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, method = "Inverse", sm = gs("smrate"),
incr = gs("incr"), allincr = gs("allincr"),
addincr = gs("addincr"), level = gs("level"),
level.comb = gs("level.comb"), comb.fixed = gs("comb.fixed"),
comb.random = gs("comb.random"), hakn = gs("hakn"),
method.tau = ifelse(!is.na(charmatch(tolower(method), "glmm", nomatch =
NA)), "ML", gs("method.tau")), tau.preset = NULL, TE.tau = NULL,
tau.common = gs("tau.common"), prediction = gs("prediction"),
level.predict = gs("level.predict"), null.effect = NA,
method.bias = gs("method.bias"), backtransf = gs("backtransf"),
irscale = 1, irunit = "person-years", title = gs("title"),
complab = gs("complab"), outclab = "", byvar, bylab,
print.byvar = gs("print.byvar"), byseparator = gs("byseparator"),
keepdata = gs("keepdata"), warn = gs("warn"), control = NULL, ...)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.
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 logical indicating if incr is considered
for all studies if at least one study has zero events. If FALSE
(default), incr is considered only in studies with zero
events.
A logical indicating if incr is used for all
studies irrespective of number of events.
The level used to calculate confidence intervals for individual studies.
The level used to calculate confidence intervals for pooled estimates.
A logical indicating whether a fixed effect meta-analysis should be conducted.
A logical indicating whether a random effects meta-analysis should be conducted.
A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.
A character string indicating which method is used to estimate the between-study variance \(\tau^2\), see Details.
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.
A logical indicating whether a prediction interval should be printed.
The level used to calculate prediction interval for a new study.
A numeric value specifying the effect under the null hypothesis.
A character string indicating which test is to
be used. Either "rank", "linreg", or "mm",
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.
Title of meta-analysis / systematic review.
Comparison label.
Outcome label.
An optional vector containing grouping information
(must be of same length as event).
A character string with a label for the grouping variable.
A logical indicating whether the name of the grouping variable should be printed in front of the group labels.
A character string defining the separator between label and levels of grouping variable.
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.
Additional arguments passed on to
rma.glmm function.
An object of class c("metarate", "meta") with corresponding
print, summary, and forest functions. The
object is a list containing the following components:
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
Estimated (un)transformed incidence rate and its standard error for individual studies.
Lower and upper confidence interval limits for individual studies.
z-value and p-value for test of treatment effect for individual studies.
Weight of individual studies (in fixed and random effects model).
Estimated overall (un)transformed incidence rate and standard error (fixed effect model).
Lower and upper confidence interval limits (fixed effect model).
z-value and p-value for test of overall effect (fixed effect model).
Estimated overall (un)transformed incidence rate and standard error (random effects model).
Lower and upper confidence interval limits (random effects model).
z-value or t-value and corresponding p-value for test of overall effect (random effects model).
As defined above.
Standard error utilised for prediction interval.
Lower and upper limits of prediction interval.
Number of studies combined in meta-analysis.
Heterogeneity statistic Q.
Degrees of freedom for heterogeneity statistic.
P-value of heterogeneity test.
Heterogeneity statistic for likelihood-ratio test
(only if method = "GLMM").
Degrees of freedom for likelihood-ratio test
P-value of likelihood-ratio test.
Square-root of between-study variance.
Standard error of square-root of between-study variance.
Scaling factor utilised internally to calculate common tau-squared across subgroups.
A character string indicating method used for
pooling: "Inverse"
Degrees of freedom for test of treatment effect for
Hartung-Knapp method (only if hakn = TRUE).
Levels of grouping variable - if byvar is not
missing.
Estimated treatment effect and
standard error in subgroups (fixed effect model) - if
byvar is not missing.
Lower and upper confidence
interval limits in subgroups (fixed effect model) - if
byvar is not missing.
z-value and p-value for test of
treatment effect in subgroups (fixed effect model) - if
byvar is not missing.
Estimated treatment effect and
standard error in subgroups (random effects model) - if
byvar is not missing.
Lower and upper confidence
interval limits in subgroups (random effects model) - if
byvar is not missing.
z-value or t-value and
corresponding p-value for test of treatment effect in subgroups
(random effects model) - if byvar is not missing.
Weight of subgroups (in fixed and
random effects model) - if byvar is not missing.
Degrees of freedom for test of treatment effect
for Hartung-Knapp method in subgroups - if byvar is not
missing and hakn = TRUE.
Harmonic mean of number of observations in
subgroups (for back transformation of Freeman-Tukey Double
arcsine transformation) - if byvar is not missing.
Number of events in subgroups - if byvar is
not missing.
Number of observations in subgroups - if byvar is
not missing.
Number of studies combined within subgroups - if
byvar is not missing.
Number of all studies in subgroups - if byvar
is not missing.
Overall within subgroups heterogeneity statistic Q
(based on fixed effect model) - if byvar is not missing.
Overall within subgroups heterogeneity statistic
Q (based on random effects model) - if byvar is not
missing (only calculated if argument tau.common is TRUE).
Degrees of freedom for test of overall within
subgroups heterogeneity - if byvar is not missing.
P-value of within subgroups heterogeneity
statistic Q (based on fixed effect model) - if byvar is
not missing.
P-value of within subgroups heterogeneity
statistic Q (based on random effects model) - if byvar is
not missing.
Overall between subgroups heterogeneity statistic
Q (based on fixed effect model) - if byvar is not
missing.
Overall between subgroups heterogeneity statistic
Q (based on random effects model) - if byvar is not
missing.
Degrees of freedom for test of overall between
subgroups heterogeneity - if byvar is not missing.
P-value of between subgroups heterogeneity
statistic Q (based on fixed effect model) - if byvar is
not missing.
P-value of between subgroups heterogeneity
statistic Q (based on random effects model) - if byvar is
not missing.
Square-root of between-study variance within subgroups
- if byvar is not missing.
Scaling factor utilised internally to calculate common
tau-squared across subgroups - if byvar is not missing.
Heterogeneity statistic H within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic H within subgroups - if byvar is
not missing.
Heterogeneity statistic I2 within subgroups - if
byvar is not missing.
Lower and upper confidence limti for
heterogeneity statistic I2 within subgroups - if byvar is
not missing.
Increment added to number of events.
As defined above.
Original data (set) used in function call (if
keepdata = TRUE).
Information on subset of original data used in
meta-analysis (if keepdata = TRUE).
GLMM object generated by call of
rma.glmm function (fixed effect model).
GLMM object generated by call of
rma.glmm function (random effects model).
Function call.
Version of R package meta used to create object.
Version of R package metafor used for GLMMs.
Fixed effect and random effects meta-analysis 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")
Freeman-Tukey 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. 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.
For several arguments defaults settings are utilised (assignments
using gs function). 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
meta-analysis 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 meta-analysis based on the inverse variance
method. For Freeman-Tukey 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 the 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 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 DerSimonian-Laird estimate (1986) is used in the random effects
model if method.tau = "DL". 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
\(\tau^2\) (argument method.tau) are also available:
Restricted maximum-likelihood estimator (method.tau =
"REML")
Maximum-likelihood estimator (method.tau = "ML")
Hunter-Schmidt estimator (method.tau = "HS")
Sidik-Jonkman 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
between-study variance.
DerSimonian R & Laird N (1986): Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--88
Freeman MF & Tukey JW (1950): Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607--11
Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A, 172, 137--59
Knapp G & Hartung J (2003): Improved tests for a random effects meta-regression 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 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
Viechtbauer W (2010): Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48
# NOT RUN {
# 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)
# }
# NOT RUN {
forest(m2)
forest(m3)
forest(m4)
# }
# NOT RUN {
m5 <- metarate(40:37, c(100, 200, 300, 400), sm = "IRFT")
m5
# }
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