Table 1 Summary of the simulation scenarios

Number of studies

Balanced direct comparisons

K_AB = K_AC = K_BC = 1, …, 7

Imbalanced direct comparisons

K_AB = 1, K_AC = 4, K_BC = 7 (and K_AB = 1, K_AC = 4, K_BC = 3 for the typical loop)

Treatment effects

Comparison AB

OR_AB = 0.73

Comparison AC

OR_AC = 1

Comparison BC

OR_BC = exp{log(OR_AC) - log(OR_AB) + IF_ABC}

Inconsistency in the network

Inconsistency Factor

IF_ABC = {0, 0.3, 0.45, 0.6, 1}

Heterogeneity in the network

Subjective outcome

τ² ~ LN(-2.13, 1.58²)

All-cause mortality outcome

τ² ~ LN(-4.06, 1.45²)

Trial arm size $\left({\mathrm{n}}_{\mathrm{A},{\mathrm{k}}_1}={\mathrm{n}}_{\mathrm{B},{\mathrm{k}}_1}=\mathrm{n}\right)$

Small

n ~ U(20, 50)

Moderate

n ~ U(50, 150)

Large

n ~ U(150, 300) (and n ~ U(120, 160) for the typical loop)

Frequency of events

Average risk for frequent events

${\mathrm{AR}}_{\mathrm{AB},{\mathrm{k}}_1}~\mathrm{U}\left(0.25,0.75\right)$

Average risk for rare events

${\mathrm{AR}}_{\mathrm{AB},{\mathrm{k}}_1}~\mathrm{U}\left(0.05,0.15\right)$

Approaches to estimate the variances of the direct pairwise summary effects

Inverse variance method

Knapp-Hartung method