Network Meta-Analysis

Core Idea

Network meta-analysis (NMA) extends standard pairwise meta-analysis to simultaneously compare multiple treatments by combining direct evidence (from head-to-head trials) with indirect evidence (inferred through common comparators). If Treatment A has been compared to placebo and Treatment B has been compared to the same placebo, NMA estimates the A-vs-B difference indirectly through the shared comparator — even without a direct A-vs-B trial. The network of all available comparisons is modeled simultaneously, producing a coherent set of relative treatment effects and enabling ranking of all treatments. The critical assumption is consistency (also called coherence): direct and indirect evidence for a given comparison agree. Inconsistency suggests that the treatment effects depend on which comparator was used, potentially indicating effect modification, heterogeneity across study populations, or violation of the transitivity assumption.

Explainer

Clinical practice requires choosing among multiple treatments, but most trials compare only two at a time — typically a new treatment against placebo or against one active comparator. Clinicians wanting to choose among five antidepressants, three blood pressure drugs, or six surgical techniques face a fragmented evidence base with many missing head-to-head comparisons. Network meta-analysis synthesizes this fragmented evidence into a coherent framework that estimates all pairwise treatment effects simultaneously.

The key insight is that indirect evidence can supplement direct evidence. If Trial 1 shows that Drug A beats placebo with OR = 2.0, and Trial 2 shows that Drug B beats placebo with OR = 1.5, the indirect comparison suggests Drug A beats Drug B with OR ≈ 2.0/1.5 = 1.33. This inference requires the transitivity assumption: the relative effects would be the same regardless of which comparator was used, which means the trials must be sufficiently similar in population, design, and conduct. NMA combines all direct and indirect evidence, weighting each by its precision, to produce a complete matrix of pairwise comparisons.

The analysis is typically conducted in a Bayesian framework (using MCMC methods in software like WinBUGS, OpenBUGS, or R's gemtc package), though frequentist approaches exist. Bayesian NMA naturally produces posterior distributions for all treatment effects, enabling probabilistic statements like "there is a 73% probability that Treatment B is the most effective." These treatment rankings — while appealing for clinical communication — must be interpreted cautiously, as they are sensitive to the precision and number of available comparisons.

The most important threat to NMA validity is inconsistency: disagreement between direct and indirect evidence for the same comparison. If the A-vs-B estimate from direct trials conflicts with the A-vs-B estimate inferred through the network, the transitivity assumption may be violated — perhaps the trials contributing indirect evidence enrolled different populations, used different outcome definitions, or involved different versions of the comparator treatment. Consistency can be assessed globally (does the model fit improve when inconsistency parameters are added?) and locally (do specific loops in the network show discrepant direct and indirect estimates?). When inconsistency is detected, the NMA results for those comparisons should be viewed skeptically, and the sources of inconsistency should be investigated through subgroup or meta-regression analyses.