Fixed and random effects meta-analysis based on estimates (e.g. log
hazard ratios) and their standard errors; inverse variance weighting
is used for pooling.
An optional data frame containing the study information.
subset
An optional vector specifying a subset of studies to be used.
sm
A character string indicating underlying summary measure,
e.g., "RD", "RR", "OR", "ASD",
"MD", "SMD".
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.
n.e
Number of observations in experimental group.
n.c
Number of observations in control group.
hakn
A logical indicating whether 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 τ^2. Either
"DL", "PM", "REML", "ML", "HS",
"SJ", "HE", or "EB", can be abbreviated.
tau.preset
Prespecified value for the square-root of the
between-study variance τ^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.bias
A character string indicating which test is to be
used. Either "rank", "linreg", or "mm", can
be abbreviated. See function metabias
backtransf
A logical indicating whether results should be
back transformed in printouts and plots. If backtransf=TRUE
(default), results for sm="OR" are printed as odds ratios
rather than log odds ratios and results for sm="ZCOR" are
printed as correlations rather than Fisher's z transformed
correlations, for example.
title
Title of meta-analysis / systematic review.
complab
Comparison label.
outclab
Outcome label.
label.e
Label for experimental group.
label.c
Label for control group.
label.left
Graph label on left side of forest plot.
label.right
Graph label on right side of forest plot.
byvar
An optional vector containing grouping information (must
be of same length as TE).
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.
warn
A logical indicating whether warnings should be printed
(e.g., if studies are excluded from meta-analysis due to zero
standard errors).
Details
Generic method for meta-analysis, only treatment estimates and their
standard error are needed. The method is useful, e.g., for pooling
of survival data (using log hazard ratio and standard errors as
input). The inverse variance method is used for pooling. By default,
the DerSimonian-Laird estimate (1986) is used in the random effects
model (method.tau="DL").
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.
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 metagen 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 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 τ^2
(argument method.tau) are also available:
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.
Value
An object of class c("metagen", "meta") with corresponding
print, summary, plot function. The object is a
list containing the following components:
Lower and upper confidence interval limits
for individual studies.
zval, pval
z-value and p-value for test of treatment
effect for individual studies.
w.fixed, w.random
Weight of individual studies (in fixed and
random effects model).
TE.fixed, seTE.fixed
Estimated overall treatment effect and
standard error (fixed effect model).
lower.fixed, upper.fixed
Lower and upper confidence interval limits
(fixed effect model).
zval.fixed, pval.fixed
z-value and p-value for test of
overall treatment effect (fixed effect model).
TE.random, seTE.random
Estimated overall treatment effect and
standard error (random effects model).
lower.random, upper.random
Lower and upper confidence interval limits
(random effects model).
zval.random, pval.random
z-value or t-value and corresponding
p-value for test of overall treatment effect (random effects
model).
prediction, level.predict
As defined above.
seTE.predict
Standard error utilised for prediction interval.
lower.predict, upper.predict
Lower and upper limits of prediction interval.
k
Number of studies combined in meta-analysis.
Q
Heterogeneity statistic.
df.Q
Degrees of freedom for heterogeneity statistic.
tau
Square-root of between-study variance.
se.tau
Standard error of square-root of between-study variance.
C
Scaling factor utilised internally to calculate common
tau-squared across subgroups.
method
Pooling method: "Inverse".
df.hakn
Degrees of freedom for test of treatment effect for
Hartung-Knapp method (only if hakn=TRUE).
bylevs
Levels of grouping variable - if byvar is not
missing.
TE.fixed.w, seTE.fixed.w
Estimated treatment effect and
standard error in subgroups (fixed effect model) - if byvar
is not missing.
lower.fixed.w, upper.fixed.w
Lower and upper confidence
interval limits in subgroups (fixed effect model) - if
byvar is not missing.
zval.fixed.w, pval.fixed.w
z-value and p-value for test of
treatment effect in subgroups (fixed effect model) - if
byvar is not missing.
TE.random.w, seTE.random.w
Estimated treatment effect and
standard error in subgroups (random effects model) - if
byvar is not missing.
lower.random.w, upper.random.w
Lower and upper confidence
interval limits in subgroups (random effects model) - if
byvar is not missing.
zval.random.w, pval.random.w
z-value or t-value and
corresponding p-value for test of treatment effect in subgroups
(random effects model) - if byvar is not missing.
w.fixed.w, w.random.w
Weight of subgroups (in fixed and
random effects model) - if byvar is not missing.
df.hakn.w
Degrees of freedom for test of treatment effect for
Hartung-Knapp method in subgroups - if byvar is not missing
and hakn=TRUE.
n.harmonic.mean.w
Harmonic mean of number of observations in
subgroups (for back transformation of Freeman-Tukey Double arcsine
transformation) - if byvar is not missing.
n.e.w
Number of observations in experimental group in
subgroups - if byvar is not missing.
n.c.w
Number of observations in control group in subgroups -
if byvar is not missing.
k.w
Number of studies combined within subgroups - if
byvar is not missing.
k.all.w
Number of all studies in subgroups - if byvar
is not missing.
Q.w
Heterogeneity statistics within subgroups - if
byvar is not missing.
Q.w.fixed
Overall within subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Q.w.random
Overall within subgroups heterogeneity statistic Q
(based on random effects model) - if byvar is not missing
(only calculated if argument tau.common is TRUE).
df.Q.w
Degrees of freedom for test of overall within
subgroups heterogeneity - if byvar is not missing.
Q.b.fixed
Overall between subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Q.b.random
Overall between subgroups heterogeneity statistic
Q (based on random effects model) - if byvar is not
missing.
df.Q.b
Degrees of freedom for test of overall between
subgroups heterogeneity - if byvar is not missing.
tau.w
Square-root of between-study variance within subgroups
- if byvar is not missing.
C.w
Scaling factor utilised internally to calculate common
tau-squared across subgroups - if byvar is not missing.
H.w
Heterogeneity statistic H within subgroups - if
byvar is not missing.
lower.H.w, upper.H.w
Lower and upper confidence limti for
heterogeneity statistic H within subgroups - if byvar is
not missing.
I2.w
Heterogeneity statistic I2 within subgroups - if
byvar is not missing.
lower.I2.w, upper.I2.w
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups - if byvar is
not missing.
keepdata
As defined above.
data
Original data (set) used in function call (if
keepdata=TRUE).
subset
Information on subset of original data used in
meta-analysis (if keepdata=TRUE).
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, 177–188.
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, 2693–2710,
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.
See Also
update.meta, metabin, metacont, print.meta
Examples
data(Fleiss93)
meta1 <- metabin(event.e, n.e, event.c, n.c, data=Fleiss93, sm="RR", method="I")
meta1
#
# Identical results by using the following commands:
#
meta1
metagen(meta1$TE, meta1$seTE, sm="RR")
forest(metagen(meta1$TE, meta1$seTE, sm="RR"))
#
# Meta-analysis with prespecified between-study variance
#
summary(metagen(meta1$TE, meta1$seTE, sm="RR", tau.preset=sqrt(0.1)))
#
# Meta-analysis of survival data:
#
logHR <- log(c(0.95, 1.5))
selogHR <- c(0.25, 0.35)
metagen(logHR, selogHR, sm="HR")
#
# Paule-Mandel method to estimate between-study variance
# Data from Paule & Mandel (1982)
#
average <- c(27.044, 26.022, 26.340, 26.787, 26.796)
variance <- c(0.003, 0.076, 0.464, 0.003, 0.014)
#
summary(metagen(average, sqrt(variance), sm="MD", method.tau="PM"))