Table 4

Parameter	True value	Distribution	OLS	EMP	RES
R(0.2)	0.794	lognormal	0.796(0.039)	0.795(0.044)	0.795(0.036)
R(0.4)	0.861		0.863(0.031)	0.864(0.036)	0.862(0.030)
R(0.7)	0.924		0.926(0.023)	0.926(0.027)	0.924(0.023)
AUC	0.863		0.864(0.027)	0.864(0.027)	0.863(0.026)
R(0.2)	0.794	lognormal-scaled	0.795(0.039)	0.796(0.043)	0.794(0.036)
R(0.4)	0.861		0.862(0.032)	0.863(0.037)	0.861(0.030)
R(0.7)	0.924		0.925(0.024)	0.925(0.028)	0.923(0.023)
AUC	0.863		0.863(0.028)	0.863(0.028)	0.862(0.026)
R(0.2)	0.794	lognormal-shift	0.794(0.039)	0.795(0.043)	0.818(0.043)
R(0.4)	0.861		0.861(0.031)	0.861(0.036)	0.900(0.031)
R(0.7)	0.924		0.923(0.023)	0.923(0.027)	0.961(0.017)
AUC	0.863		0.862(0.027)	0.862(0.027)	0.888(0.027)
R(0.2)	0.794	non Box-Cox	0.796(0.038)	0.796(0.044)	0.764(0.051)
R(0.4)	0.861		0.863(0.031)	0.864(0.036)	0.887(0.037)
R(0.7)	0.924		0.926(0.023)	0.926(0.027)	0.968(0.017)
AUC	0.863		0.864(0.027)	0.864(0.027)	0.862(0.029)

Table 4: Inference of the ROC curve by the semiparametric least squares based method (OLS), the nonparametric method (EMP) and the parametric method (RES). Cases and controls are drawn from log-normal distributions and modified as noted. (α₀, α₁) = (1.2, 0.45). ( n_D ,

) = (100, 100). Sample means and sampling standard errors from 1000 simulations are shown.