Calculation of common effect and random effects estimates (incidence
rate ratio or incidence rate difference) for meta-analyses with
event counts. Mantel-Haenszel, 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.
metainc(
event.e,
time.e,
event.c,
time.c,
studlab,
data = NULL,
subset = NULL,
exclude = NULL,
cluster = NULL,
method = if (sm == "IRSD") "Inverse" else "MH",
sm = gs("sminc"),
incr = gs("incr"),
method.incr = gs("method.incr"),
model.glmm = "UM.FS",
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 = 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"),
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"),
method.bias = gs("method.bias"),
n.e = NULL,
n.c = NULL,
backtransf = if (sm == "IRSD") FALSE else 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 = "",
label.e = gs("label.e"),
label.c = gs("label.c"),
label.left = gs("label.left"),
label.right = gs("label.right"),
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("metainc", "meta") with corresponding
generic functions (see meta-object).
Number of events in experimental group.
Person time at risk in experimental group.
Number of events in control group.
Person time at risk in control group.
An optional vector with study labels.
An optional data frame containing the study information, i.e., event.e, time.e, event.c, and time.c.
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.
A character string indicating which method is to be
used for pooling of studies. One of "MH",
"Inverse", "Cochran", or "GLMM" can be
abbreviated.
A character string indicating which summary measure
("IRR", "IRD", "IRSD", or "VE") is to
be used for pooling of studies, see Details.
A numerical value which is added to cell frequencies for studies with a zero cell count, see Details.
A character string indicating which continuity
correction method should be used ("only0",
"if0all", or "all"), see Details.
A character string indicating which GLMM should
be used. One of "UM.FS", "UM.RS", and
"CM.EL", see Details.
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 character string indicating which test is to
be used. Either "Begg", "Egger", or
"Thompson", can be abbreviated. See function
metabias.
Number of observations in experimental group (optional).
Number of observations in control group (optional).
A logical indicating whether results for
incidence rate ratio (sm = "IRR") and vaccine efficacy or
vaccine effectiveness (sm = "VE") should be back
transformed in printouts and plots. If TRUE (default), results
will be presented as incidence rate ratios or vaccine efficacy /
effectiveness; otherwise log incidence rate ratios or log vaccine
rate ratios will be shown.
A numeric defining a scaling factor for printing of incidence rate differences.
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.
Label for experimental group.
Label for control group.
Graph label on left side of forest plot.
Graph label on right side of forest plot.
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 warnings should be printed
(e.g., if incr is added to studies with zero cell
frequencies).
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
Calculation of common and random effects estimates for meta-analyses 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")
Vaccine efficacy or vaccine effectiveness (sm = "VE")
Note, log incidence rate ratio (logIRR) and log vaccine ratio
(logVR) are mathematical identical, however, back-transformed
results differ as vaccine efficacy or effectiveness is defined as
VE = 100 * (1 - IRR).
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.
By default, both common effect and random effects models are
considered (see arguments common and
random). If method is "MH" (default), the
Mantel-Haenszel method is used to calculate the common 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 (Bayne-Jones, 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 meta-analysis
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 meta-analysis 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. | Mixed-effects Poisson regression model with random study effects |
(model.glmm = "UM.RS", i.e., Unconditional
Model - Random Study effects) | |
| 3. | Generalised linear mixed model (conditional Poisson-Normal) |
(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:
common effect model (with fixed treatment effect) and random effects
model (with random treatment effects).
Three approaches are available to apply a continuity correction:
Only studies with a zero cell count (method.incr =
"only0", default)
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")
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 meta-analysis based
on the inverse variance method. For Mantel-Haenszel 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.
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.
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.
A prediction interval will only be shown if prediction =
TRUE.
Bayne-Jones S et al. (1964): Smoking and Health: Report of the Advisory Committee to the Surgeon General of the United States. U-23 Department of Health, Education, and Welfare. Public Health Service Publication No. 1103.
Greenland S & Robins JM (1985): Estimation of a common effect parameter from sparse follow-up data. Biometrics, 41, 55--68
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, metabin,
update.meta, print.meta
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 meta-analysis 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)
if (FALSE) {
# Meta-analysis 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
# Mixed-effects Poisson regression model (random study effects)
#
update(m4, model.glmm = "UM.RS", nAGQ = 1)
#
# Generalised linear mixed model (conditional Poisson-Normal)
#
update(m4, model.glmm = "CM.EL")
}
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