. Author manuscript; available in PMC: 2020 Jan 15.

Published in final edited form as: Stat Med. 2018 Sep 12;38(1):100–114. doi: 10.1002/sim.7966

TABLE 4.

Renal artery stenosis study example: Estimate, variance, 95% confidence interval (CI) and corresponding length of 95% CI for ROC(t), AUC and pAUC(t₀, t₁) estimators using the empirical method and IPW methods with the estimated sampling probabilities ${\hat{p}}^{Str}$ and ${\hat{p}}^{Aux}$ .

	Method	Est	Var×N	95% CI	Length of 95% CI
ROC (0.1)	Empirical	0.296	4.632	(0.092, 0.500)	0.409
	IPW with ${\hat{p}}^{Str}$	0.367	3.336	(0.194, 0.541)	0.347
	IPW with ${\hat{p}}^{Aux}$	0.388	2.081	(0.251, 0.525)	0.274
ROC (0.2)	Empirical	0.449	2.263	(0.306, 0.592)	0.286
	IPW with ${\hat{p}}^{Str}$	0.480	2.189	(0.339, 0.620)	0.281
	IPW with ${\hat{p}}^{Aux}$	0.500	1.805	(0.372, 0.628)	0.255
AUC	Empirical	0.665	0.619	(0.590, 0.740)	0.149
	IPW with ${\hat{p}}^{Str}$	0.682	0.677	(0.604, 0.760)	0.156
	IPW with ${\hat{p}}^{Aux}$	0.709	0.565	(0.638, 0.781)	0.143
pAUC(0, 0.1)	Empirical	0.014	0.012	(0.003, 0.024)	0.021
	IPW with ${\hat{p}}^{Str}$	0.017	0.028	(0.001, 0.033)	0.032
	IPW with ${\hat{p}}^{Aux}$	0.018	0.024	(0.004, 0.033)	0.029
pAUC(0, 0.2)	Empirical	0.053	0.063	(0.029, 0.077)	0.048
	IPW with ${\hat{p}}^{Str}$	0.068	0.070	(0.043, 0.093)	0.050
	IPW with ${\hat{p}}^{Aux}$	0.069	0.057	(0.047, 0.092)	0.045