Table 2 Overview of simulated scenarios

Network geometry

Well-connected network

    Studies/Pairwise comparisons

\(k=28\)

Interventions

\(n=8\)

single: A, B, C, D, 

combined: \(A+B,A+C,C+D,\)

reference: placebo P

Additivity assumption on relative intervention effects

    Scenario A: Additive effects

\(\delta _{A+B,P} = \delta _{A,P} + \delta _{B,P}\)

\(\delta _{A+C,P} = \delta _{A,P} + \delta _{C,P}\)

\(\delta _{C+D,P} = \delta _{C,P} + \delta _{D,P}\)

    Scenario B: Mild violation of additivity assumption

       B1: combined intervention \(A+B\)

\(\delta _{A+B,P} = \delta _{A,P} + \delta _{B,P} + \lambda _{AB}, e^{\lambda _{AB}} = 1.5\)

       B2: combined intervention \(C+D\)

\(\delta _{C+D,P} = \delta _{C,P} + \delta _{D,P} + \lambda _{CD}, e^{\lambda _{CD}} = 1.5\)

    Scenario C: Strong violation of additivity assumption

       C1: combined intervention \(A+B\)

\(\delta _{A+B,P} = \delta _{A,P} + \delta _{B,P} + \lambda _{AB}\), \(e^{\lambda _{AB}} = 2.0\)

       C2: combined intervention \(C+D\)

\(\delta _{C+D,P} = \delta _{C,P} + \delta _{D,P} + \lambda _{CD}\), \(e^{\lambda _{CD}} = 2.0\)

Heterogeneity

    No heterogeneity

\(\tau ^2=0.00\)

    Low heterogeneity

\(\tau ^2=0.01\)

    Moderate heterogeneity

\(\tau ^2=0.10\)

Inconsistency

No inconsistency

Other simulation parameters

    True relative intervention effects

\(e^{\delta _{A,P}}= 1.40\), \(e^{\delta _{B,P}} = 1.20\), \(e^{\delta _{C,P}}= 2.30\), and \(e^{\delta _{D,P}}= 1.50\)

    Baseline probability

\(p_{P}=0.1\)

    Patients per study arm

\(n_i\sim \mathcal {U}(50, 200)\)

    Iterations

\(M=1000\)