netmeta(TE, seTE, treat1, treat2, studlab, data=NULL, subset=NULL, sm, level=0.95, level.comb=0.95, comb.fixed=TRUE, comb.random=FALSE, reference.group="", all.treatments=NULL, seq=NULL, tau.preset=NULL, title="", warn=TRUE)"RD", "RR", "OR", "AS",
"MD", "SMD", or "HR"."NULL". If
TRUE, matrices with all treatment effects, and confidence
limits will be printed.netmeta with corresponding print,
summary, forest, and netrank function. The
object is a list containing the following components:
c("")."NULL". If
TRUE, matrices with all treatment effects, and
confidence limits will be printed.Let n be the number of different treatments in a network and let m be the number of existing comparisons (edges) between the treatments. If there are only two-arm studies, m is the number of studies. Let TE and seTE be the vectors of observed effects and their standard errors. Let W be the mxm diagonal matrix that contains the inverse variance 1/seTE^2. The given comparisons define the network structure. Therefrom an mxn design matrix B is formed; for more precise information, see Rücker (2012). Moreover, the nxn Laplacian matrix L and its Moore-Penrose pseudoinverse L+ are calculated (both matrices play an important role in graph theory and electrical network theory). Using these matrices, the variances based on both direct and indirect comparisons can be estimated. Moreover, the hat matrix H can be estimated by H = BL+B^tW = B(B^t W B)^+B^tW and finally consistent treatment effects can be estimated by applying the hat matrix to the observed (potentially inconsistent) effects. H is a projection matrix which maps the observed effects onto the consistent (n-1)-dimensional subspace. This is the Aitken estimator (Senn et al., 2013). As in pairwise meta-analysis, the Q statistic measures the deviation from consistency. Q can be separated into parts for each pairwise meta-analysis and a part for remaining inconsistency between comparisons.
Often multi-arm studies are included in a network meta-analysis. In multi-arm studies, the treatment effects on different comparisons are not independent, but correlated. This is accounted for by reweighting all comparisons of each multi-arm study. The method is described in Rücker (2012) and Rücker and Schwarzer (2014).
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, e.g., study label
"Willms1999" for the three-arm study in the data example (Senn et
al., 2013). The function netmeta then automatically accounts for
within-study correlation by reweighting all comparisons of each
multi-arm study.
Data entry for this function is in contrast-based format,
that is, data are given as contrasts (differences) between two
treatments (argument TE) with standard error (argument
seTE). In principle, meta-analysis functions from R package
meta, e.g. metabin for binary outcomes or
metacont for continuous outcomes, can be used to
calculate treatment effects separately for each treatment comparison
which is a rather tedious enterprise. If data are provided in
arm-based format, that is, data are given for each treatment
arm separately (e.g. number of events and participants for binary
outcomes), a much more convenient way to transform data into
contrast-based form is available. Function pairwise
can automatically transform data with binary outcomes (using the
metabin function from R package meta),
continuous outcomes (metacont function), incidence
rates (metainc function), and generic outcomes
(metagen function). Additional arguments of these
functions can be provided, e.g., to calculate Hedges' g or
Cohen's d for continuous outcomes (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, treatment effects and standard errors
must be provided for each of p(p - 1)/2 possible
comparisons. 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.
A simple random effects model assuming that a constant heterogeneity
variance is added to each comparison of the network can be defined
via a generalised methods of moments estimate of the between-studies
variance tau^2 (Jackson et al., 2012). This is added to the observed
sampling variance seTE^2 of each comparison in the network (before
appropriate adjustment for multi-arm studies). Then, as in standard
pairwise meta-analysis, the procedure is repeated with the resulting
enlarged standard errors.
Rücker G (2012), Network meta-analysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312--324.
Rücker G and Schwarzer G (2014), Reduce dimension or reduce weights? Comparing two approaches to multi-arm studies in network meta-analysis. Statistics in Medicine, 33, 4353--4369.
Schwarzer G, Carpenter JR and Rücker G (2015), Meta-Analysis with R (Use-R!). Springer International Publishing, Switzerland
Senn S, Gavini F, Magrez D, and Scheen A (2013), Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22(2), 169--189. First published online 2012 Jan 3.
pairwise, forest.netmeta, netrank, metagendata(Senn2013)
#
# Fixed effect model (default)
#
net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
data=Senn2013, sm="MD")
net1
net1$Q.decomp
#
# Comparison with reference group
#
netmeta(TE, seTE, treat1, treat2, studlab,
data=Senn2013, sm="MD", reference="plac")
#
# Random effects model
#
net2 <- netmeta(TE, seTE, treat1, treat2, studlab,
data=Senn2013, sm="MD", comb.random=TRUE)
net2
#
# Change printing order of treatments (placebo first)
#
trts <- c("plac", "acar", "benf", "metf", "migl", "piog",
"rosi", "sita", "sulf", "vild")
net3 <- netmeta(TE, seTE, treat1, treat2, studlab,
data=Senn2013, sm="MD",
seq=trts)
print(summary(net3), digits=2)
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