#
data(woodyplants)
meta8 <- metacont(n.elev, mean.elev, sd.elev,
n.amb, mean.amb, sd.amb,
data=woodyplants, sm="ROM")
summary(meta8)
summary(meta8, backtransf=FALSE)
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