Network Meta-Analysis for Decision-Making

7Checking for Inconsistency

7.1 Introduction

Chapters 1, 2 and 4 have shown how, given a connected network of comparisons, network meta-analysis produces an internally coherent set of estimates of the efficacy of any treatment in the network relative to any other. A key assumption of network meta-analysis is that of evidence consistency. The requirement, in effect, is that in every trial i in the network, regardless of the actual treatments that were compared, the true effect of treatment Y relative to treatment X is the same in a fixed effects model or exchangeable between-trials in a random effects model (Chapter 2). From this exchangeability assumption, the ‘consistency equations’ (equation (2.9)) can be deduced.

Where doubts have been expressed about network meta-analysis, these have focused on the consistency equations because, unlike the exchangeability assumptions from which they are derived, which are notoriously difficult to verify, the consistency equations offer a clear prediction about relationships in the data that can be statistically tested. However, it is important to note that failure to detect inconsistency does not imply consistency since tests for inconsistency are inherently underpowered (Veroniki et al., 2014) (see also Chapter 12). As with other interaction effects, the evidence required to confidently rule out any but the most glaring inconsistency is seldom available, and in many cases, such as networks without any loops, there is no way of testing ...