network meta-analysis

The Cochrane Handbook for Systematic Reviews of Interventions describes a network meta-analysis as one that combines direct and indirect estimates across a network of interventions in a single analysis. The direct part is ordinary: trials that compared two treatments head to head. The indirect part is the addition. If one set of trials compared treatment A against a placebo and another set compared treatment B against the same placebo, the shared comparator acts as a bridge, and a relative effect for A against B can be estimated even though no trial ever ran that comparison.

The bridge holds only under an assumption, and the handbook states it plainly: that the different sets of randomised trials are similar, on average, in all important factors other than the intervention comparison being made. Its test is whether the competing interventions are jointly randomisable, meaning they could in principle have appeared together in one multi-arm trial. Where the trials of one treatment enrolled a different sort of participant, or ran for a different length of time, or measured at a different point, that assumption weakens, and with it every indirect estimate resting on it.

The check available afterwards is coherence. Incoherence, in the handbook's words, occurs when different sources of information for a particular relative effect are in disagreement, which is to say the direct and the indirect estimate of the same comparison do not match. Where a comparison rests on indirect evidence alone there is no direct estimate to disagree with, so the check cannot be run there at all. A network meta-analysis therefore produces a ranking in which the top place may rest on far fewer trials and participants than the headline count suggests, and the number behind each individual comparison is worth more attention than the position it earned.