Table 2.

Simulation results on screening performance in ultra-high dimensional cases

				SII		MB		C Index		QaSIS (α = 0.25)		QaSIS (α = 0.5)
Case	n	ρ	p*	ℛ (IQR)	$\mathcal{S}$	ℛ (IQR)	$\mathcal{S}$	ℛ (IQR)	$\mathcal{S}$	ℛ (IQR)	$\mathcal{S}$	ℛ (IQR)	$\mathcal{S}$
I	200	0	4	92.5 (84.75)	0.16	118.5 (86)	0.09	122 (86.5)	0.14	195.5 (30.5)	0	129 (72.25)	0.02
		0.4	4	93 (71.5)	0.12	143.5 (64.75)	0.01	136 (97.75)	0.08	187 (37)	0	133 (84.5)	0.10
		0.8	4	18.5 (41.25)	0.63	73.5 (125.25)	0.28	72 (108.5)	0.29	183.5 (76)	0.03	61 (90.5)	0.39
	400	0	4	71.5 (69.5)	0.44	110.5 (94)	0.27	99 (101.75)	0.36	199 (17)	0.02	119 (95)	0.22
		0.4	4	60 (75.75)	0.56	136 (81.75)	0.14	135 (89.5)	0.17	194.5 (36.5)	0.01	126.5 (79)	0.14
		0.8	4	6 (10)	1	60 (113.5)	0.52	26 (92.5)	0.67	184.5 (65.75)	0.07	35 (74.25)	0.63
II	200	0	3	4.5 (8)	0.95	15 (46.25)	0.70	101 (72.5)	0.07	53.5 (112.25)	0.45	26 (43.5)	0.67
		0.4	3	3 (1)	1	14 (36.75)	0.69	76.5 (92.5)	0.26	189 (65.25)	0.09	28.5 (53)	0.59
		0.8	3	3 (0)	1	12.5 (30.5)	0.76	13 (40.25)	0.72	200 (0)	0	4 (2)	0.99
	400	0	3	3 (0)	1	3 (4)	0.97	108.5 (96)	0.30	20 (72.5)	0.68	10.5 (18.25)	0.92
		0.4	3	3 (0)	1	4 (7)	0.97	41.5 (91.25)	0.61	199 (27.75)	0.10	14 (19)	0.91
		0.8	3	3 (0)	1	5 (5.75)	0.98	5 (5)	0.96	200 (0)	0.01	3 (0.25)	1
III	200	0	4	53.5 (54.25)	0.33	96.5 (99.75)	0.20	93 (107.25)	0.21	183 (57.25)	0.02	108 (91.75)	0.14
		0.4	4	42.5 (61.25)	0.45	82.5 (90.75)	0.21	109 (90.5)	0.18	170 (51.75)	0.01	86 (94.75)	0.18
		0.8	4	4 (1)	0.99	6 (6.25)	0.94	7 (10.25)	0.88	188 (50)	0.01	13 (32.25)	0.75
	400	0	4	48 (44.25)	0.67	86 (100.75)	0.40	113.5 (98)	0.28	174 (52)	0.03	102 (99)	0.31
		0.4	4	14 (25.75)	0.91	48.5 (108.5)	0.55	75 (106.5)	0.47	179.5 (54.75)	0.08	68 (86)	0.49
		0.8	4	4 (1)	1	6 (2)	0.99	5 (1)	1	197 (27.25)	0.02	7 (6.25)	0.98
IV	200	0	4	6.5 (9)	0.93	108 (86.75)	0.10	107 (103)	0.17	186.5 (58.25)	0.01	16 (28.25)	0.76
		0.5	4	21 (43.5)	0.64	100 (82)	0.10	135 (75.75)	0.07	179.5 (36.5)	0.01	45.5 (84.5)	0.42
		1	4	17 (37.25)	0.67	98 (89.5)	0.13	149 (72.75)	0.06	187 (29.25)	0	48 (68.5)	0.40
	400	0	4	4 (0.25)	1	122 (116)	0.32	(101.5) (94.25)	0.31	189.5 (56.25)	0.08	4 (2)	0.99
		0.5	4	7 (15.25)	0.95	86.5 (90.5)	0.35	144 (85.25)	0.16	182 (47.75)	0.01	18.5 (40.25)	0.83
		1	4	6 (12.25)	0.95	93.5 (85.5)	0.34	154.5 (78)	0.12	186.5 (23.5)	0	41.5 (84.25)	0.63
V	200	0	4	4 (1)	0.98	125.5 (100.25)	0.10	104 (87.5)	0.11	190 (41)	0.01	49 (61.25)	0.37
		0.5	4	5 (3)	0.96	136 (71.75)	0.05	183.5 (47.75)	0.01	183 (42.25)	0	24.5 (27.5)	0.72
		1	4	11 (19.25)	0.79	172.5 (52.25)	0	197 (21.25)	0	168.5 (53.25)	0	42 (42.25)	0.43
	400	0	4	4 (0)	1	96 (96.25)	0.31	105.5 (98.25)	0.34	192.5 (33)	0.01	17.5 (33)	0.83
		0.5	4	4 (0)	1	144.5 (79.5)	0.17	190 (30.25)	0	176 (72.25)	0.05	10 (12.25)	0.99
		1	4	5 (4)	0.98	178.5 (43.5)	0.01	199 (4.25)	0	164 (61.5)	0.05	30.5 (33)	0.87
VI	200	0	8	82 (82.5)	0.18	103 (85.75)	0.15	114 (96.25)	0.12	197 (14)	0	142.5 (70)	0
		0.4	8	149 (71)	0.01	160 (57.75)	0.01	155 (93)	0.01	193 (20)	0	161 (52.75)	0
		0.8	8	8 (2)	0.95	8 (4)	0.95	8.5 (2)	0.95	199 (5)	0	43.5 (67.25)	0.45
	400	0	8	67.5 (71.25)	0.49	103 (94.25)	0.30	106.5 (108)	0.30	198.5 (9)	0	124.5 (62.5)	0.11
		0.4	8	135 (59.25)	0.14	160 (59.75)	0.07	136.5 (88.75)	0.14	195.5 (19.25)	0	147 (65.25)	0.06
		0.8	8	8 (0)	1	8 (0)	1	8 (0)	1	200 (2)	0	36 (45.75)	0.76

p*: number of truly important markers; ℛ: median of minimum model size that covers all important markers; IQR: inter-quartile range of minimum model size that covers all important markers; $\mathcal{S}$: empirical probability that the set of top [n/log(n)] markers after screening includes all important markers.