Table IV.

Estimated AUC and its 95% confidence intervals. Beta distribution α₀ = 0.4, β₀ = 0.6 for healthy population, and α₁ = (0.45, …, 0.6), β₁ = 1 − α₁ for diseased population.

		Mean AUC							Confidence interval
(n0, n1)	p	PW	SW	MM	MVN	LR	Ridge	LASSO	PW	SW	MM	MVN	LR	Ridge	LASSO
Copula Σ0 = Σ1 = 0.85Ip×p + 0.15Jp×p (equal covariance in diseased and healthy groups)
(25,25)	10	0.6761	0.6554	0.6760	0.6571	0.6548	0.6896	0.6482	(0.512, 0.826)	(0.477, 0.805)	(0.512, 0.818)	(0.478, 0.821)	(0.486, 0.819)	(0.502, 0.835)	(0.500, 0.808)
	20	0.7003	0.6561	0.6907	0.6506	0.6334	0.7161	0.6624	(0.499, 0.850)	(0.485, 0.827)	(0.523, 0.834)	(0.483, 0.808)	(0.467, 0.797)	(0.534, 0.854)	(0.488, 0.835)
	50	0.7329	0.6524	0.7233	0.5868	0.5730	0.7483	0.6864	(0.546, 0.874)	(0.485, 0.819)	(0.558, 0.853)	(0.458, 0.734)	(0.454, 0.726)	(0.594, 0.883)	(0.500, 0.850)
	100	0.7510	0.6413	0.7373	0.6800	0.5603	0.7735	0.6975	(0.571, 0.888)	(0.469, 0.806)	(0.581, 0.882)	(0.494, 0.827)	(0.453, 0.693)	(0.638, 0.886)	(0.500, 0.837)
	200	0.7747	0.6201	0.7561	0.7445	0.5586	0.7961	0.7105	(0.587, 0.892)	(0.466, 0.805)	(0.610, 0.893)	(0.587, 0.872)	(0.451, 0.684)	(0.667, 0.908)	(0.500, 0.854)
(100,100)	10	0.7173	0.7063	0.6864	0.7105	0.7103	0.7180	0.7117	(0.642, 0.788)	(0.626, 0.785)	(0.610, 0.762)	(0.632, 0.784)	(0.632, 0.785)	(0.644, 0.787)	(0.630, 0.784)
	20	0.7442	0.7204	0.7020	0.7289	0.7274	0.7450	0.7350	(0.674, 0.814)	(0.637, 0.798)	(0.624, 0.775)	(0.645, 0.800)	(0.643, 0.798)	(0.671, 0.811)	(0.656, 0.804)
	50	0.7728	0.7249	0.7285	0.7446	0.7332	0.7821	0.7616	(0.706, 0.832)	(0.638, 0.803)	(0.659, 0.791)	(0.662, 0.815)	(0.650, 0.809)	(0.710, 0.843)	(0.686, 0.828)
	100	0.7834	0.7202	0.7449	0.7348	0.6924	0.8116	0.7797	(0.718, 0.847)	(0.634, 0.806)	(0.672, 0.812)	(0.647, 0.808)	(0.600, 0.778)	(0.753, 0.869)	(0.707, 0.846)
	200	0.7916	0.7164	0.7606	0.5643	0.5431	0.8520	0.7978	(0.724, 0.851)	(0.629, 0.797)	(0.689, 0.823)	(0.480, 0.667)	(0.479, 0.632)	(0.796, 0.903)	(0.727, 0.859)
Copula Σ0 = 0.9Ip×p + 0.1Jp×p and Σ1 = 0.85Ip×p + 0.15Jp×p (unequal covariance)
(25,25)	10	0.6797	0.6594	0.6826	0.6629	0.6612	0.6959	0.6524	(0.499, 0.834)	(0.491, 0.816)	(0.515, 0.826)	(0.470, 0.826)	(0.483, 0.822)	(0.526, 0.842)	(0.500, 0.816)
	20	0.7096	0.6632	0.7030	0.6571	0.6382	0.7250	0.6704	(0.525, 0.858)	(0.483, 0.826)	(0.544, 0.845)	(0.480, 0.813)	(0.469, 0.798)	(0.561, 0.864)	(0.499, 0.837)
	50	0.7462	0.6617	0.7379	0.5889	0.5722	0.7597	0.6963	(0.573, 0.882)	(0.486, 0.824)	(0.586, 0.866)	(0.459, 0.744)	(0.453, 0.731)	(0.606, 0.890)	(0.500, 0.856)
	100	0.7678	0.6410	0.7519	0.6918	0.5638	0.7878	0.7081	(0.600, 0.894)	(0.472, 0.813)	(0.603, 0.882)	(0.502, 0.834)	(0.459, 0.699)	(0.656, 0.898)	(0.500, 0.850)
	200	0.7937	0.6183	0.7732	0.7607	0.5599	0.8104	0.7204	(0.643, 0.906)	(0.461, 0.795)	(0.622, 0.901)	(0.611, 0.885)	(0.459, 0.685)	(0.678, 0.917)	(0.500, 0.864)
(100,100)	10	0.7231	0.7133	0.6925	0.7171	0.7170	0.7242	0.7177	(0.649, 0.794)	(0.633, 0.787)	(0.614, 0.767)	(0.641, 0.790)	(0.640, 0.790)	(0.648, 0.793)	(0.638, 0.791)
	20	0.7542	0.7318	0.7136	0.7383	0.7368	0.7542	0.7441	(0.684, 0.820)	(0.650, 0.803)	(0.635, 0.789)	(0.658, 0.809)	(0.655, 0.807)	(0.684, 0.820)	(0.670, 0.814)
	50	0.7868	0.7408	0.7437	0.7535	0.7417	0.7928	0.7734	(0.719, 0.842)	(0.657, 0.817)	(0.673, 0.812)	(0.672, 0.823)	(0.658, 0.816)	(0.722, 0.852)	(0.701, 0.838)
	100	0.7988	0.7367	0.7623	0.7408	0.6980	0.8209	0.7912	(0.735, 0.860)	(0.648, 0.821)	(0.691, 0.826)	(0.650, 0.815)	(0.600, 0.780)	(0.763, 0.876)	(0.721, 0.857)
	200	0.8085	0.7337	0.7797	0.5663	0.5424	0.8580	0.8083	(0.744, 0.865)	(0.650, 0.813)	(0.717, 0.840)	(0.488, 0.657)	(0.475, 0.632)	(0.800, 0.907)	(0.739, 0.867)

AUC, area under the receiver operating characteristic curve; PW, pairwise; SW, stepwise; MM, min–max; MVN, multivariate normal; LR, logistic regression; LASSO, Least Absolute Shrinkage and Selection Operator.

(n₀, n₁), sample sizes in healthy/diseased groups.

p, the number of markers.