Description Usage Arguments Details Value Author(s) References See Also Examples
Calculation of fixed effect and random effects estimates (incidence
rate ratio or incidence rate difference) for metaanalyses with
event counts. MantelHaenszel, Cochran, inverse variance 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.
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  metainc(
event.e,
time.e,
event.c,
time.c,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
method = if (sm == "IRSD") "Inverse" else "MH",
sm = gs("sminc"),
incr = gs("incr"),
allincr = gs("allincr"),
addincr = gs("addincr"),
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 = gs("method.bias"),
n.e = NULL,
n.c = NULL,
backtransf = if (sm == "IRSD") FALSE else gs("backtransf"),
irscale = 1,
irunit = "personyears",
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"),
keepdata = gs("keepdata"),
warn = gs("warn"),
control = NULL,
...
)

event.e 
Number of events in experimental group. 
time.e 
Person time at risk in experimental group. 
event.c 
Number of events in control group. 
time.c 
Person time at risk in control group. 
studlab 
An optional vector with study labels. 
data 
An optional data frame containing the study information, i.e., event.e, time.e, event.c, and time.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 
A numerical value which is added to each cell frequency for studies with a zero cell count, see Details. 
allincr 
A logical indicating if 
addincr 
A logical indicating if 
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 is to
be used. Either 
n.e 
Number of observations in experimental group (optional). 
n.c 
Number of observations in control group (optional). 
backtransf 
A logical indicating whether results for
incidence rate ratio ( 
irscale 
A numeric defining a scaling factor for printing of incidence rate differences. 
irunit 
A character string specifying the time unit used to calculate rates, e.g. personyears. 
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. 
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 comparing two incidence rates.
The following measures of treatment effect are available:
Incidence Rate Ratio (sm = "IRR"
)
Incidence Rate Difference (sm = "IRD"
)
Square root transformed Incidence Rate Difference (sm =
"IRSD"
)
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 is used to calculate the fixed effect
estimate (Greenland & Robbins, 1985); if method
is
"Inverse"
, inverse variance weighting is used for pooling;
if method
is "Cochran"
, the Cochran method is used
for pooling (BayneJones, 1964, Chapter 8).
A distinctive and frequently overlooked advantage of incidence
rates is that individual patient data (IPD) can be extracted from
count data. Accordingly, statistical methods for IPD, i.e.,
generalised linear mixed models, can be utilised in a metaanalysis
of incidence rate ratios (Stijnen et al., 2010). These methods are
available (argument method = "GLMM"
) by calling the
rma.glmm
function from R package
metafor internally.
Three different GLMMs are available for metaanalysis of incidence
rate ratios using argument model.glmm
(which corresponds to
argument model
in the rma.glmm
function):
1.  Poisson regression model with fixed study effects (default) 
(model.glmm = "UM.FS" , i.e., Unconditional
Model  Fixed Study effects) 

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

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

Details on these three GLMMs as well as additional arguments which
can be provided using argument '...
' in metainc
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 (argument incr
). 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 MantelHaenszel method, Cochran
method, and GLMMs, nothing is added to zero cell counts.
Accordingly, estimates for these methods 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("metainc", "meta")
with corresponding
print
, summary
, and forest
functions. The
object is a list containing the following components:
event.e, time.e, event.c, time.c, studlab, exclude, 
As defined above. 
sm, method, incr, allincr, addincr, model.glmm, warn, 
As defined above. 
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 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 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. 
sparse 
Logical flag indicating if any study included in metaanalysis has any zero cell frequencies. 
incr.event 
Increment added to number of events. 
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 
time.e.w 
Total person time in subgroups (experimental
group)  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 
time.c.w 
Total person time in subgroups (control group)  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
BayneJones S et al. (1964): Smoking and Health: Report of the Advisory Committee to the Surgeon General of the United States. U23 Department of Health, Education, and Welfare. Public Health Service Publication No. 1103.
DerSimonian R & Laird N (1986): Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–88
Greenland S & Robins JM (1985): Estimation of a common effect parameter from sparse followup data. Biometrics, 41, 55–68
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–59
Jackson D, Law M, Rücker G, Schwarzer G (2017): The HartungKnapp modification for randomeffects metaanalysis: A useful refinement but are there any residual concerns? Statistics in Medicine, 36, 3923–34
Knapp G & Hartung J (2003): Improved tests for a random effects metaregression with a single covariate. Statistics in Medicine, 22, 2693–710
Paule RC & Mandel J (1982): Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377–85
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
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
metabin
, update.meta
,
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  data(smoking)
m1 < metainc(d.smokers, py.smokers, d.nonsmokers, py.nonsmokers,
data = smoking, studlab = study)
print(m1, digits = 2)
m2 < update(m1, method = "Cochran")
print(m2, digits = 2)
data(lungcancer)
m3 < metainc(d.smokers, py.smokers,
d.nonsmokers, py.nonsmokers,
data = lungcancer, studlab = study)
print(m3, digits = 2)
# Redo Cochran metaanalysis with inflated standard errors
#
# All cause mortality
#
TEa < log((smoking$d.smokers/smoking$py.smokers) /
(smoking$d.nonsmokers/smoking$py.nonsmokers))
seTEa < sqrt(1 / smoking$d.smokers + 1 / smoking$d.nonsmokers +
2.5 / smoking$d.nonsmokers)
metagen(TEa, seTEa, sm = "IRR", studlab = smoking$study)
# Lung cancer mortality
#
TEl < log((lungcancer$d.smokers/lungcancer$py.smokers) /
(lungcancer$d.nonsmokers/lungcancer$py.nonsmokers))
seTEl < sqrt(1 / lungcancer$d.smokers + 1 / lungcancer$d.nonsmokers +
2.25 / lungcancer$d.nonsmokers)
metagen(TEl, seTEl, sm = "IRR", studlab = lungcancer$study)
## Not run:
# Metaanalysis using generalised linear mixed models
# (only if R packages 'metafor' and 'lme4' are available)
# Poisson regression model (fixed study effects)
#
m4 < metainc(d.smokers, py.smokers, d.nonsmokers, py.nonsmokers,
data = smoking, studlab = study, method = "GLMM")
m4
# Mixedeffects Poisson regression model (random study effects)
#
update(m4, model.glmm = "UM.RS", nAGQ = 1)
#
# Generalised linear mixed model (conditional PoissonNormal)
#
update(m4, model.glmm = "CM.EL")
## End(Not run)

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