Table 1 Setting of simulation parameters

Group/group α g β gj γ ig ρ ig ε ijg
Study 1: Control $$\mathcal {N}(0, 1)$$ 0 $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
Study 1: Disease A $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
Study 2: Control $$\mathcal {N}(0, 1)$$ 0 $$\mathcal {N}(2, 1)$$ InvGamma(1,2) $$\mathcal {N}(0, 1)$$
Study 2: Disease B $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(2, 1)$$ InvGamma(1,2) $$\mathcal {N}(0, 1)$$
Study 3: Control $$\mathcal {N}(0, 1)$$ 0 $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
Study 3: Disease A $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
Study 4: Control $$\mathcal {N}(0, 1)$$ 0 $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
Study 4: Disease A $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ $$\mathcal {N}(0, 1)$$ InvGamma(1,1) $$\mathcal {N}(0, 1)$$
1. Simulation nos. 1a and 1b involve studies 1 and 2, only, while simulation no. 2 involves all four studies 