Table 1.

Simulation scenarios used to evaluate the relative efficiency of ordinal regression (OR) versus direct ROC modeling (DM) fitting algorithms. After assigning a subject his case-control status and covariate value, a normally distributed variable with mean indicated in the table and standard deviation equal to 1 was generated and categorized as described in the text. The categorical covariate with 4 levels is represented as 3 dummy variables (X₂, X₃, X₄) = (0, 0, 0) for level 1, (1, 0, 0) for level 2, (0, 1, 0) for level 3, (0, 0, 1) for level 4. The continuous covariate is denoted by X.

Covariate	Covariate Effects on FPR	Covariate Effects on ROC	Mean in controls	Mean in Cases
none	no	no	0	1.19
categorical	yes	no	−0.2 +0.1X2+0.3X3+0.4X4	1.19−0.2+0.1X2+0.3X3+0.4X4
continuous	yes	no	X	1.19+X
categorical	yes	yes	−0.2 +0.1X2+0.3X3+0.4X4	1.19−0.2+0.15X2+0.5X3+0.65X4
continuous	yes	yes	0.5X	1.19+X

FPR: false positive rate

ROC: receiver operating characteristic