Description Usage Arguments Details Value Author(s) References See Also Examples
Calculation of fixed 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.
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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63  metabin(
event.e,
n.e,
event.c,
n.c,
studlab,
data = NULL,
subset = NULL,
exclude = 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"),
allincr = gs("allincr"),
addincr = gs("addincr"),
allstudies = gs("allstudies"),
MH.exact = gs("MH.exact"),
RR.Cochrane = gs("RR.Cochrane"),
Q.Cochrane = gs("Q.Cochrane") & method == "MH" & method.tau == "DL",
model.glmm = "UM.FS",
level = gs("level"),
level.comb = gs("level.comb"),
comb.fixed = gs("comb.fixed"),
comb.random = gs("comb.random"),
overall = comb.fixed  comb.random,
overall.hetstat = comb.fixed  comb.random,
hakn = gs("hakn"),
adhoc.hakn = gs("adhoc.hakn"),
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"),
prediction = gs("prediction"),
level.predict = gs("level.predict"),
method.bias = ifelse(sm == "OR", "Harbord", ifelse(sm == "DOR", "Deeks",
gs("method.bias"))),
backtransf = gs("backtransf"),
pscale = 1,
text.fixed = gs("text.fixed"),
text.random = gs("text.random"),
text.predict = gs("text.predict"),
text.w.fixed = gs("text.w.fixed"),
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"),
byvar,
bylab,
print.byvar = gs("print.byvar"),
byseparator = gs("byseparator"),
test.subgroup = gs("test.subgroup"),
print.CMH = gs("print.CMH"),
keepdata = gs("keepdata"),
warn = gs("warn"),
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. 
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
each cell frequency for studies with a zero cell count or the
character string 
allincr 
A logical indicating if 
addincr 
A logical indicating if 
allstudies 
A logical indicating if studies with zero or all
events in both groups are to be included in the metaanalysis
(applies only if 
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 
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. 
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. 
hakn 
A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals. 
adhoc.hakn 
A character string indicating whether an ad hoc variance correction should be applied in the case of an arbitrarily small HartungKnapp variance estimate, see Details. 
method.tau 
A character string indicating which method is
used to estimate the betweenstudy variance τ^2 and its
square root τ. Either 
method.tau.ci 
A character string indicating which method is
used to estimate the confidence interval of τ^2 and
τ. Either 
tau.preset 
Prespecified value for the square root of the betweenstudy variance τ^2. 
TE.tau 
Overall treatment effect used to estimate the betweenstudy variance τ^2. 
tau.common 
A logical indicating whether tausquared should be the same across subgroups. 
prediction 
A logical indicating whether a prediction interval should be printed. 
level.predict 
The level used to calculate prediction interval for a new study. 
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.fixed 
A character string used in printouts and forest plot to label the pooled fixed 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.fixed 
A character string used to label weights of fixed 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. 
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. 
test.subgroup 
A logical value indicating whether to print results of test for subgroup differences. 
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 
control 
An optional list to control the iterative process to
estimate the betweenstudy variance τ^2. This argument
is passed on to 
... 
Additional arguments passed on to

Calculation of fixed 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"
)
Note, mathematically, odds ratios and diagnostic odds ratios are identical, however, the labels in printouts and figures differ.
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 fixed effect and random effects models are
considered (see arguments comb.fixed
and
comb.random
). If method
is "MH"
(default), the
MantelHaenszel method (Greenland & Robins, 1985; Robins et al.,
1986) is used to calculate the fixed 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 (Yussuf 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
fixed 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. Accordlingly, 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 fixed 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:
fixed effect model (with fixed treatment effect) and random effects
model (with random treatment effects).
For studies with a zero cell count, by default, 0.5 is added to all
cell frequencies of these studies; if incr
is "TACC"
a treatment arm continuity correction is used instead (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
is TRUE
. This continuity correction is used both to
calculate individual study results with confidence limits and to
conduct metaanalysis based on the inverse variance method. For
Peto method and GLMMs no continuity correction is used. For the
MantelHaenszel method, by default (if MH.exact
is FALSE),
incr
is added to all 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.
The following methods to estimate the betweenstudy variance τ^2 are available for the inverse variance method:
DerSimonianLaird estimator (method.tau = "DL"
)
PauleMandel estimator (method.tau = "PM"
)
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"
)
See metagen
for more information on these
estimators. Note, the maximumlikelihood method is utilized for
GLMMs.
The following methods to calculate a confidence interval for τ^2 and τ are available.
Argument  Method 
method.tau.ci = "J"  Method by Jackson 
method.tau.ci = "BJ"  Method by Biggerstaff and Jackson 
method.tau.ci = "QP"  QProfile method 
See metagen
for more information on these
methods. For GLMMs, no confidence intervals for τ^2 and
τ are calculated. Likewise, no confidence intervals for
τ^2 and τ are calculated if method.tau.ci =
""
.
Hartung and Knapp (2001a,b) proposed an alternative method for random effects metaanalysis based on a refined variance estimator for the treatment estimate. Simulation studies (Hartung and Knapp, 2001a,b; IntHout et al., 2014; Langan et al., 2019) show improved coverage probabilities compared to the classic random effects method.
In rare settings with very homogeneous treatment estimates, the HartungKnapp variance estimate can be arbitrarily small resulting in a very narrow confidence interval (Knapp and Hartung, 2003; Wiksten et al., 2016). In such cases, an ad hoc variance correction has been proposed by utilising the variance estimate from the classic random effects model with the HK method (Knapp and Hartung, 2003; IQWiQ, 2020). An alternative approach is to use the wider confidence interval of classic fixed or random effects metaanalysis and the HK method (Wiksten et al., 2016; Jackson et al., 2017).
Argument adhoc.hakn
can be used to choose the ad hoc
method:
Argument  Ad hoc method 
adhoc.hakn = ""  not used 
adhoc.hakn = "se"  use variance correction if HK standard error is smaller 
than standard error from classic random effects  
metaanalysis (Knapp and Hartung, 2003)  
adhoc.hakn = "iqwig6"  use variance correction if HK confidence interval 
is narrower than CI from classic random effects model  
with DerSimonianLaird estimator (IQWiG, 2020)  
adhoc.hakn = "ci"  use wider confidence interval of classic random effects 
and HK metaanalysis  
(Hybrid method 2 in Jackson et al., 2017) 
For GLMMs, a method similar to Knapp and Hartung (2003) is
implemented, see description of argument tdist
in
rma.glmm
, and the ad hoc variance
correction is not available.
A prediction interval for the proportion in a new study (Higgins et
al., 2009) is calculated if arguments prediction
and
comb.random
are TRUE
. Note, the definition of
prediction intervals varies in the literature. This function
implements equation (12) of Higgins et al., (2009) which proposed a
t distribution with K2 degrees of freedom where
K corresponds to the number of studies in the metaanalysis.
Argument byvar
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 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
.
An object of class c("metabin", "meta")
with corresponding
print
, summary
, and forest
functions. The
object is a list containing the following components:
event.e, n.e, event.c, n.c, studlab, exclude, 
As defined above. 
sm, method, incr, allincr, addincr, 
As defined above. 
allstudies, MH.exact, RR.Cochrane, Q.Cochrane, model.glmm, 
As defined above. 
warn, level, level.comb, comb.fixed, comb.random, 
As defined above. 
overall, overall.hetstat, 
As defined above. 
hakn, adhoc.hakn, method.tau, method.tau.ci, 
As defined above. 
tau.preset, TE.tau, method.bias, 
As defined above. 
tau.common, title, complab, outclab, 
As defined above. 
label.e, label.c, label.left, label.right, 
As defined above. 
byvar, bylab, print.byvar, byseparator 
As defined above. 
TE, seTE 
Estimated treatment effect and standard error of individual studies. 
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, e.g., log risk ratio or risk difference, and standard error (fixed effect model). 
lower.fixed, upper.fixed 
Lower and upper confidence interval limits (fixed effect model). 
statistic.fixed, pval.fixed 
zvalue and pvalue for test of overall treatment effect (fixed effect model). 
TE.random, seTE.random 
Estimated overall treatment effect, e.g., log risk ratio or risk difference, and standard error (random effects model). 
lower.random, upper.random 
Lower and upper confidence interval limits (random effects model). 
statistic.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. 
k 
Number of studies combined in metaanalysis. 
Q 
Heterogeneity statistic Q. 
df.Q 
Degrees of freedom for heterogeneity statistic. 
pval.Q 
Pvalue of heterogeneity test. 
Q.LRT 
Heterogeneity statistic for likelihoodratio test
(only if 
df.Q.LRT 
Degrees of freedom for likelihoodratio test 
pval.Q.LRT 
Pvalue of likelihoodratio test. 
tau2 
Betweenstudy variance τ^2. 
se.tau2 
Standard error of τ^2. 
lower.tau2, upper.tau2 
Lower and upper limit of confidence interval for τ^2. 
tau 
Squareroot of betweenstudy variance τ. 
lower.tau, upper.tau 
Lower and upper limit of confidence interval for τ. 
H 
Heterogeneity statistic H. 
lower.H, upper.H 
Lower and upper confidence limit for heterogeneity statistic H. 
I2 
Heterogeneity statistic I^2. 
lower.I2, upper.I2 
Lower and upper confidence limit for heterogeneity statistic I^2. 
Rb 
Heterogeneity statistic R_b. 
lower.Rb, upper.Rb 
Lower and upper confidence limit for heterogeneity statistic R_b. 
Q.CMH 
CochranMantelHaenszel test statistic for overall effect. 
df.Q.CMH 
Degrees of freedom for CochranMantelHaenszel test statistic. 
pval.Q.CMH 
Pvalue of CochranMantelHaenszel test. 
incr.e, incr.c 
Increment added to cells in the experimental and control group, respectively. 
sparse 
Logical flag indicating if any study included in metaanalysis has any zero cell frequencies. 
doublezeros 
Logical flag indicating if any study has zero cell frequencies in both treatment groups. 
df.hakn 
Degrees of freedom for test of treatment effect for
HartungKnapp method (only if 
k.MH 
Number of studies combined in metaanalysis using MantelHaenszel method. 
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 
statistic.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

statistic.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 
event.e.w 
Number of
events in experimental group in subgroups  if 
n.e.w 
Number of observations in
experimental group in subgroups  if 
event.c.w 
Number of events in control 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.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 
pval.Q.w.fixed 
Pvalue
of within subgroups heterogeneity statistic Q (based on fixed
effect model)  if 
pval.Q.w.random 
Pvalue of within subgroups heterogeneity
statistic Q (based on random effects model)  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 
pval.Q.b.fixed 
Pvalue
of between subgroups heterogeneity statistic Q (based on fixed
effect model)  if 
pval.Q.b.random 
Pvalue of between subgroups heterogeneity
statistic Q (based on random effects model)  if 
tau.w 
Squareroot of betweenstudy variance
within subgroups  if 
H.w 
Heterogeneity statistic H within subgroups  if

lower.H.w, upper.H.w 
Lower
and upper confidence limit for heterogeneity statistic H within
subgroups  if 
I2.w 
Heterogeneity statistic I^2 within subgroups 
if 
lower.I2.w,
upper.I2.w 
Lower and upper confidence limit for heterogeneity
statistic I^2 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 
.glmm.fixed 
GLMM object generated by call of

.glmm.random 
GLMM object generated by call of

call 
Function call. 
version 
Version of R package meta used to create object. 
version.metafor 
Version of R package metafor used for GLMMs. 
Guido Schwarzer sc@imbi.unifreiburg.de
Bakbergenuly I, Hoaglin DC, Kulinskaya E (2020): Methods for estimating betweenstudy variance and overall effect in metaanalysis of oddsratios. Research Synthesis Methods, DOI: 10.1002/jrsm.1404
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
Hartung J & Knapp G (2001): A refined method for the metaanalysis of controlled clinical trials with binary outcome. Statistics in Medicine, 20, 3875–89
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–59
IQWiG (2020): General Methods: Version 6.0. https://www.iqwig.de/en/aboutus/methods/methodspaper/
Knapp G & Hartung J (2003): Improved tests for a random effects metaregression with a single covariate. Statistics in Medicine, 22, 2693–710
Review Manager (RevMan) [Computer program]. Version 5.4. The Cochrane Collaboration, 2020
Paule RC & Mandel J (1982): Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377–85
Pettigrew HM, Gart JJ, Thomas DG (1986): The bias and higher cumulants of the logarithm of a binomial variate. Biometrika, 73, 425–35
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
Viechtbauer W (2010): Conducting metaanalyses in R with the metafor package. Journal of Statistical Software, 36, 1–48
Wiksten A, Rücker G, Schwarzer G (2016): HartungKnapp method is not always conservative compared with fixedeffect metaanalysis. Statistics in Medicine, 35, 2503–15
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
update.meta
, forest
,
funnel
, metabias
,
metacont
, metagen
,
metareg
, 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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121  # 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),
method = "Inverse")
summary(m1)
# Use different subset of Olkin (1995)
#
m2 < metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = year < 1970,
method = "Inverse", studlab = author)
summary(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,
sm = "OR", method = "Inverse", studlab = author)
# Same metaanalysis result using 'update.meta' function
m3 < update(m2, sm = "OR")
summary(m3)
# Metaanalysis based on MantelHaenszel method (with odds ratio as
# summary measure)
#
m4 < update(m3, method = "MH")
summary(m4)
# Metaanalysis based on Peto method (only available for odds ratio
# as summary measure)
#
m5 < update(m3, method = "Peto")
summary(m5)
## Not run:
# Metaanalysis using generalised linear mixed models (only if R
# packages 'metafor' and 'lme4' are available)
#
if (suppressMessages(require(metafor, quietly = TRUE, warn = FALSE)) &
require(lme4, quietly = TRUE)) {
# Logistic regression model with (k = 4) fixed study effects
# (default: model.glmm = "UM.FS")
#
m6 < metabin(ev.exp, n.exp, ev.cont, n.cont,
data = Olkin1995, subset = year < 1970,
method = "GLMM")
# Same results:
m6 < update(m2, method = "GLMM")
summary(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)
summary(m7)
# Generalised linear mixed model (conditional
# HypergeometricNormal) (R package 'BiasedUrn' must be available)
#
if (require(BiasedUrn, quietly = TRUE)) {
m8 < update(m6, model.glmm = "CM.EL")
summary(m8)
}
# Generalised linear mixed model (conditional BinomialNormal)
#
m9 < update(m6, model.glmm = "CM.AL")
summary(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,
data = Olkin1995, method = "GLMM")
summary(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, ..."
#
summary(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 fixed effect model
#
if (require(BiasedUrn, quietly = TRUE)) {
system.time(m11 < update(m10, model.glmm = "CM.EL"))
summary(m11)
}
# Generalised linear mixed model (conditional BinomialNormal)
# (less than 1 second with Intel Core i73667U, 2.0GHz)
#
summary(update(m10, model.glmm = "CM.AL"))
}
## End(Not run)

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