Statisticsmedium

Network Meta-Analysis (NMA) Was Proposed About 20 Years Ago - Is It Sufficient?

Question

Network meta-analysis (NMA) was proposed about 20 years ago to compare the effects of multiple treatments. Is it sufficient if one of the following assumptions holds? Evaluate the assumptions of consistency, transitivity, and common heterogeneity.

Evaluating the three fundamental assumptions of network meta-analysis.

Answer

No single assumption alone is sufficient — all three must hold simultaneously

1What Is Network Meta-Analysis?

Network meta-analysis (NMA) extends traditional pairwise meta-analysis to compare **multiple treatments simultaneously**. It combines direct evidence (head-to-head trials) with indirect evidence (through a common comparator).

  Treatment Network:

         A
        / \
  direct/   \direct
      /     \
     B ───── C
       indirect

  A vs C can be estimated indirectly via B

2The Transitivity Assumption

**Transitivity** means trials comparing different treatment sets are sufficiently similar in effect modifiers (patient population, follow-up duration, etc). If A-vs-B trials have different patient populations than B-vs-C trials, indirect comparison A-vs-C may be biased.

Transitivity

Transitivity is a **necessary but not sufficient** condition. It cannot be tested statistically — it must be assessed by clinical judgment, examining whether trial populations, settings, and co-interventions are comparable across the network.

3The Consistency Assumption

**Consistency** means direct and indirect evidence agree. For a closed loop A-B-C, the direct A-vs-C estimate should match the indirect estimate derived from A-vs-B and B-vs-C.

Consistency

Unlike transitivity, consistency **can be tested statistically** using node-splitting or design-by-treatment interaction tests. Significant inconsistency signals violation of the NMA assumptions.

4The Common Heterogeneity Assumption

NMA typically assumes a **common heterogeneity parameter**

\tau^2

across all treatment comparisons. This means the between-study variance is the same whether comparing A-vs-B, A-vs-C, or B-vs-C.

5Evaluating Sufficiency

Assumption	Testable?	Alone Sufficient?	Relationship
Transitivity	No (clinical judgment)	No	Prerequisite for consistency
Consistency	Yes (node-splitting)	No	Requires transitivity
Common τ²	Yes (model comparison)	No	Independent assumption

Transitivity alone sufficient?No

Consistency alone sufficient?No

Common τ² alone sufficient?No

ALL THREE REQUIREDYes

Hierarchy of Assumptions

Transitivity → Consistency → Valid NMA. Transitivity is a **prerequisite** for consistency (if transitivity fails, consistency cannot hold). All three assumptions must be satisfied for valid network meta-analysis results.

Quiz

Test your understanding with these questions.

Is any single assumption (transitivity, consistency, or common heterogeneity) alone sufficient for valid NMA?

What does 'consistency' mean in the context of NMA?