netmeta (version 0.7-0)

decomp.design: Design-based decomposition of Cochran's Q in network meta-analysis

Description

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.

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 $tau^2$ of a random effects model on which a between-designs Q statistic (see Q.inc.random.preset) will be based. Design-specific contributions of this Q

Value

• A list containing the following components:
• Q.decomp
  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.
• Q.het.design
  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.
• Q.inc.detach
  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.
• Q.inc.design
  A named vector with contributions of single designs to the between design Q statistic given in Q.decomp.
• Q.inc.random
  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).
• Q.inc.random.preset
  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).
• Q.inc.design.random.preset
  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.
• residuals.inc.detach
  Matrix with residuals, i.e. design-specific direct estimates minus the corresponding network estimates after detaching the design of the column.
• residuals.inc.detach.random.preset
  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.
• call
  Function call.
• version
  Version of R package netmeta used to create object.

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.

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, 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(29), 3805--3820.

See Also

netmeta, netheat

Examples

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)