Provides three models for the network meta-analysis of binary data (Mantel-Haenszel method, based on the non-central hypergeometric distribution, and the inverse variance method).
netmetabin(
event1,
n1,
event2,
n2,
treat1,
treat2,
studlab,
data = NULL,
subset = NULL,
sm,
method = "MH",
cc.pooled = FALSE,
incr = gs("incr"),
allincr = gs("allincr"),
addincr = gs("addincr"),
allstudies = gs("allstudies"),
level = gs("level"),
level.comb = gs("level.comb"),
comb.fixed = gs("comb.fixed"),
comb.random = method == "Inverse" & (gs("comb.random") | !is.null(tau.preset)),
prediction = FALSE,
level.predict = gs("level.predict"),
reference.group = "",
baseline.reference = TRUE,
all.treatments = NULL,
seq = NULL,
tau.preset = NULL,
tol.multiarm = 0.001,
tol.multiarm.se = tol.multiarm,
details.chkmultiarm = FALSE,
sep.trts = ":",
nchar.trts = 666,
backtransf = gs("backtransf"),
title = "",
keepdata = gs("keepdata"),
warn = TRUE
)Number of events (first treatment).
Number of observations (first treatment).
Number of events (second treatment).
Number of observations (second treatment)
Label/Number for first treatment.
Label/Number for second treatment.
An optional - but important! - vector with study labels (see Details).
An optional data frame containing the study information.
An optional vector specifying a subset of studies to be used.
A character string indicating underlying summary measure,
i.e., "RD", "RR", "OR", "ASD".
A character string indicating which method is to be
used for pooling of studies. One of "Inverse",
"MH", or "NCH", can be abbreviated.
A logical indicating whether incr should be
used as a continuity correction, when calculating the network
meta-analysis estimates.
A numerical value which is added to each cell count, i.e., to the numbers of events and non-events, of all treatment arms in studies with zero events or non-events in any of the treatment arms ("continuity correction").
A logical indicating whether incr should be
added to each cell count of all studies if a continuity
correction was used for at least one study (only considered if
method = "Inverse"). If FALSE (default), incr is
used as continuity correction only for studies with zero events
or zero non-events in any of the treatment arms.
A logical indicating whether incr should be
added to each cell count of all studies, irrespective of zero
cell counts (only considered if method = "Inverse").
A logical indicating whether studies with zero
events or non-events in all treatment arms should be included in
an inverse variance meta-analysis (applies only if method =
"Inverse" and sm is equal to either "RR" or
"OR").
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 effects (common effects) network meta-analysis should be conducted.
A logical indicating whether a random effects network meta-analysis should be conducted.
A logical indicating whether a prediction
interval should be printed (only considered if method =
"Inverse").
The level used to calculate prediction
interval for a new study (only considered if method =
"Inverse").
Reference treatment.
A logical indicating whether results
should be expressed as comparisons of other treatments versus the
reference treatment (default) or vice versa. This argument is
only considered if reference.group has been specified.
A logical or "NULL". If TRUE,
matrices with all treatment effects, and confidence limits will
be printed.
A character or numerical vector specifying the sequence of treatments in printouts.
An optional value for manually setting the
square-root of the between-study variance \(\tau^2\) (only
considered if method = "Inverse").
A numeric for the tolerance for consistency of
treatment estimates in multi-arm studies which are consistent by
design (only considered if method = "Inverse").
A numeric for the tolerance for consistency
of standard errors in multi-arm studies which are consistent by
design (only considered if method = "Inverse").
A logical indicating whether treatment
estimates and / or variances of multi-arm studies with
inconsistent results or negative multi-arm variances should be
printed (only considered if method = "Inverse").
A character used in comparison names as separator between treatment labels.
A numeric defining the minimum number of characters used to create unique treatment names (see Details).
A logical indicating whether results should be
back transformed in printouts and forest plots. If
backtransf = TRUE, results for sm = "OR" are
presented as odds ratios rather than log odds ratios, for
example.
Title of meta-analysis / systematic review.
A logical indicating whether original data (set) should be kept in netmeta object.
A logical indicating whether warnings should be printed (e.g., if studies are excluded from meta-analysis due to zero standard errors).
An object of class netmetabin and netmeta with
corresponding print, summary, forest, and
netrank functions. The object is a list containing the
following components:
As defined above.
As defined above.
Estimate of treatment effect, i.e. difference between first and second treatment (e.g. log odds ratio).
Standard error of treatment estimate.
Total number of studies.
Total number of pairwise comparisons.
Total number of treatments.
Total number of designs (corresponding to the unique set of treatments compared within studies).
Treatments included in network meta-analysis.
Number of studies evaluating a treatment.
Number of observations receiving a treatment.
Number of events observed for a treatment.
Study labels coerced into a factor with its levels sorted alphabetically.
Number of arms for each study.
Unique list of designs present in the network. A design corresponds to the set of treatments compared within a study.
nxn matrix with estimated overall treatment effects and standard errors for fixed effects model.
nxn matrices with lower and upper confidence interval limits for fixed effects model.
nxn matrices with z-value and p-value for test of overall treatment effect under fixed effects model.
nxn matrix with
estimated overall treatment effects and standard errors for
random effects model (only available if method =
"Inverse").
nxn matrices with
lower and upper confidence interval limits for random effects
model (only available if method = "Inverse").
nxn matrices with
z-value and p-value for test of overall treatment effect under
random effects model (only available if method =
"Inverse").
nxn matrix with estimated treatment effects and standard errors from direct evidence under fixed effects model.
nxn matrices with lower and upper confidence interval limits from direct evidence under fixed effects model.
nxn matrices with z-value and p-value for test of overall treatment effect from direct evidence under fixed effects model.
nxn
matrix with estimated treatment effects and standard errors from
direct evidence under random effects model (only available if
method = "Inverse").
nxn
matrices with lower and upper confidence interval limits from
direct evidence under random effects model (only available if
method = "Inverse").
nxn
matrices with z-value and p-value for test of overall treatment
effect from direct evidence under random effects model (only
available if method = "Inverse").
Overall heterogeneity / inconsistency statistic.
Degrees of freedom for test of heterogeneity / inconsistency.
P-value for test of heterogeneity / inconsistency.
I-squared, lower and upper confidence
limits (only available if method = "Inverse").
Square-root of between-study variance (only available if
method = "Inverse").
Adjacency matrix (nxn).
Hat matrix (mxm)
nxn matrix with number of observations in direct comparisons.
nxn matrix with number of events in direct comparisons.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
As defined above.
Data set (in contrast-based format).
List with data in arm-based format (each list element corresponds to a single design).
Function call.
Version of R package netmeta used to create object.
This function implements three models for the network meta-analysis of binary data:
The Mantel-Haenszel network meta-analysis model, as described
in Efthimiou et al. (2019) (method = "MH");
a network meta-analysis model using the non-central
hypergeometric distribution with the Breslow approximation, as
described in Stijnen et al. (2010) (method = "NCH");
the inverse variance method for network meta-analysis
(method = "Inverse"), also provided by
netmeta.
Comparisons belonging to multi-arm studies are identified by
identical study labels (argument studlab). It is therefore
important to use identical study labels for all comparisons
belonging to the same multi-arm study.
Data entry for this function is in contrast-based format,
that is, each line of the data corresponds to a single pairwise
comparison between two treatments (arguments treat1,
treat2, event1, n1, event2, and
n2). If data are provided in arm-based format, that
is, number of events and participants are given for each treatment
arm separately, function pairwise can be used to
transform the data to contrast-based format (see help page
of function pairwise).
Note, all pairwise comparisons must be provided for a multi-arm
study. Consider a multi-arm study of p treatments with known
variances. For this study, the number of events and observations
must be provided for each treatment, for each of p(p
- 1) / 2 possible comparisons in separate lines in the data. For
instance, a three-arm study contributes three pairwise comparisons,
a four-arm study even six pairwise comparisons. Function
pairwise automatically calculates all pairwise
comparisons for multi-arm studies.
For method = "Inverse", both fixed effects and random
effects models are calculated regardless of values choosen for
arguments comb.fixed and comb.random. Accordingly,
the network estimates for the random effects model can be extracted
from component TE.random of an object of class
"netmeta" even if argument comb.random = FALSE.
However, all functions in R package netmeta will adequately
consider the values for comb.fixed and
comb.random. E.g. function
print.summary.netmeta will not print results for the
random effects model if comb.random = FALSE.
For the random-effects model, the direct treatment estimates are based on the common between-study variance \(\tau^2\) from the network meta-analysis.
For method = "MH" and method = "NCH", only a fixed
effects model is available.
By default, treatment names are not abbreviated in
printouts. However, in order to get more concise printouts,
argument nchar.trts can be used to define the minimum number
of characters for abbreviated treatment names (see
abbreviate, argument minlength). R function
treats is utilised internally to create abbreviated
treatment names.
Names of treatment comparisons are created by concatenating
treatment labels of pairwise comparisons using sep.trts as
separator (see paste). These comparison names are
used in the covariance matrices Cov.fixed and
Cov.random and in some R functions, e.g,
decomp.design. By default, a colon is used as the
separator. If any treatment label contains a colon the following
characters are used as separator (in consecutive order):
"-", "_", "/", "+", ".",
"|", and "*". If all of these characters are used in
treatment labels, a corresponding error message is printed asking
the user to specify a different separator.
Efthimiou O, R<U+00FC>cker G, Schwarzer G, Higgins J, Egger M, Salanti G (2019): A Mantel-Haenszel model for network meta-analysis of rare events. Statistics in Medicine, 1--21, https://doi.org/10.1002/sim.8158
Senn S, Gavini F, Magrez D, Scheen A (2013): Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22, 169--89
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
# NOT RUN {
data(Dong2013)
# Only consider first ten studies (to reduce runtime of example)
#
first10 <- subset(Dong2013, id <= 10)
# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, death, randomized, studlab = id,
data = first10, sm = "OR")
# Conduct Mantel-Haenszel network meta-analysis (without continuity
# correction)
#
nb1 <- netmetabin(p1, ref = "plac")
nb1
# Obtain the league table
#
netleague(nb1)
# }
# NOT RUN {
# Conduct Mantel-Haenszel network meta-analysis for the whole
# dataset
#
p2 <- pairwise(treatment, death, randomized, studlab = id,
data = Dong2013, sm = "OR")
netmetabin(p2, ref = "plac")
# Conduct network meta-analysis using the non-central
# hypergeometric model (without continuity correction)
#
netmetabin(p2, ref = "plac", method = "NCH")
# Conduct Mantel-Haenszel network meta-analysis (with continuity
# correction of 0.5; include all studies)
#
netmetabin(p2, ref = "plac", cc.pooled = TRUE)
data(Gurusamy2011)
p3 <- pairwise(treatment, death, n, studlab = study,
data = Gurusamy2011, sm = "OR")
# Conduct Mantel-Haenszel network meta-analysis (without continuity
# correction)
#
netmetabin(p3, ref = "cont")
# }
# NOT RUN {
# }
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