Computational and Mathematical Methods in Medicine

Research Article

Comparison of Variable Selection Methods for Time-to-Event Data in High-Dimensional Settings

Table 5

Number of genes that overlaps between methods for the same samples and true-positive rates among common genes, for each simulated dataset and selection method.


		Training fraction		Intersection (number of common genes/true-positive rates among common genes)
		Training fraction		LASSO-pcvl	Elastic Net	BSS Enet	CoxBoost	RSF

500	12	1/2	LASSO-cvl	11 (5-29)/0.7 (0.35-1)	25 (7-53)/0.35 (0.15-1)	18 (7-27)/0.47 (0.26-1)	22 (7-40)/0.38 (0.17-1)	6 (1-12)/0.71 (0.2-1)
			LASSO-pcvl		11 (5-29)/0.7 (0.33-1)	11 (5-24)/0.71 (0.41-1)	11 (5-29)/0.7 (0.33-1)	4 (1-12)/0.86 (0.5-1)
			Elastic Net			20 (8-29)/0.45 (0.29-0.88)	24 (8-48)/0.35 (0.17-0.78)	7 (3-14)/0.67 (0.2-1)
			BSS Enet				18 (7-28)/0.44 (0.28-0.8)	7 (1-12)/0.75 (0.25-1)
			CoxBoost					6 (1-13)/0.71 (0.2-1)
	50	1/2	LASSO-cvl	42 (13-74)/0.64 (0.46-0.95)	62 (40-93)/0.49 (0.37-0.65)	40 (28-56)/0.71 (0.52-0.84)	53 (24-80)/0.55 (0.41-0.92)	12 (4-19)/0.79 (0.44-1)
			LASSO-pcvl		44 (13-74)/0.63 (0.45-0.95)	35 (13-48)/0.74 (0.59-0.95)	42 (13-72)/0.65 (0.45-0.95)	11 (3-18)/0.86 (0.56-1)
			Elastic Net			43 (29-57)/0.71 (0.52-0.82)	57 (24-79)/0.54 (0.38-0.92)	14 (5-21)/0.77 (0.37-1)
			BSS Enet				40 (22-53)/0.72 (0.53-0.95)	11 (2-18)/0.89 (0.57-1)
			CoxBoost					12 (4-20)/0.81 (0.5-1)

750	12	1/2	LASSO-cvl	13 (7-25)/0.69 (0.4-1)	25 (12-50)/0.36 (0.18-0.75)	19 (11-29)/0.47 (0.3-0.79)	23 (12-43)/0.39 (0.2-0.75)	7 (4-12)/0.83 (0.5-1)
			LASSO-pcvl		13 (7-25)/0.68 (0.4-1)	12 (6-23)/0.73 (0.43-1)	13 (7-24)/0.69 (0.38-1)	6 (3-10)/1 (0.6-1)
			Elastic Net			22 (11-33)/0.45 (0.3-0.75)	26 (12-50)/0.36 (0.2-0.75)	8 (4-14)/0.8 (0.54-1)
			BSS Enet				20 (11-33)/0.45 (0.3-0.82)	8 (4-12)/0.86 (0.43-1)
			CoxBoost					7 (3-12)/0.8 (0.57-1)
	50	1/2	LASSO-cvl	43 (27-68)/0.73 (0.5-0.91)	71 (51-90)/0.51 (0.37-0.69)	49 (39-65)/0.7 (0.55-0.85)	60 (36-79)/0.58 (0.43-0.81)	14 (6-22)/0.85 (0.67-1)
			LASSO-pcvl		44 (27-68)/0.73 (0.5-0.92)	40 (27-57)/0.79 (0.61-0.94)	42 (27-65)/0.74 (0.52-0.92)	12 (7-20)/0.93 (0.71-1)
			Elastic Net			52 (42-68)/0.68 (0.55-0.83)	62 (36-83)/0.56 (0.43-0.81)	16 (7-23)/0.83 (0.6-1)
			BSS Enet				47 (34-63)/0.71 (0.56-0.86)	14 (8-22)/0.9 (0.73-1)
			CoxBoost					14 (6-22)/0.88 (0.71-1)

1000	12	1/2	LASSO-cvl	15 (8-28)/0.59 (0.32-0.92)	34 (11-79)/0.28 (0.11-0.73)	26 (11-51)/0.35 (0.18-0.73)	31 (11-55)/0.29 (0.16-0.73)	8 (4-12)/0.89 (0.45-1)
			LASSO-pcvl		15 (8-28)/0.59 (0.32-0.92)	15 (8-27)/0.61 (0.33-0.92)	15 (8-28)/0.59 (0.32-0.92)	7 (4-11)/1 (0.62-1)
			Elastic Net			29 (14-52)/0.34 (0.17-0.61)	34 (16-62)/0.28 (0.14-0.53)	9 (4-12)/0.89 (0.42-1)
			BSS Enet				27 (13-44)/0.34 (0.2-0.59)	9 (6-12)/0.89 (0.5-1)
			CoxBoost					8 (4-11)/0.88 (0.6-1)
	50	1/2	LASSO-cvl	57 (34-77)/0.72 (0.52-0.97)	90 (70-122)/0.48 (0.35-0.61)	63 (53-88)/0.67 (0.52-0.78)	73 (54-101)/0.57 (0.45-0.78)	18 (13-24)/0.9 (0.71-1)
			LASSO-pcvl		57 (34-78)/0.72 (0.51-0.97)	53 (34-65)/0.78 (0.63-0.97)	56 (34-76)/0.73 (0.53-0.97)	17 (12-23)/0.94 (0.74-1)
			Elastic Net			66 (58-89)/0.66 (0.53-0.76)	74 (54-106)/0.56 (0.43-0.78)	20 (14-25)/0.88 (0.71-1)
			BSS Enet				60 (50-84)/0.7 (0.56-0.81)	19 (13-24)/0.94 (0.79-1)
			CoxBoost					18 (12-24)/0.94 (0.71-1)

500	12	2/3	LASSO-cvl	13 (7-25)/0.71 (0.4-1)	26 (10-55)/0.38 (0.15-0.8)	20 (9-31)/0.45 (0.3-0.8)	24 (10-46)/0.4 (0.17-0.8)	7 (3-11)/0.75 (0.43-1)
			LASSO-pcvl		13 (7-26)/0.71 (0.38-1)	13 (7-21)/0.72 (0.48-1)	13 (7-25)/0.71 (0.4-1)	5 (2-10)/1 (0.6-1)
			Elastic Net			23 (11-33)/0.43 (0.31-0.82)	28 (10-48)/0.34 (0.17-0.71)	7 (4-13)/0.71 (0.4-1)
			BSS Enet				21 (9-32)/0.44 (0.31-0.78)	7 (4-11)/0.8 (0.5-1)
			CoxBoost					7 (3-10)/0.71 (0.43-1)
	50	2/3	LASSO-cvl	52 (33-71)/0.65 (0.51-0.85)	76 (57-104)/0.49 (0.34-0.61)	51 (43-62)/0.68 (0.56-0.81)	65 (41-93)/0.55 (0.35-0.68)	14 (7-21)/0.83 (0.58-1)
			LASSO-pcvl		53 (34-72)/0.65 (0.51-0.85)	46 (34-57)/0.73 (0.61-0.92)	51 (33-65)/0.66 (0.56-0.87)	13 (7-19)/0.9 (0.64-1)
			Elastic Net			54 (45-66)/0.69 (0.56-0.82)	66 (41-99)/0.54 (0.34-0.69)	16 (10-23)/0.8 (0.48-1)
			BSS Enet				50 (37-60)/0.7 (0.6-0.82)	14 (7-20)/0.92 (0.61-1)
			CoxBoost					14 (7-21)/0.87 (0.62-1)

750	12	2/3	LASSO-cvl	11 (8-18)/0.82 (0.5-1)	23 (12-49)/0.42 (0.2-0.79)	20 (11-33)/0.5 (0.3-0.92)	21 (12-47)/0.45 (0.21-0.77)	8 (5-11)/1 (0.73-1)
			LASSO-pcvl		11 (8-18)/0.82 (0.5-1)	11 (8-17)/0.83 (0.53-1)	11 (8-18)/0.82 (0.5-1)	7 (5-10)/1 (0.86-1)
			Elastic Net			22 (13-35)/0.46 (0.29-0.85)	24 (13-49)/0.41 (0.2-0.71)	8 (5-13)/1 (0.69-1)
			BSS Enet				20 (12-32)/0.47 (0.28-0.83)	8 (5-12)/1 (0.73-1)
			CoxBoost					8 (5-12)/1 (0.7-1)
	50	2/3	LASSO-cvl	46 (31-59)/0.8 (0.62-0.97)	80 (58-111)/0.52 (0.39-0.72)	58 (46-70)/0.69 (0.59-0.85)	68 (43-87)/0.59 (0.45-0.84)	16 (12-21)/0.94 (0.76-1)
			LASSO-pcvl		46 (31-59)/0.8 (0.62-0.97)	44 (30-54)/0.83 (0.69-0.97)	46 (31-58)/0.8 (0.65-0.97)	14 (9-20)/1 (0.84-1)
			Elastic Net			62 (51-78)/0.68 (0.59-0.84)	69 (43-89)/0.59 (0.44-0.84)	17 (14-23)/0.94 (0.74-1)
			BSS Enet				55 (40-67)/0.71 (0.6-0.87)	16 (12-22)/0.94 (0.81-1)
			CoxBoost					15 (12-21)/0.94 (0.8-1)

1000	12	2/3	LASSO-cvl	15 (9-25)/0.62 (0.4-1)	42 (20-74)/0.24 (0.12-0.5)	33 (19-55)/0.29 (0.16-0.53)	37 (14-67)/0.25 (0.15-0.57)	7 (3-9)/1 (0.83-1)
			LASSO-pcvl		15 (9-25)/0.62 (0.4-1)	14 (9-25)/0.62 (0.4-1)	14 (9-25)/0.62 (0.4-1)	6 (3-9)/1 (0.8-1)
			Elastic Net			38 (21-59)/0.28 (0.18-0.52)	41 (14-70)/0.23 (0.14-0.57)	7 (4-10)/1 (0.83-1)
			BSS Enet				35 (14-53)/0.28 (0.17-0.57)	7 (4-10)/1 (0.75-1)
			CoxBoost					7 (4-9)/1 (0.83-1)
	50	2/3	LASSO-cvl	57 (45-73)/0.76 (0.6-0.91)	100 (75-144)/0.45 (0.31-0.59)	73 (59-89)/0.61 (0.5-0.74)	78 (53-110)/0.56 (0.39-0.77)	15 (11-18)/1 (0.88-1)
			LASSO-pcvl		57 (46-73)/0.75 (0.6-0.91)	55 (45-68)/0.79 (0.63-0.91)	55 (45-71)/0.76 (0.61-0.91)	15 (11-18)/1 (0.92-1)
			Elastic Net			78 (65-93)/0.59 (0.5-0.72)	79 (53-112)/0.55 (0.38-0.77)	16 (12-18)/1 (0.81-1)
			BSS Enet				67 (53-82)/0.66 (0.53-0.83)	15 (11-18)/1 (0.92-1)
			CoxBoost					15 (11-18)/1 (0.92-1)