# decomp.design

##### Design-based decomposition of Cochran's Q in network meta-analysis

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.

- Keywords
- Network meta-analysis, Inconsistency, Cochran's Q

##### Usage

`decomp.design(x, tau.preset=x$tau.preset)`

##### Arguments

- x
An object of class

`netmeta`

.- tau.preset
An optional value for the square-root of the between-study variance \(\tau^2\) (see Details).

##### Details

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`

.

##### Value

A list containing the following components:

Data frame with Q statistics (variable `Q`

)
based on the fixed 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 fixed effects
model, corresponding degrees of freedom (`df`

) and p-values
(`p.val`

) are given.

Data frame with between-designs Q statistics
(`Q`

) of the fixed 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.

##### References

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**(2), 98--110.

Krahn U, Binder H, K<U+00F6>nig 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**(29), 3805--3820.

##### See Also

##### Examples

```
# NOT RUN {
data(Senn2013)
#
# Generation of an object of class 'netmeta' with
# reference treatment 'plac', i.e. placebo
#
net1 <- netmeta(TE, seTE, treat1, treat2, studlab,
data=Senn2013, sm="MD", reference="plac")
#
# Decomposition of Cochran's Q
#
decomp.design(net1)
# }
```

*Documentation reproduced from package netmeta, version 0.9-5, License: GPL (>= 2)*