Table 2 Input and estimated parameters in Approach II
Population | Input parameters for cases and controls | Estimated parameters for the population | ||||||
|---|---|---|---|---|---|---|---|---|
ρ | Normal (μ, σ) | ρ | (μ, σ) | Unadjusted OR * | Adjusted OR ** | SD of β 0 + ∑β i X i | AUC | |
A | Cases = 0.2 Ctrls = 0.2 | μCases: (1, 2); Ctrls: (0, 0) \( \sigma \)Cases: (2, 2); Ctrls: (2, 2) | 0.25 | μ: (0.2, 0.4); \( \sigma \): (2.04, 2.15) | 1.28, 1.65 | 1.17, 1.60 | 1.13 | 0.770 |
B | Cases = 0.2 Ctrls = 0.4 | ,, | 0.40 | ,, | ,, | 1.09, 1.60 | 1.09 | 0.765 |
C | Cases = 0.2 Ctrls = - 0.2 | ,, | -0.04 | ,, | ,, | 1.34, 1.68 | 1.25 | 0.785 |
D | Cases = 0.1 Ctrls = 0.1 | ,, | 0.16 | ,, | ,, | 1.22, 1.62 | 1.17 | 0.777 |
E | Cases = - 0.1 Ctrls = - 0.1 | ,, | -0.02 | ,, | ,, | 1.35, 1.70 | 1.28 | 0.795 |
F | Cases = 0.2 Ctrls = 0.2 | μCases: (1, 3); Ctrls: (0, 0) SD Cases: (2, 2); Ctrls: (2, 2) | 0.27 | μ: (0.2, 0.6); \( \sigma \): (2.04, 2.33) | 1.28, 2.12 | 1.11, 2.07 | 1.77 | 0.858 |
G | ,, | μCases: (1, 3); Ctrls: (0, 2) SD Cases: (2, 2); Ctrls: (2, 2) | 0.23 | μ: (0.2, 0.2); \( \sigma \): (2.04, 2.04) | 1.28, 1.28 | 1.23, 1.23 | 0.67 | 0.676 |
H | ,, | μCases: (1, 2); Ctrls: (0, 0) SD Cases: (2, 3); Ctrls: (2,3) | 0.24 | μ: (0.2, 0.4); \( \sigma \): (2.04, 3.10) | 1.28, 1.25 | 1.21, 1.22 | 0.80 | 0.705 |
I | ,, | μCases: (1, 2); Ctrls: (0, 0) SD Cases: (2, 1); Ctrls: (2, 1) | 0.27 | μ: (0.2, 0.4); \( \sigma \): (2.04, 1.28) | 1.28, 7.39 | 1.05, 7.23 | 2.56 | 0.922 |