Calculation of fixed effect and random effects estimates (risk
ratio, odds ratio, risk difference, or arcsine difference) for
meta-analyses with binary outcome data. Mantel-Haenszel, inverse
variance, Peto method, and generalised linear mixed model (GLMM) are
available for pooling. For GLMMs, the
rma.glmm function from R package
metafor (Viechtbauer 2010) is called internally.
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.
method
A character string indicating which method is to be
used for pooling of studies. One of "Inverse", "MH",
"Peto", or "GLMM", can be abbreviated.
sm
A character string indicating which summary measure
("RR", "OR", "RD", or "ASD") is to be used
for pooling of studies, see Details.
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 "TACC" which stands for treatment arm continuity
correction, see Details.
allincr
A logical indicating if incr is added to each
cell frequency of all studies if at least one study has a zero cell
count. If FALSE (default), incr is added only to each cell frequency of
studies with a zero cell count.
addincr
A logical indicating if incr is added to each cell
frequency of all studies irrespective of zero cell counts.
allstudies
A logical indicating if studies with zero or all
events in both groups are to be included in the meta-analysis
(applies only if sm is equal to "RR" or "OR").
MH.exact
A logical indicating if incr is not to be added
to all cell frequencies for studies with a zero cell count to
calculate the pooled estimate based on the Mantel-Haenszel method.
RR.cochrane
A logical indicating if 2*incr instead of
1*incr is to be added to n.e and n.c in the
calculation of the risk ratio (i.e., sm="RR") for studies
with a zero cell. This is used in RevMan 5, the
Cochrane Collaboration's program for preparing and maintaining
Cochrane reviews.
model.glmm
A character string indicating which GLMM should be
used. One of "UM.FS", "UM.RS", "CM.EL", and
"CM.AL", see Details.
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.
hakn
A logical indicating whether the 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 τ^2.
tau.common
A logical indicating whether tau-squared should be
the same across subgroups.
method.bias
A character string indicating which test for
funnel plot asymmetry is to be used. Either "rank",
"linreg", "mm", "count", "score", or
"peters", can be abbreviated. See function metabias
backtransf
A logical indicating whether results for odds
ratio (sm="OR") and risk ratio (sm="RR") should be
back transformed in printouts and plots. If TRUE (default),
results will be presented as odds ratios and risk ratios;
otherwise log odds ratios and log risk ratios will be shown.
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 event.e).
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.
print.CMH
A logical indicating whether result of the
Cochran-Mantel-Haenszel 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 incr is added to studies with zero cell
frequencies).
...
Additional arguments passed on to
rma.glmm function.
Details
Treatment estimates and standard errors are calculated for each
study. The following measures of treatment effect are available:
Risk ratio (sm="RR")
Odds ratio (sm="OR")
Risk difference (sm="RD")
Arcsine difference (sm="ASD")
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 chosen 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.
By default, both fixed effect and random effects models are
considered (see arguments comb.fixed and
comb.random). If method is "MH" (default), the
Mantel-Haenszel method is used to calculate the fixed effect
estimate; if method is "Inverse", inverse variance
weighting is used for pooling; if method is "Peto",
the Peto method is used for pooling. By default, the
DerSimonian-Laird estimate (1986) is used in the random effects
model (method.tau="DL"). For the Peto method, Peto's log odds
ratio, i.e. (O - E) / V and its standard error sqrt(1 / V)
with O - E and V denoting "Observed minus
Expected" and "V", are utilised in the random effects
model. Accordingly, results of a random effects model using
sm="Peto" can be (slightly) 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 two-by-two table. Accordingly, statistical methods for IPD,
i.e., logistic regression and generalised linear mixed models, can
be utilised in a meta-analysis of binary outcomes (Stijnen et al.,
2010; Simmonds et al., 2014). 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
meta-analysis with binary outcomes using argument model.glmm
(which corresponds to argument model in the
rma.glmm function):
Logistic regression model with fixed study effects (default)
[] (model.glmm = "UM.FS", i.e., Unconditional
Model - Fixed Study effects)
Mixed-effects logistic regression model with random study
effects
[] (model.glmm = "UM.RS", i.e., Unconditional
Model - Random Study effects)
Generalised linear mixed model (conditional Hypergeometric-Normal)
[] (model.glmm = "CM.EL", i.e., Conditional
Model - Exact Likelihood)
Generalised linear mixed model (conditional Binomial-Normal)
[] (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
meta-analysis based on the inverse variance method. For Peto method
and GLMMs no continuity correction is used. For the Mantel-Haenszel
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 Mantel-Haenszel estimate and he
advocates the exact method (MH.exact=TRUE). Note, estimates
based on exact Mantel-Haenszel method or GLMM are not defined if the
number of events is zero in all studies either in the experimental
or control group.
Argument byvar can be used to conduct subgroup analysis for
all methods but GLMMs. Instead use the metareg
function for GLMMs which can also be used for continuous covariates.
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 metabin object by only specifying
arguments which should be changed.
For the random effects, the method by Hartung and Knapp (2001) is
used to adjust test statistics and confidence intervals if argument
hakn=TRUE. For GLMMs, a method similar to Knapp and Hartung
(2003) is implemented, see description of argument tdist in
rma.glmm.
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("metabin", "meta") with corresponding
print, summary, plot function. The object is a
list containing the following components:
Estimated treatment effect and standard error of individual studies.
lower, upper
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 Q.
df.Q
Degrees of freedom for heterogeneity statistic.
Q.LRT
Heterogeneity statistic for likelihood-ratio test (only
if method = "GLMM").
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.
Q.CMH
Cochran-Mantel-Haenszel test statistic for overall effect.
incr.e, incr.c
Increment added to cells in the experimental and
control group, respectively.
sparse
Logical flag indicating if any study included in
meta-analysis 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
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.
event.e.w
Number of events in experimental group in subgroups
- if byvar is not missing.
n.e.w
Number of observations in experimental group in
subgroups - if byvar is not missing.
event.c.w
Number of events in control 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).
.glmm.fixed
GLMM object generated by call of
rma.glmm function (fixed effect model).
.glmm.random
GLMM object generated by call of
rma.glmm function (random effects model).
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