metabin  R Documentation 
Calculation of common effect and random effects estimates (risk
ratio, odds ratio, risk difference, arcsine difference, or
diagnostic odds ratio) for metaanalyses with binary outcome
data. MantelHaenszel, inverse variance, Peto method, generalised
linear mixed model (GLMM), and sample size method are available for
pooling. For GLMMs, the rma.glmm
function
from R package metafor (Viechtbauer, 2010) is called
internally.
metabin(
event.e,
n.e,
event.c,
n.c,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
cluster = NULL,
method = ifelse(tau.common, "Inverse", gs("method")),
sm = ifelse(!is.na(charmatch(tolower(method), c("peto", "glmm", "ssw"), nomatch = NA)),
"OR", gs("smbin")),
incr = gs("incr"),
method.incr = gs("method.incr"),
allstudies = gs("allstudies"),
level = gs("level"),
MH.exact = gs("MH.exact"),
RR.Cochrane = gs("RR.Cochrane"),
Q.Cochrane = gs("Q.Cochrane") & method == "MH" & method.tau == "DL",
model.glmm = gs("model.glmm"),
common = gs("common"),
random = gs("random")  !is.null(tau.preset),
overall = common  random,
overall.hetstat = common  random,
prediction = gs("prediction")  !missing(method.predict),
method.tau = ifelse(!is.na(charmatch(tolower(method), "glmm", nomatch = NA)), "ML",
gs("method.tau")),
method.tau.ci = gs("method.tau.ci"),
tau.preset = NULL,
TE.tau = NULL,
tau.common = gs("tau.common"),
level.ma = gs("level.ma"),
method.random.ci = gs("method.random.ci"),
adhoc.hakn.ci = gs("adhoc.hakn.ci"),
level.predict = gs("level.predict"),
method.predict = gs("method.predict"),
adhoc.hakn.pi = gs("adhoc.hakn.pi"),
seed.predict = NULL,
method.bias = ifelse(sm == "OR", "Harbord", ifelse(sm == "DOR", "Deeks",
gs("method.bias"))),
backtransf = gs("backtransf"),
pscale = 1,
text.common = gs("text.common"),
text.random = gs("text.random"),
text.predict = gs("text.predict"),
text.w.common = gs("text.w.common"),
text.w.random = gs("text.w.random"),
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"),
subgroup,
subgroup.name = NULL,
print.subgroup.name = gs("print.subgroup.name"),
sep.subgroup = gs("sep.subgroup"),
test.subgroup = gs("test.subgroup"),
prediction.subgroup = gs("prediction.subgroup"),
seed.predict.subgroup = NULL,
byvar,
hakn,
adhoc.hakn,
print.CMH = gs("print.CMH"),
keepdata = gs("keepdata"),
warn = gs("warn"),
warn.deprecated = gs("warn.deprecated"),
control = NULL,
...
)
event.e 
Number of events in experimental group or true positives in diagnostic study. 
n.e 
Number of observations in experimental group or number of ill participants in diagnostic study. 
event.c 
Number of events in control group or false positives in diagnostic study. 
n.c 
Number of observations in control group or number of healthy participants in diagnostic study. 
studlab 
An optional vector with study labels. 
data 
An optional data frame containing the study information, i.e., event.e, n.e, event.c, and n.c. 
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. 
cluster 
An optional vector specifying which estimates come from the same cluster resulting in the use of a threelevel metaanalysis model. 
method 
A character string indicating which method is to be
used for pooling of studies. One of 
sm 
A character string indicating which summary measure
( 
incr 
Could be either a numerical value which is added to
cell frequencies for studies with a zero cell count or the
character string 
method.incr 
A character string indicating which continuity
correction method should be used ( 
allstudies 
A logical indicating if studies with zero or all
events in both groups are to be included in the metaanalysis
(applies only if 
level 
The level used to calculate confidence intervals for individual studies. 
MH.exact 
A logical indicating if 
RR.Cochrane 
A logical indicating if 2* 
Q.Cochrane 
A logical indicating if the MantelHaenszel estimate is used in the calculation of the heterogeneity statistic Q which is implemented in RevMan 5, the program for preparing and maintaining Cochrane reviews. 
model.glmm 
A character string indicating which GLMM should
be used. One of 
common 
A logical indicating whether a common effect metaanalysis should be conducted. 
random 
A logical indicating whether a random effects metaanalysis should be conducted. 
overall 
A logical indicating whether overall summaries should be reported. This argument is useful in a metaanalysis with subgroups if overall results should not be reported. 
overall.hetstat 
A logical value indicating whether to print heterogeneity measures for overall treatment comparisons. This argument is useful in a metaanalysis with subgroups if heterogeneity statistics should only be printed on subgroup level. 
prediction 
A logical indicating whether a prediction interval should be printed. 
method.tau 
A character string indicating which method is
used to estimate the betweenstudy variance 
method.tau.ci 
A character string indicating which method is
used to estimate the confidence interval of 
tau.preset 
Prespecified value for the square root of the
betweenstudy variance 
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. 
level.ma 
The level used to calculate confidence intervals for metaanalysis estimates. 
method.random.ci 
A character string indicating which method
is used to calculate confidence interval and test statistic for
random effects estimate (see 
adhoc.hakn.ci 
A character string indicating whether an
ad hoc variance correction should be applied in the case
of an arbitrarily small HartungKnapp variance estimate (see

level.predict 
The level used to calculate prediction interval for a new study. 
method.predict 
A character string indicating which method is
used to calculate a prediction interval (see

adhoc.hakn.pi 
A character string indicating whether an
ad hoc variance correction should be applied for
prediction interval (see 
seed.predict 
A numeric value used as seed to calculate
bootstrap prediction interval (see 
method.bias 
A character string indicating which test for
funnel plot asymmetry is to be used. Either 
backtransf 
A logical indicating whether results for odds
ratio ( 
pscale 
A numeric defining a scaling factor for printing of risk differences. 
text.common 
A character string used in printouts and forest plot to label the pooled common effect estimate. 
text.random 
A character string used in printouts and forest plot to label the pooled random effects estimate. 
text.predict 
A character string used in printouts and forest plot to label the prediction interval. 
text.w.common 
A character string used to label weights of common effect model. 
text.w.random 
A character string used to label weights of random effects model. 
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. 
subgroup 
An optional vector to conduct a metaanalysis with subgroups. 
subgroup.name 
A character string with a name for the subgroup variable. 
print.subgroup.name 
A logical indicating whether the name of the subgroup variable should be printed in front of the group labels. 
sep.subgroup 
A character string defining the separator between name of subgroup variable and subgroup label. 
test.subgroup 
A logical value indicating whether to print results of test for subgroup differences. 
prediction.subgroup 
A logical indicating whether prediction intervals should be printed for subgroups. 
seed.predict.subgroup 
A numeric vector providing seeds to calculate bootstrap prediction intervals within subgroups. Must be of same length as the number of subgroups. 
byvar 
Deprecated argument (replaced by 'subgroup'). 
hakn 
Deprecated argument (replaced by 'method.random.ci'). 
adhoc.hakn 
Deprecated argument (replaced by 'adhoc.hakn.ci'). 
print.CMH 
A logical indicating whether result of the CochranMantelHaenszel test for overall effect should be printed. 
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 
warn.deprecated 
A logical indicating whether warnings should be printed if deprecated arguments are used. 
control 
An optional list to control the iterative process to
estimate the betweenstudy variance 
... 
Additional arguments passed on to

Calculation of common and random effects estimates for metaanalyses with binary outcome data.
The following measures of treatment effect are available (Rücker et al., 2009):
Risk ratio (sm = "RR"
)
Odds ratio (sm = "OR"
)
Risk difference (sm = "RD"
)
Arcsine difference (sm = "ASD"
)
Diagnostic Odds ratio (sm = "DOR"
)
Vaccine efficacy or vaccine effectiveness (sm = "VE"
)
Note, mathematically, odds ratios and diagnostic odds ratios are
identical, however, the labels in printouts and figures
differ. Furthermore, log risk ratio (logRR) and log vaccine ratio
(logVR) are mathematical identical, however, backtransformed
results differ as vaccine efficacy or effectiveness is defined as
VE = 100 * (1  RR)
.
A threelevel random effects metaanalysis model (Van den Noortgate
et al., 2013) is utilized if argument cluster
is used and at
least one cluster provides more than one estimate. Internally,
rma.mv
is called to conduct the analysis and
weights.rma.mv
with argument type =
"rowsum"
is used to calculate random effects weights.
Default settings are utilised for several arguments (assignments
using gs
function). These defaults can be changed for
the current R session using the settings.meta
function.
Furthermore, R function update.meta
can be used to
rerun a metaanalysis with different settings.
By default, both common effect (also called common effect) and
random effects models are considered (see arguments common
and random
). If method
is "MH"
(default), the
MantelHaenszel method (Greenland & Robins, 1985; Robins et al.,
1986) is used to calculate the common effect estimate; if
method
is "Inverse"
, inverse variance weighting is
used for pooling (Fleiss, 1993); if method
is "Peto"
,
the Peto method is used for pooling (Yusuf et al., 1985); if
method
is "SSW"
, the sample size method is used for
pooling (Bakbergenuly et al., 2020).
While the MantelHaenszel and Peto method are defined under the
common effect model, random effects variants based on these methods
are also implemented in metabin
. Following RevMan 5, the
MantelHaenszel estimator is used in the calculation of the
betweenstudy heterogeneity statistic Q which is used in the
DerSimonianLaird estimator (DerSimonian and Laird,
1986). Accordingly, the results for the random effects
metaanalysis using the MantelHaenszel or inverse variance method
are typically very similar. For the Peto method, Peto's log odds
ratio, i.e. (OE) / V
and its standard error sqrt(1 /
V)
with OE
and V
denoting "Observed minus Expected"
and its variance, are utilised in the random effects
model. Accordingly, results of a random effects model using
sm = "Peto"
can be different to results from a random
effects model using sm = "MH"
or sm = "Inverse"
.
A distinctive and frequently overlooked advantage of binary
endpoints is that individual patient data (IPD) can be extracted
from a twobytwo table. Accordingly, statistical methods for IPD,
i.e., logistic regression and generalised linear mixed models, can
be utilised in a metaanalysis of binary outcomes (Stijnen et al.,
2010; Simmonds et al., 2016). These methods are available (argument
method = "GLMM"
) for the odds ratio as summary measure by
calling the rma.glmm
function from R package
metafor internally.
Four different GLMMs are available for
metaanalysis with binary outcomes using argument model.glmm
(which corresponds to argument model
in the
rma.glmm
function):
1.  Logistic regression model with common study effects (default) 
(model.glmm = "UM.FS" , i.e., Unconditional
Model  Fixed Study effects) 

2.  Mixedeffects logistic regression model with random study effects 
(model.glmm = "UM.RS" , i.e., Unconditional
Model  Random Study effects) 

3.  Generalised linear mixed model (conditional HypergeometricNormal) 
(model.glmm = "CM.EL" , i.e., Conditional
Model  Exact Likelihood) 

4.  Generalised linear mixed model (conditional BinomialNormal) 
(model.glmm = "CM.AL" , i.e., Conditional
Model  Approximate Likelihood)

Details on these four GLMMs as well as additional arguments which
can be provided using argument '...
' in metabin
are
described in rma.glmm
where you can also
find information on the iterative algorithms used for estimation.
Note, regardless of which value is used for argument
model.glmm
, results for two different GLMMs are calculated:
common effect model (with fixed treatment effect) and random
effects model (with random treatment effects).
Three approaches are available to apply a continuity correction:
Only studies with a zero cell count (method.incr =
"only0"
)
All studies if at least one study has a zero cell count
(method.incr = "if0all"
)
All studies irrespective of zero cell counts
(method.incr = "all"
)
By default, a continuity correction is only applied to studies with
a zero cell count (method.incr = "only0"
). This method
showed the best performance for the odds ratio in a simulation
study under the random effects model (Weber et al., 2020).
The continuity correction method is used both to calculate individual study results with confidence limits and to conduct metaanalysis based on the inverse variance method. For the risk difference, the method is only considered to calculate standard errors and confidence limits. For Peto method and GLMMs no continuity correction is used in the metaanalysis. Furthermore, the continuity correction is ignored for individual studies for the Peto method.
For studies with a zero cell count, by default, 0.5 (argument
incr
) is added to all cell frequencies for the odds ratio or
only the number of events for the risk ratio (argument
RR.Cochrane = FALSE
, default). The increment is added to all
cell frequencies for the risk ratio if argument RR.Cochrane =
TRUE
. For the risk difference, incr
is only added to all
cell frequencies to calculate the standard error. Finally, a
treatment arm continuity correction is used if incr = "TACC"
(Sweeting et al., 2004; Diamond et al., 2007).
For odds ratio and risk ratio, treatment estimates and standard
errors are only calculated for studies with zero or all events in
both groups if allstudies = TRUE
.
For the MantelHaenszel method, by default (if MH.exact
is
FALSE), incr
is added to cell frequencies of a study with a
zero cell count in the calculation of the pooled risk ratio or odds
ratio as well as the estimation of the variance of the pooled risk
difference, risk ratio or odds ratio. This approach is also used in
other software, e.g. RevMan 5 and the Stata procedure
metan. According to Fleiss (in Cooper & Hedges, 1994), there is no
need to add 0.5 to a cell frequency of zero to calculate the
MantelHaenszel estimate and he advocates the exact method
(MH.exact
= TRUE). Note, estimates based on exact
MantelHaenszel method or GLMM are not defined if the number of
events is zero in all studies either in the experimental or control
group.
Argument subgroup
can be used to conduct subgroup analysis for
a categorical covariate. The metareg
function can be
used instead for more than one categorical covariate or continuous
covariates.
Arguments subset
and exclude
can be used to exclude
studies from the metaanalysis. Studies are removed completely from
the metaanalysis using argument subset
, while excluded
studies are shown in printouts and forest plots using argument
exclude
(see Examples in metagen
).
Metaanalysis results are the same for both arguments.
Internally, both common effect and random effects models are
calculated regardless of values choosen for arguments
common
and 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 random = FALSE
. However, all functions in R
package meta will adequately consider the values for
common
and random
. E.g. function
print.meta
will not print results for the random
effects model if random = FALSE
.
A prediction interval will only be shown if prediction =
TRUE
.
An object of class c("metabin", "meta")
with corresponding
generic functions (see metaobject
).
Guido Schwarzer guido.schwarzer@uniklinikfreiburg.de
Bakbergenuly I, Hoaglin DC, Kulinskaya E (2020): Methods for estimating betweenstudy variance and overall effect in metaanalysis of oddsratios. Research Synthesis Methods, 11, 426–42
Cooper H & Hedges LV (1994): The Handbook of Research Synthesis. Newbury Park, CA: Russell Sage Foundation
Diamond GA, Bax L, Kaul S (2007): Uncertain Effects of Rosiglitazone on the Risk for Myocardial Infarction and Cardiovascular Death. Annals of Internal Medicine, 147, 578–81
DerSimonian R & Laird N (1986): Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–88
Fleiss JL (1993): The statistical basis of metaanalysis. Statistical Methods in Medical Research, 2, 121–45
Greenland S & Robins JM (1985): Estimation of a common effect parameter from sparse followup data. Biometrics, 41, 55–68
Review Manager (RevMan) [Computer program]. Version 5.4. The Cochrane Collaboration, 2020
Robins J, Breslow N, Greenland S (1986): Estimators of the MantelHaenszel Variance Consistent in Both Sparse Data and LargeStrata Limiting Models. Biometrics, 42, 311–23
Rücker G, Schwarzer G, Carpenter J, Olkin I (2009): Why add anything to nothing? The arcsine difference as a measure of treatment effect in metaanalysis with zero cells. Statistics in Medicine, 28, 721–38
Simmonds MC, Higgins JP (2016): A general framework for the use of logistic regression models in metaanalysis. Statistical Methods in Medical Research, 25, 2858–77
StataCorp. 2011. Stata Statistical Software: Release 12. College Station, TX: StataCorp LP.
Stijnen T, Hamza TH, Ozdemir P (2010): Random effects metaanalysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046–67
Sweeting MJ, Sutton AJ, Lambert PC (2004): What to add to nothing? Use and avoidance of continuity corrections in metaanalysis of sparse data. Statistics in Medicine, 23, 1351–75
Van den Noortgate W, LópezLópez JA, MarínMartínez F, SánchezMeca J (2013): Threelevel metaanalysis of dependent effect sizes. Behavior Research Methods, 45, 576–94
Viechtbauer W (2010): Conducting metaanalyses in R with the metafor package. Journal of Statistical Software, 36, 1–48
Weber F, Knapp G, Ickstadt K, Kundt G, Glass Ä (2020): Zerocell corrections in randomeffects metaanalyses. Research Synthesis Methods, 11, 913–9
Yusuf S, Peto R, Lewis J, Collins R, Sleight P (1985): Beta blockade during and after myocardial infarction: An overview of the randomized trials. Progress in Cardiovascular Diseases, 27, 335–71
metapackage
, update.meta
,
forest
, funnel
,
metabias
, metacont
,
metagen
, metareg
,
print.meta
# Calculate odds ratio and confidence interval for a single study
#
metabin(10, 20, 15, 20, sm = "OR")
# Different results (due to handling of studies with double zeros)
#
metabin(0, 10, 0, 10, sm = "OR")
metabin(0, 10, 0, 10, sm = "OR", allstudies = TRUE)
# Use subset of Olkin (1995) to conduct metaanalysis based on
# inverse variance method (with risk ratio as summary measure)
#
data(Olkin1995)
m1 < metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = c(41, 47, 51, 59),
studlab = paste(author, year),
method = "Inverse")
m1
# Show results for individual studies
summary(m1)
# Use different subset of Olkin (1995)
#
m2 < metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = year < 1970,
studlab = paste(author, year),
method = "Inverse")
m2
forest(m2)
# Metaanalysis with odds ratio as summary measure
#
m3 < metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = year < 1970,
studlab = paste(author, year),
sm = "OR", method = "Inverse")
# Same metaanalysis result using 'update.meta' function
m3 < update(m2, sm = "OR")
m3
# Metaanalysis based on MantelHaenszel method (with odds ratio as
# summary measure)
#
m4 < update(m3, method = "MH")
m4
# Metaanalysis based on Peto method (only available for odds ratio
# as summary measure)
#
m5 < update(m3, method = "Peto")
m5
## Not run:
# Metaanalysis using generalised linear mixed models
# (only if R package 'lme4' is available)
#
# Logistic regression model with (k = 4) fixed study effects
# (default: model.glmm = "UM.FS")
#
m6 < metabin(ev.exp, n.exp, ev.cont, n.cont,
studlab = paste(author, year),
data = Olkin1995, subset = year < 1970, method = "GLMM")
# Same results:
m6 < update(m2, method = "GLMM")
m6
# Mixedeffects logistic regression model with random study effects
# (warning message printed due to argument 'nAGQ')
#
m7 < update(m6, model.glmm = "UM.RS")
#
# Use additional argument 'nAGQ' for internal call of 'rma.glmm'
# function
#
m7 < update(m6, model.glmm = "UM.RS", nAGQ = 1)
m7
# Generalised linear mixed model (conditional HypergeometricNormal)
# (R package 'BiasedUrn' must be available)
#
m8 < update(m6, model.glmm = "CM.EL")
m8
# Generalised linear mixed model (conditional BinomialNormal)
#
m9 < update(m6, model.glmm = "CM.AL")
m9
# Logistic regression model with (k = 70) fixed study effects
# (about 18 seconds with Intel Core i73667U, 2.0GHz)
#
m10 < metabin(ev.exp, n.exp, ev.cont, n.cont,
studlab = paste(author, year),
data = Olkin1995, method = "GLMM")
m10
# Mixedeffects logistic regression model with random study effects
#  about 50 seconds with Intel Core i73667U, 2.0GHz
#  several warning messages, e.g. "failure to converge, ..."
#
update(m10, model.glmm = "UM.RS")
# Conditional HypergeometricNormal GLMM
#  long computation time (about 12 minutes with Intel Core
# i73667U, 2.0GHz)
#  estimation problems for this very large dataset:
# * warning that Choleski factorization of Hessian failed
# * confidence interval for treatment effect smaller in random
# effects model compared to common effect model
#
system.time(m11 < update(m10, model.glmm = "CM.EL"))
m11
# Generalised linear mixed model (conditional BinomialNormal)
# (less than 1 second with Intel Core i73667U, 2.0GHz)
#
update(m10, model.glmm = "CM.AL")
## End(Not run)
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