Metaanalysis of single incidence rates
Description
Calculation of an overall incidence rate from studies reporting a
single incidence rate. 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.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  metarate(event, time, studlab,
data=NULL, subset=NULL, method = "Inverse",
sm=.settings$smrate,
incr=.settings$incr, allincr=.settings$allincr,
addincr=.settings$addincr,
level=.settings$level, level.comb=.settings$level.comb,
comb.fixed=.settings$comb.fixed, comb.random=.settings$comb.random,
hakn=.settings$hakn,
method.tau=
ifelse(!is.na(charmatch(tolower(method), "glmm", nomatch = NA)),
"ML", .settings$method.tau),
tau.preset=NULL, TE.tau=NULL,
tau.common=.settings$tau.common,
prediction=.settings$prediction, level.predict=.settings$level.predict,
method.bias=.settings$method.bias,
backtransf=.settings$backtransf,
irscale=1, irunit="personyears",
title=.settings$title, complab=.settings$complab, outclab="",
byvar, bylab, print.byvar=.settings$print.byvar,
byseparator = .settings$byseparator,
keepdata=.settings$keepdata,
warn=.settings$warn,
...)

Arguments
event 
Number of events. 
time 
Person time at risk. 
studlab 
An optional vector with study labels. 
data 
An optional data frame containing the study information, i.e., event and time. 
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 
sm 
A character string indicating which summary measure
( 
incr 
A numeric which is added to the event number of studies with zero events, i.e., studies with an incidence rate of 0. 
allincr 
A logical indicating if 
addincr 
A logical indicating if 
level 
The level used to calculate confidence intervals for individual studies. 
level.comb 
The level used to calculate confidence intervals for pooled estimates. 
comb.fixed 
A logical indicating whether a fixed effect metaanalysis should be conducted. 
comb.random 
A logical indicating whether a random effects metaanalysis should be conducted. 
prediction 
A logical indicating whether a prediction interval should be printed. 
level.predict 
The level used to calculate prediction interval for a new study. 
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 betweenstudy variance τ^2, see Details. 
tau.preset 
Prespecified value for the squareroot of the betweenstudy variance τ^2. 
TE.tau 
Overall treatment effect used to estimate the betweenstudy variance tausquared. 
tau.common 
A logical indicating whether tausquared should be the same across subgroups. 
method.bias 
A character string indicating which test is to be
used. Either 
backtransf 
A logical indicating whether results for
transformed rates (argument 
irscale 
A numeric defining a scaling factor for printing of rates. 
irunit 
A character specifying the time unit used to calculate rates, e.g. personyears. 
title 
Title of metaanalysis / systematic review. 
complab 
Comparison label. 
outclab 
Outcome label. 
byvar 
An optional vector containing grouping information (must
be of same length as 
bylab 
A character string with a label for the grouping variable. 
print.byvar 
A logical indicating whether the name of the grouping variable should be printed in front of the group labels. 
byseparator 
A character string defining the separator between label and levels of grouping variable. 
keepdata 
A logical indicating whether original data (set) should be kept in meta object. 
warn 
A logical indicating whether the addition of 
... 
Additional arguments passed on to

Details
Fixed effect and random effects metaanalysis of single incidence rates to calculate an overall rate. The following transformations of incidence rates are implemented to calculate an overall rate:
Log transformation (
sm="IRLN"
, default)Square root transformation (
sm="IRS"
)FreemanTukey Double arcsine transformation (
sm="IRFT"
)No transformation (
sm="IR"
)
Note, you should use R function metainc
to compare
incidence rates of pairwise comparisons instead of using
metarate
for each treatment arm separately which will break
randomisation in randomised controlled trials.
Argument irscale
can be used to rescale rates,
e.g. irscale=1000
means that rates are expressed as events
per 1000 time units, e.g. personyears. This is useful in situations
with (very) low rates. Argument irunit
can be used to specify
the time unit used in individual studies (default:
"personyears"). This information is printed in summaries and forest
plots if argument irscale
is not equal to 1.
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 choosen for arguments
comb.fixed
and comb.random
. Accordingly, the estimate
for the random effects model can be extracted from component
TE.random
of an object of class "meta"
even if
argument comb.random=FALSE
. However, all functions in R
package meta will adequately consider the values for
comb.fixed
and comb.random
. E.g. function
print.meta
will not print results for the random
effects model if comb.random=FALSE
.
A random intercept Poisson regression model can be utilised for the
metaanalysis of incidence rates (Stijnen et al., 2010). This method
is available (argument method = "GLMM"
) by calling the
rma.glmm
function from R package
metafor internally.
If the summary measure is equal to "IR" or "IRLN", a continuity
correction is applied if any study has zero events, i.e., an
incidence rate of 0. By default, 0.5 is used as continuity
correction (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 FreemanTukey and square root transformation and GLMMs
no continuity correction is used.
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
metaanalysis of an existing metarate object by only specifying
arguments which should be changed.
For the random effects, the method by Hartung and Knapp (2003) is
used to adjust test statistics and confidence intervals if argument
hakn=TRUE
.
The DerSimonianLaird estimate (1986) is used in the random effects
model if method.tau="DL"
. The iterative PauleMandel method
(1982) to estimate the betweenstudy variance is used if argument
method.tau="PM"
. Internally, R function paulemandel
is
called which is based on R function mpaule.default from R package
metRology from S.L.R. Ellison <s.ellison at lgc.co.uk>.
If R package metafor (Viechtbauer 2010) is installed, the
following methods to estimate the betweenstudy variance
τ^2 (argument method.tau
) are also available:
Restricted maximumlikelihood estimator (
method.tau="REML"
)Maximumlikelihood estimator (
method.tau="ML"
)HunterSchmidt estimator (
method.tau="HS"
)SidikJonkman estimator (
method.tau="SJ"
)Hedges estimator (
method.tau="HE"
)Empirical Bayes estimator (
method.tau="EB"
).
For these methods the R function rma.uni
of R package
metafor is called internally. See help page of R function
rma.uni
for more details on these methods to estimate
betweenstudy variance.
Value
An object of class c("metarate", "meta")
with corresponding
print
, summary
, plot
function. The object is a
list containing the following components:
event, n, studlab, 

sm, incr, allincr, addincr, method.ci, 

level, level.comb, 
As defined above. 
comb.fixed, comb.random, 

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

tau.common, title, complab, outclab, 

byvar, bylab, print.byvar, byseparator, warn 

TE, seTE 
Estimated (un)transformed incidence rate and its standard error for 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 (un)transformed incidence rate and standard error (fixed effect model). 
lower.fixed, upper.fixed 
Lower and upper confidence interval limits (fixed effect model). 
zval.fixed, pval.fixed 
zvalue and pvalue for test of overall effect (fixed effect model). 
TE.random, seTE.random 
Estimated overall (un)transformed incidence rate and standard error (random effects model). 
lower.random, upper.random 
Lower and upper confidence interval limits (random effects model). 
zval.random, pval.random 
zvalue or tvalue and corresponding pvalue for test of overall 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. 
tau 
Squareroot of betweenstudy variance. 
se.tau 
Standard error of squareroot of betweenstudy variance. 
C 
Scaling factor utilised internally to calculate common tausquared across subgroups. 
method 
A character string indicating method used
for pooling: 
df.hakn 
Degrees of freedom for test of treatment effect for
HartungKnapp method (only if 
bylevs 
Levels of grouping variable  if 
TE.fixed.w, seTE.fixed.w 
Estimated treatment effect and
standard error in subgroups (fixed effect model)  if 
lower.fixed.w, upper.fixed.w 
Lower and upper confidence
interval limits in subgroups (fixed effect model)  if

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

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

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

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

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

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

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

lower.I2.w, upper.I2.w 
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups  if 
incr.event 
Increment added to number of events. 
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. 
Author(s)
Guido Schwarzer sc@imbi.unifreiburg.de
References
DerSimonian R & Laird N (1986), Metaanalysis in clinical trials. Controlled Clinical Trials, 7, 177–188.
Freeman MF & Tukey JW (1950), Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607–611.
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009), A reevaluation of randomeffects metaanalysis. Journal of the Royal Statistical Society: Series A, 172, 137–159.
Knapp G & Hartung J (2003), Improved Tests for a Random Effects Metaregression with a Single Covariate. Statistics in Medicine, 22, 2693–2710, doi: 10.1002/sim.1482 .
Paule RC & Mandel J (1982), Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377–385.
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.
See Also
update.meta
, metacont
, metagen
, print.meta
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  #
# Apply various metaanalysis methods to estimate incidence rates
#
m1 < metarate(4:1, c(10, 20, 30, 40))
m2 < update(m1, sm="IR")
m3 < update(m1, sm="IRS")
m4 < update(m1, sm="IRFT")
#
m1
m2
m3
m4
#
forest(m1)
forest(m1, irscale=100)
forest(m1, irscale=100, irunit="persondays")
forest(m1, backtransf = FALSE)
# forest(m2)
# forest(m3)
# forest(m4)
#
m5 < metarate(40:37, c(100, 200, 300, 400), sm="IRFT")
m5

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