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A network meta-analysis jointly compares several treatments using a graph of direct Randomized controlled trials and indirect treatment comparisons. If effects are measured relative to a reference treatment, consistency means ${\delta }_{ij}={\delta }_{i0}-{\delta }_{j0}$. A connected graph identifies all relative effects under that model. Transitivity in network meta-analysis is the substantive comparability assumption supporting these relations; inconsistency can be assessed when the network has loops.

Write $y_{WP}$ and $y_{AP}$ for the estimated log odds ratios relative to the common control. Indirect treatment comparison uses the consistency relation ${\delta }_{WA}={\delta }_{WP}-{\delta }_{AP}$. For independent trials, subtraction adds their variances, givingThe substantive assumption is transitivity in network meta-analysis: the study populations, outcome definitions and follow-up are sufficiently comparable, particularly in their distributions of effect modifiers, that the two control comparisons estimate effects applicable to the same target population. The common control's name alone does not justify that assumption. This also assumes comparable marginal odds ratios; these need not equal covariate-adjusted odds ratios even without confounding.

Using the supplied rounded variances and the given standard normal quantile, the approximate confidence interval isOn the odds ratio scale this is $e^{-1.26}\simeq 0.284$, with approximate limits $(0.104,0.771)$. The estimated odds of recurrent stroke under treatment $W$ are about 28% of those under $A$, a reduction of about 72% in odds. The interval excludes equal odds, so this comparison provides evidence of lower odds under $W$ if the indirect treatment comparison assumptions hold. These are odds, not a 72% reduction in probability; a confidence interval describes the long-run coverage of the procedure, not a posterior probability for this particular interval.

A network meta-analysis can offer three distinct benefits, assuming a connected treatment network and credible transitivity in network meta-analysis.

These are potential benefits, not guarantees: heterogeneous effect modifiers, inconsistent evidence, disconnected networks or imprecise rankings can defeat them.

Transitivity requires the studies of different treatment comparisons to be sufficiently comparable in distributions of effect modifiers, outcome definitions and other design features to support an indirect treatment comparison in one target population. For example, a treatment that works differently by disease severity cannot safely be compared indirectly across trials with systematically different severity distributions. Statistical consistency is an implication of suitable transitivity and modeling assumptions, not a substitute for assessing them.