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.
metarate(
event,
time,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
cluster = NULL,
n = NULL,
method = "Inverse",
sm = gs("smrate"),
incr = gs("incr"),
method.incr = gs("method.incr"),
method.ci = gs("method.ci.rate"),
level = gs("level"),
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,
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"),
null.effect = NA,
method.bias = gs("method.bias"),
backtransf = gs("backtransf"),
irscale = 1,
irunit = "person-years",
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 = "",
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"),
byvar,
hakn,
adhoc.hakn,
keepdata = gs("keepdata"),
warn = gs("warn"),
warn.deprecated = gs("warn.deprecated"),
control = NULL,
...
)An object of class c("metarate", "meta") with corresponding
generic functions (see meta-object).
Number of events.
Person time at risk.
An optional vector with study labels.
An optional data frame containing the study information, i.e., event and time.
An optional vector specifying a subset of studies to be used.
An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
An optional vector specifying which estimates come from the same cluster resulting in the use of a three-level meta-analysis model.
Number of observations.
A character string indicating which method is to be
used for pooling of studies. One of "Inverse" and
"GLMM", can be abbreviated.
A character string indicating which summary measure
("IR", "IRLN", "IRS", or "IRFT") is
to be used for pooling of studies, see Details.
A numeric which is added to the event number of studies with zero events, i.e., studies with an incidence rate of 0.
A character string indicating which continuity
correction method should be used ("only0",
"if0all", or "all"), see Details.
A character string indicating whether to use approximate normal ("NAsm") or exact Poisson ("Poisson") confidence limits.
The level used to calculate confidence intervals for individual studies.
A logical indicating whether a common effect meta-analysis should be conducted.
A logical indicating whether a random effects meta-analysis should be conducted.
A logical indicating whether overall summaries should be reported. This argument is useful in a meta-analysis with subgroups if overall results should not be reported.
A logical value indicating whether to print heterogeneity measures for overall treatment comparisons. This argument is useful in a meta-analysis with subgroups if heterogeneity statistics should only be printed on subgroup level.
A logical indicating whether a prediction interval should be printed.
A character string indicating which method is
used to estimate the between-study variance \(\tau^2\) and its
square root \(\tau\) (see meta-package).
A character string indicating which method is
used to estimate the confidence interval of \(\tau^2\) and
\(\tau\) (see meta-package).
Prespecified value for the square root of the between-study variance \(\tau^2\).
Overall treatment effect used to estimate the between-study variance tau-squared.
A logical indicating whether tau-squared should be the same across subgroups.
The level used to calculate confidence intervals for meta-analysis estimates.
A character string indicating which method
is used to calculate confidence interval and test statistic for
random effects estimate (see meta-package).
A character string indicating whether an
ad hoc variance correction should be applied in the case
of an arbitrarily small Hartung-Knapp variance estimate (see
meta-package).
The level used to calculate prediction interval for a new study.
A character string indicating which method is
used to calculate a prediction interval (see
meta-package).
A character string indicating whether an
ad hoc variance correction should be applied for
prediction interval (see meta-package).
A numeric value specifying the effect under the null hypothesis.
A character string indicating which test is to
be used. Either "Begg", "Egger", or
"Thompson", can be abbreviated. See function
metabias.
A logical indicating whether results for
transformed rates (argument sm != "IR") should be back
transformed in printouts and plots. If TRUE (default), results
will be presented as incidence rates; otherwise transformed rates
will be shown.
A numeric defining a scaling factor for printing of rates.
A character string specifying the time unit used to calculate rates, e.g. person-years.
A character string used in printouts and forest plot to label the pooled common effect estimate.
A character string used in printouts and forest plot to label the pooled random effects estimate.
A character string used in printouts and forest plot to label the prediction interval.
A character string used to label weights of common effect model.
A character string used to label weights of random effects model.
Title of meta-analysis / systematic review.
Comparison label.
Outcome label.
An optional vector to conduct a meta-analysis with subgroups.
A character string with a name for the subgroup variable.
A logical indicating whether the name of the subgroup variable should be printed in front of the group labels.
A character string defining the separator between name of subgroup variable and subgroup label.
A logical value indicating whether to print results of test for subgroup differences.
A logical indicating whether prediction intervals should be printed for subgroups.
Deprecated argument (replaced by 'subgroup').
Deprecated argument (replaced by 'method.random.ci').
Deprecated argument (replaced by 'adhoc.hakn.ci').
A logical indicating whether original data (set) should be kept in meta object.
A logical indicating whether the addition of
incr to studies with zero events should result in a
warning.
A logical indicating whether warnings should be printed if deprecated arguments are used.
An optional list to control the iterative process to
estimate the between-study variance \(\tau^2\). This argument
is passed on to rma.uni or
rma.glmm, respectively.
Additional arguments passed on to
rma.glmm function and to catch deprecated
arguments.
Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de
This function provides methods for common effect and random effects
meta-analysis of single incidence rates to calculate an overall
rate. 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.
The following transformations of incidence rates are implemented to calculate an overall rate:
Log transformation (sm = "IRLN", default)
Square root transformation (sm = "IRS")
Freeman-Tukey Double arcsine transformation (sm =
"IRFT")
No transformation (sm = "IR")
List elements TE, TE.common, TE.random, etc.,
contain the transformed incidence rates. In printouts and plots
these values are back transformed if argument backtransf =
TRUE (default).
By default (argument method = "Inverse"), the inverse
variance method (Borenstein et al., 2010) is used for pooling by
calling metagen internally. A random intercept
Poisson regression model (Stijnen et al., 2010) can be utilised
instead with argument method = "GLMM" which calls the
rma.glmm function from R package
metafor.
A three-level random effects meta-analysis 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 meta-analysis with different settings.
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")
If the summary measure (argument sm) is equal to "IR" or
"IRLN", the continuity correction is applied if a 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
meta-analysis based on the inverse variance method.
For the Freeman-Tukey (Freeman & Tukey, 1950) and square root transformation as well as GLMMs no continuity correction is used.
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.
Argument null.effect can be used to specify the rate used
under the null hypothesis in a test for an overall effect.
By default (null.effect = NA), no hypothesis test is
conducted as it is unclear which value is a sensible choice for the
data at hand. An overall rate of 2, for example, could be tested
by setting argument null.effect = 2.
Note, all tests for an overall effect are two-sided with the
alternative hypothesis that the effect is unequal to
null.effect.
Arguments subset and exclude can be used to exclude
studies from the meta-analysis. Studies are removed completely from
the meta-analysis using argument subset, while excluded
studies are shown in printouts and forest plots using argument
exclude (see Examples in metagen).
Meta-analysis 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.
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. person-years. This is useful in situations
with (very) low rates. Argument irunit can be used to
specify the time unit used in individual studies (default:
"person-years"). This information is printed in summaries and
forest plots if argument irscale is not equal to 1.
A prediction interval will only be shown if prediction =
TRUE.
Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010): A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods, 1, 97--111
Freeman MF & Tukey JW (1950): Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607--11
Stijnen T, Hamza TH, Ozdemir P (2010): Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046--67
Van den Noortgate W, López-López JA, Marín-Martínez F, Sánchez-Meca J (2013): Three-level meta-analysis of dependent effect sizes. Behavior Research Methods, 45, 576--94
Viechtbauer W (2010): Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48
meta-package, update.meta,
metacont, metagen,
print.meta
# Apply various meta-analysis 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 = "person-days")
forest(m1, backtransf = FALSE)
if (FALSE) {
forest(m2)
forest(m3)
forest(m4)
}
m5 <- metarate(40:37, c(100, 200, 300, 400), sm = "IRFT")
m5
Run the code above in your browser using DataLab