This function performs a design-based decomposition of Cochran's Q for assessing the homogeneity in the whole network, the homogeneity within designs, and the homogeneity/consistency between designs. It allows also an assessment of the consistency assumption after detaching the effect of single designs.
decomp.design(
x,
tau.preset = x$tau.preset,
warn = gs("warn"),
nchar.trts = x$nchar.trts
)Network meta-analysis with a single design: NULL. Otherwise,
a list containing the following components:
Data frame with Q statistics (variable Q)
based on the common effects model to assess the
homogeneity/consistency in the whole network, within designs, and
between designs. Corresponding degrees of freedom (df) and
p-values (p.val) are also given.
Data frame with design-specific decomposition
of the within-designs Q statistic (Q) of the common effects
model, corresponding degrees of freedom (df) and p-values
(p.val) are given.
Data frame with between-designs Q statistics
(Q) of the common effects model after detaching of single
designs, corresponding degrees of freedom (df) and
p-values (p.val) are given.
A named vector with contributions of single
designs to the between design Q statistic given in
Q.decomp.
Data frame with between-designs Q statistic
(Q) based on a random effects model with square-root of
between-study variance tau.within estimated embedded in a
full design-by-treatment interaction model, corresponding degrees
of freedom (df) and p-value (p.val).
Data frame with between-designs Q
statistic (Q) based on a random effects model with
prespecified square-root of between-study variance
tau.preset in the case if argument tau.preset is
not NULL, corresponding degrees of freedom (df) and
p-value (p.val).
A named vector with contributions
of single designs to the between design Q statistic based on a
random effects model with prespecified square-root of
between-study variance tau.preset in the case if argument
tau.preset is given.
Matrix with residuals, i.e. design-specific direct estimates minus the corresponding network estimates after detaching the design of the column.
Matrix with residuals
analogous to residuals.inc.detach but based on a random
effects model with prespecified square-root of between-study
variance tau.preset in the case if argument
tau.preset is not NULL.
Function call.
Version of R package netmeta used to create object.
An object of class netmeta.
An optional value for the square-root of the between-study variance \(\tau^2\) (see Details).
A logical indicating whether warnings should be printed.
A numeric defining the minimum number of characters used to create unique treatment names.
Ulrike Krahn ulrike.krahn@bayer.com, Jochem König koenigjo@uni-mainz.de
In the context of network meta-analysis and the assessment of the homogeneity and consistency assumption, a generalized Cochran's Q statistic for multivariate meta-analysis can be used as shown in Krahn et al. (2013). This Q statistic can be decomposed in a sum of within-design Q statistics and one between-designs Q statistic that incorporates the concept of design inconsistency, see Higgins et al. (2012).
For assessing the inconsistency in a random effects model, the
between-designs Q statistic can be calculated based on a full
design-by-treatment interaction random effects model (see Higgins
et al., 2012). This Q statistic will be automatically given in the
output (\(\tau^2\) estimated by the method of moments (see Jackson
et al., 2012). Alternatively, the square-root of the between-study
variance can be prespecified by argument tau.preset to
obtain a between-designs Q statistic (in Q.inc.random), its
design-specific contributions Q.inc.design.random.preset) as
well as residuals after detaching of single designs
(residuals.inc.detach.random.preset).
Since an inconsistent treatment effect of one design can
simultaneously inflate several residuals, Krahn et al. (2013)
suggest for locating the inconsistency in a network to fit a set of
extended models allowing for example for a deviating effect of each
study design in turn. The recalculated between-designs Q statistics
are given in list component Q.inc.detach. The change of the
inconsistency contribution of single designs can be investigated in
more detail by a net heat plot (see function
netheat). Designs where only one treatment is involved in
other designs of the network or where the removal of corresponding
studies would lead to a splitting of the network do not contribute
to the inconsistency assessment. These designs are not included in
Q.inc.detach.
Higgins JPT, Jackson D, Barrett JK, Lu G, Ades AE, White IR (2012): Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods, 3, 98--110
Krahn U, Binder H, König J (2013): A graphical tool for locating inconsistency in network meta-analyses. BMC Medical Research Methodology, 13, 35
Jackson D, White IR and Riley RD (2012): Quantifying the impact of between-study heterogeneity in multivariate meta-analyses. Statistics in Medicine, 31, 3805--20
netmeta, netheat
# \donttest{
data(Senn2013)
# Only consider first five studies (to reduce runtime of example)
#
studies <- unique(Senn2013$studlab)
Senn2013.5 <- subset(Senn2013, studlab %in% studies[1:5])
# Conduct network meta-analysis with placebo as reference treatment
#
net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
data = Senn2013.5, sm = "MD", reference = "plac")
# Decomposition of Cochran's Q
#
decomp.design(net1)
# }
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