Description Usage Arguments Details Value Author(s) References See Also Examples
Fixed and random effects metaanalysis based on estimates (e.g. log hazard ratios) and their standard errors; inverse variance weighting is used for pooling.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  metagen(TE, seTE, studlab,
data=NULL, subset=NULL, exclude=NULL, sm="",
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"),
n.e=NULL, n.c=NULL,
backtransf=gs("backtransf"),
pscale=1, irscale = 1, irunit = "personyears",
title=gs("title"), complab=gs("complab"), outclab="",
label.e=gs("label.e"), label.c=gs("label.c"),
label.left=gs("label.left"), label.right=gs("label.right"),
byvar, bylab, print.byvar=gs("print.byvar"),
byseparator = gs("byseparator"),
keepdata=gs("keepdata"),
warn=gs("warn"))

TE 
Estimate of treatment effect, e.g., log hazard ratio or risk difference. 
seTE 
Standard error of treatment estimate. 
studlab 
An optional vector with study labels. 
data 
An optional data frame containing the study information. 
subset 
An optional vector specifying a subset of studies to be used. 
exclude 
An optional vector specifying studies to exclude from metaanalysis, however, to include in printouts and forest plots. 
sm 
A character string indicating underlying summary measure,
e.g., 
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 metaanalysis should be conducted. 
comb.random 
A logical indicating whether a random effects metaanalysis 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. 
null.effect 
A numeric value specifying the effect under the null hypothesis. 
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 betweenstudy variance τ^2. Either

tau.preset 
Prespecified value for the squareroot of the betweenstudy variance τ^2. 
TE.tau 
Overall treatment effect used to estimate the betweenstudy variance tausquared. 
tau.common 
A logical indicating whether tausquared should be the same across subgroups. 
method.bias 
A character string indicating which test is to be
used. Either 
backtransf 
A logical indicating whether results should be
back transformed in printouts and plots. If 
pscale 
A numeric giving scaling factor for printing of single
event probabilities or risk differences, i.e. if argument

irscale 
A numeric defining a scaling factor for printing of
single incidence rates or incidence rate differences, i.e. if
argument 
irunit 
A character specifying the time unit used to calculate rates, e.g. personyears. 
title 
Title of metaanalysis / 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 
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. 
byseparator 
A character string defining the separator between label and levels of grouping variable. 
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 metaanalysis due to zero standard errors). 
Generic method for metaanalysis, 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.
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
metaanalysis 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 DerSimonianLaird estimate (1986) is used in the random effects
model if method.tau="DL"
. The iterative PauleMandel method
(1982) to estimate the betweenstudy 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 betweenstudy variance
τ^2 (argument method.tau
) are also available:
Restricted maximumlikelihood estimator (method.tau="REML"
)
Maximumlikelihood estimator (method.tau="ML"
)
HunterSchmidt estimator (method.tau="HS"
)
SidikJonkman 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
betweenstudy variance.
Argument pscale
can be used to rescale single proportions or
risk differences, e.g. pscale=1000
means that proportions are
expressed as events per 1000 observations. This is useful in
situations with (very) low event probabilities.
Argument irscale
can be used to rescale single rates or rate
differences, e.g. irscale=1000
means that rates are expressed
as events per 1000 time units, e.g. personyears. This is useful in
situations with (very) low rates. Argument irunit
can be used
to specify the time unit used in individual studies (default:
"personyears"). This information is printed in summaries and forest
plots if argument irscale
is not equal to 1.
An object of class c("metagen", "meta")
with corresponding
print
, summary
, and forest
functions. The
object is a list containing the following components:
TE, seTE, studlab, exclude, n.e, n.c 

sm, level, level.comb, 

comb.fixed, comb.random, 

hakn, method.tau, tau.preset, TE.tau, method.bias, 

tau.common, title, complab, outclab, 

label.e, label.c, label.left, label.right, 

byvar, bylab, print.byvar, byseparator, warn 
As defined above. 
lower, upper 
Lower and upper confidence interval limits for individual studies. 
zval, pval 
zvalue and pvalue 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 
zvalue and pvalue 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 
zvalue or tvalue and corresponding pvalue 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. 
null.effect 
As defined above. 
k 
Number of studies combined in metaanalysis. 
Q 
Heterogeneity statistic. 
df.Q 
Degrees of freedom for heterogeneity statistic. 
tau 
Squareroot of betweenstudy variance. 
se.tau 
Standard error of squareroot of betweenstudy variance. 
C 
Scaling factor utilised internally to calculate common tausquared across subgroups. 
method 
Pooling method: 
df.hakn 
Degrees of freedom for test of treatment effect for
HartungKnapp method (only if 
bylevs 
Levels of grouping variable  if 
TE.fixed.w, seTE.fixed.w 
Estimated treatment effect and
standard error in subgroups (fixed effect model)  if 
lower.fixed.w, upper.fixed.w 
Lower and upper confidence
interval limits in subgroups (fixed effect model)  if

zval.fixed.w, pval.fixed.w 
zvalue and pvalue for test of
treatment effect in subgroups (fixed effect model)  if

TE.random.w, seTE.random.w 
Estimated treatment effect and
standard error in subgroups (random effects model)  if

lower.random.w, upper.random.w 
Lower and upper confidence
interval limits in subgroups (random effects model)  if

zval.random.w, pval.random.w 
zvalue or tvalue and
corresponding pvalue for test of treatment effect in subgroups
(random effects model)  if 
w.fixed.w, w.random.w 
Weight of subgroups (in fixed and
random effects model)  if 
df.hakn.w 
Degrees of freedom for test of treatment effect for
HartungKnapp method in subgroups  if 
n.harmonic.mean.w 
Harmonic mean of number of observations in
subgroups (for back transformation of FreemanTukey Double arcsine
transformation)  if 
n.e.w 
Number of observations in experimental group in
subgroups  if 
n.c.w 
Number of observations in control group in subgroups 
if 
k.w 
Number of studies combined within subgroups  if

k.all.w 
Number of all studies in subgroups  if 
Q.w 
Heterogeneity statistics within subgroups  if

Q.w.fixed 
Overall within subgroups heterogeneity statistic Q
(based on fixed effect model)  if 
Q.w.random 
Overall within subgroups heterogeneity statistic Q
(based on random effects model)  if 
df.Q.w 
Degrees of freedom for test of overall within
subgroups heterogeneity  if 
Q.b.fixed 
Overall between subgroups heterogeneity statistic Q
(based on fixed effect model)  if 
Q.b.random 
Overall between subgroups heterogeneity statistic
Q (based on random effects model)  if 
df.Q.b 
Degrees of freedom for test of overall between
subgroups heterogeneity  if 
tau.w 
Squareroot of betweenstudy variance within subgroups
 if 
C.w 
Scaling factor utilised internally to calculate common
tausquared across subgroups  if 
H.w 
Heterogeneity statistic H within subgroups  if

lower.H.w, upper.H.w 
Lower and upper confidence limti for
heterogeneity statistic H within subgroups  if 
I2.w 
Heterogeneity statistic I2 within subgroups  if

lower.I2.w, upper.I2.w 
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups  if 
keepdata 
As defined above. 
data 
Original data (set) used in function call (if

subset 
Information on subset of original data used in
metaanalysis (if 
call 
Function call. 
version 
Version of R package meta used to create object. 
Guido Schwarzer [email protected]
Cooper H & Hedges LV (1994), The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation.
DerSimonian R & Laird N (1986), Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–188.
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009), A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–159.
Knapp G & Hartung J (2003), Improved Tests for a Random Effects Metaregression 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 MetaAnalyses in R with the Metafor Package. Journal of Statistical Software, 36, 1–48.
update.meta
, metabin
, metacont
, print.meta
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  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"))
#
# Metaanalysis with prespecified betweenstudy variance
#
summary(metagen(meta1$TE, meta1$seTE, sm="RR", tau.preset=sqrt(0.1)))
#
# Metaanalysis of survival data:
#
logHR < log(c(0.95, 1.5))
selogHR < c(0.25, 0.35)
metagen(logHR, selogHR, sm="HR")
#
# PauleMandel method to estimate betweenstudy 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"))

Loading 'meta' package (version 4.84).
Type 'help(meta)' for a brief overview.
RR 95%CI %W(fixed) %W(random)
1 0.7420 [0.5223; 1.0543] 2.4 7.8
2 0.6993 [0.4828; 1.0129] 2.1 7.2
3 0.8270 [0.6487; 1.0545] 4.9 13.6
4 0.8209 [0.5269; 1.2789] 1.5 5.3
5 0.8193 [0.5927; 1.1326] 2.8 8.9
6 1.1183 [0.9411; 1.3289] 9.7 20.4
7 0.9142 [0.8596; 0.9722] 76.6 36.8
Number of studies combined: k = 7
RR 95%CI z pvalue
Fixed effect model 0.9137 [0.8658; 0.9643] 3.28 0.0010
Random effects model 0.8929 [0.8006; 0.9959] 2.03 0.0419
Quantifying heterogeneity:
tau^2 = 0.0074; H = 1.29 [1.00; 1.98]; I^2 = 39.6% [0.0%; 74.6%]
Test of heterogeneity:
Q d.f. pvalue
9.93 6 0.1277
Details on metaanalytical method:
 Inverse variance method
 DerSimonianLaird estimator for tau^2
RR 95%CI %W(fixed) %W(random)
1 0.7420 [0.5223; 1.0543] 2.4 7.8
2 0.6993 [0.4828; 1.0129] 2.1 7.2
3 0.8270 [0.6487; 1.0545] 4.9 13.6
4 0.8209 [0.5269; 1.2789] 1.5 5.3
5 0.8193 [0.5927; 1.1326] 2.8 8.9
6 1.1183 [0.9411; 1.3289] 9.7 20.4
7 0.9142 [0.8596; 0.9722] 76.6 36.8
Number of studies combined: k = 7
RR 95%CI z pvalue
Fixed effect model 0.9137 [0.8658; 0.9643] 3.28 0.0010
Random effects model 0.8929 [0.8006; 0.9959] 2.03 0.0419
Quantifying heterogeneity:
tau^2 = 0.0074; H = 1.29 [1.00; 1.98]; I^2 = 39.6% [0.0%; 74.6%]
Test of heterogeneity:
Q d.f. pvalue
9.93 6 0.1277
Details on metaanalytical method:
 Inverse variance method
 DerSimonianLaird estimator for tau^2
RR 95%CI %W(fixed) %W(random)
1 0.7420 [0.5223; 1.0543] 2.4 7.8
2 0.6993 [0.4828; 1.0129] 2.1 7.2
3 0.8270 [0.6487; 1.0545] 4.9 13.6
4 0.8209 [0.5269; 1.2789] 1.5 5.3
5 0.8193 [0.5927; 1.1326] 2.8 8.9
6 1.1183 [0.9411; 1.3289] 9.7 20.4
7 0.9142 [0.8596; 0.9722] 76.6 36.8
Number of studies combined: k = 7
RR 95%CI z pvalue
Fixed effect model 0.9137 [0.8658; 0.9643] 3.28 0.0010
Random effects model 0.8929 [0.8006; 0.9959] 2.03 0.0419
Quantifying heterogeneity:
tau^2 = 0.0074; H = 1.29 [1.00; 1.98]; I^2 = 39.6% [0.0%; 74.6%]
Test of heterogeneity:
Q d.f. pvalue
9.93 6 0.1277
Details on metaanalytical method:
 Inverse variance method
 DerSimonianLaird estimator for tau^2
Number of studies combined: k = 7
RR 95%CI z pvalue
Fixed effect model 0.9137 [0.8658; 0.9643] 3.28 0.0010
Random effects model 0.8507 [0.6565; 1.1022] 1.22 0.2210
Quantifying heterogeneity:
tau^2 = 0.1000; H = 1.29 [1.00; 1.98]; I^2 = 39.6% [0.0%; 74.6%]
Test of heterogeneity:
Q d.f. pvalue
9.93 6 0.1277
Details on metaanalytical method:
 Inverse variance method
 Preset betweenstudy variance: tau^2 = 0.1000
HR 95%CI %W(fixed) %W(random)
1 0.9500 [0.5820; 1.5507] 66.2 64.4
2 1.5000 [0.7554; 2.9786] 33.8 35.6
Number of studies combined: k = 2
HR 95%CI z pvalue
Fixed effect model 1.1085 [0.7440; 1.6516] 0.51 0.6126
Random effects model 1.1178 [0.7281; 1.7162] 0.51 0.6105
Quantifying heterogeneity:
tau^2 = 0.0118; H = 1.06; I^2 = 11.3%
Test of heterogeneity:
Q d.f. pvalue
1.13 1 0.2883
Details on metaanalytical method:
 Inverse variance method
 DerSimonianLaird estimator for tau^2
Number of studies combined: k = 5
MD 95%CI z pvalue
Fixed effect model 26.8869 [26.8155; 26.9583] 738.00 < 0.0001
Random effects model 26.7121 [26.3767; 27.0476] 156.09 < 0.0001
Quantifying heterogeneity:
tau^2 = 0.1052; H = 2.38 [1.57; 3.61]; I^2 = 82.3% [59.4%; 92.3%]
Test of heterogeneity:
Q d.f. pvalue
22.63 4 0.0002
Details on metaanalytical method:
 Inverse variance method
 PauleMandel estimator for tau^2
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