Figure 3.

Observed number of events in risk deciles for case-control setting when models with p = 4 binary X were updated using one continuous marker Z following a mixture distribution of normals. $z\sim 0.9N({\alpha }_{01}+{\alpha }_{\text{X}1}^{\prime }\text{X},1)+0.1N({\alpha }_{02}+{\alpha }_{\text{X}2}^{\prime }\text{X},1)$ P(X) = 0.2, α₀₁ = 0, α_X1 = (0.7, 0.7,−0.7,−0.7)′, α₀2 = 0.5, αX₂ = (1, 1,-1,-1)′, P(Y) = 0.05, β_X = (0.5, 0.5, −0.5, −0.5)′, β_Z = 1,n_cases = n_controls = 250. Log-new=Logistic new, LR-j=LR-joint, LR-s=LR-separate, LR-i=LR-ind, LR-o=LR-offset, LR-sh=LR-shrink. See also Supplemental Table S9.