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

* \b[Comparisons without a direct trial.] A path through common comparators permits an <indirect treatment comparison> of treatments that have never been randomized against one another.
* \b[Greater precision.] Combining consistent direct and indirect evidence can reduce the <variance> of a treatment-effect estimate and make more complete use of the trials than separate pairwise <meta-analyses>.
* \b[Coherent decisions across many treatments.] A joint <statistical model> estimates all relative effects on one scale, allowing treatment rankings and their uncertainty to inform a choice among several options rather than presenting disconnected pairs.

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

Solution

Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 207 / 1 / d / Solution

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.

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 Incoming links: Network meta-analysis