A graphical tool for locating inconsistency in network meta-analyses

Table 1 The network Q statistics and the degrees of freedom of their corresponding chi-squared distribution

Null hypothesis	Q statistic	Degrees of freedom
Homogeneity in the whole network	Q ^net	$d f_{Q^{net}} : = (\sum_{s \in S} (N_{s} - 1)) - T$
Homogeneity within designs	Q ^het	$d f_{Q^{het}} : = \sum_{d = 1}^{D} d f_{Q_{d}^{het}}$
Homogeneity within design d	$Q_{d}^{het}$	$d f_{Q_{d}^{het}} : = (\sum_{s \in S_{d}} (N_{s} - 1)) - N_{d} + 1$
Consistency between designs	Q ^inc	$d f_{Q^{inc}} : = (\sum_{d = 1}^{D} (N_{d} - 1)) - T$
Consistency between designs after	$Q_{(d)}^{inc}$	$d f_{Q_{(d)}^{inc}} : = d f_{Q^{inc}} - N_{d} + 1$
detaching the effect of design d

In a network with T+1 treatments and a set of studies $S$ , d=1,…,D designs are observed. The set of studies with design d is given by $S_{d}$ . The numbers of treatments in study s and in design d are given by N _s and N _d respectively.

ISSN: 1471-2288