Calculation of fixed 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, method = "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"), 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"), method.bias = gs("method.bias"),
n.e = NULL, n.c = NULL, backtransf = gs("backtransf"),
irscale = 1, irunit = "person-years", 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"),
keepdata = gs("keepdata"), warn = gs("warn"), control = NULL, ...)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.
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" or "IRD") is to be used for pooling of
studies, see Details.
A numerical value which is added to each cell frequency for studies with a zero cell count, see Details.
A logical indicating if incr is added to each
cell frequency of all studies if at least one study has a zero
cell count. If FALSE (default), incr is added only to each
cell frequency of studies with a zero cell count.
A logical indicating if incr is added to each
cell frequency of all studies irrespective of zero cell counts.
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.
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 \(\tau^2\). Either
"DL", "PM", "REML", "ML",
"HS", "SJ", "HE", or "EB", can be
abbreviated.
Prespecified value for the square-root of the between-study variance \(\tau^2\).
Overall treatment effect used to estimate the between-study variance \(\tau^2\).
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 character string indicating which test for
funnel plot asymmetry is to be used. Either "linreg" or
"rank", 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") should be back
transformed in printouts and plots. If TRUE (default), results
will be presented as incidence rate ratios; otherwise log
incidence 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.
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 containing grouping information
(must be of same length as event.e).
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 warnings should be printed
(e.g., if incr is added to studies with zero cell
frequencies).
Additional arguments passed on to
rma.glmm function.
An object of class c("metainc", "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 treatment effect and standard error of 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 treatment effect and standard error (fixed effect model).
Lower and upper confidence interval limits (fixed effect model).
z-value and p-value for test of overall treatment effect (fixed effect model).
Estimated overall treatment effect 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 treatment 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.
Logical flag indicating if any study included in meta-analysis has any zero cell frequencies.
Increment added to number of events.
Degrees of freedom for test of treatment effect for
Hartung-Knapp method (only if hakn = TRUE).
Number of studies combined in meta-analysis using Mantel-Haenszel method.
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 experimental group in
subgroups - if byvar is not missing.
Total person time in subgroups (experimental
group) - if byvar is not missing.
Number of observations in experimental group in
subgroups - if byvar is not missing.
Number of events in control group in subgroups -
if byvar is not missing.
Total person time in subgroups (control group) - if
byvar is not missing.
Number of observations in control group 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.
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.
Treatment estimates and standard errors are calculated for each study. The following measures of treatment effect are available:
Incidence Rate Ratio (sm = "IRR")
Incidence Rate Difference (sm = "IRD")
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.
By default, both fixed effect and random effects models are
considered (see arguments comb.fixed and
comb.random). If method is "MH" (default), the
Mantel-Haenszel 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 (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) |
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 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 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 metainc 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.
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. http://profiles.nlm.nih.gov/ps/retrieve/ResourceMetadata/NNBBMQ
DerSimonian R & Laird N (1986): Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177--88
Greenland S & Robins JM (1985): Estimation of a common effect parameter from sparse follow-up data. Biometrics, 41, 55--68
Hartung J & Knapp G (2001): A refined method for the meta-analysis of controlled clinical trials with binary outcome. Statistics in Medicine, 20, 3875--89
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 {
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)
# }
# NOT RUN {
# 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")
# }
# NOT RUN {
# }
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