Table 1 Interchangeable interpretations of the transitivity assumption (Salanti [5])

(a) Similar interventions in different trials

 The interventions of the network do not differ systematically across the corresponding trials. Namely, in a triangle network with interventions A, B, and C, intervention A would be similar in AB and AC trials. The same holds for intervention B which appears in BC and AB trials, and intervention C in AC and BC trials

(b) Missing-at-random treatments

 Missing interventions in each trial of the network are missing for reasons unrelated to their benefit-harm profile. Namely, interventions A, B, and C are randomly missing in BC, AC, and AB trials

(c) Exchangeable missing and observed relative treatment effects

 Underlying treatment effects of any observed and unobserved comparison do not differ beyond what is expected by the between-trial heterogeneity alone. For instance, the AB trials provide evidence for comparison AB only. Under the random-effects model, had these trials included intervention C, the underlying treatment effect of AC and BC comparisons could have been estimated, assuming that these missing treatment effects are exchangeable with the corresponding underlying treatment effects estimated directly in AC and BC trials, respectively

(d) Jointly randomisable participants

 If all network interventions could be investigated in one trial, the participants would be eligible to be randomised to any intervention. Namely, the participants share a similar demographic and clinical profile that makes them suitable for any network intervention for their underlying condition

(e) Similar treatment comparisons concerning important effect modifiers

 Different observed treatment comparisons comprise clusters of several trials. These clusters are considered to be similar regarding the distribution of important effect modifiers. Hence, if AB and AC trials are similar in terms of the distribution of important effect modifiers, the indirect estimate for BC using these two sets of trials will be valid