Table 2.

Median (IQR) number of predictors correctly and incorrectly selected in simulation scenarios with low signal (R² = 0.1)

Method	Scenario 1, ρ = 0.2		Scenario 1, ρ = 0.8		Scenario 2, ρ = 0.2		Scenario 2, ρ = 0.8		Scenario 3
	# correct	# incorrect	# correct	# incorrect	# correct	# incorrect	# correct	# incorrect	# correct
TRUTH	10	0	10	0	2	0	2	0	9
Preserved Type I error
All in one	1 (1, 2)	0 (0, 1)	0 (0, 1)	0 (0, 1)	2 (1, 2)	0 (0, 1)	1 (0, 1)	0 (0, 1)	1 (0, 1)
WQS - data splitting	5 (4, 6)	2 (2, 3)	3 (2, 4)	3 (2, 4)	2 (2, 2)	3 (2, 4)	2 (1, 2)	3 (3, 4)	6 (5, 6)
Modified WQS
L1 - data splitting	3 (2, 4)	1 (1, 2)	2 (1, 2)	1 (1, 2)	2 (1, 2)	1 (0, 2)	1 (1, 1)	2 (1, 2)	3 (2, 4)
L1 - permutation test	5 (4, 6)	2 (1, 2.25)	2 (2, 3)	2 (1, 2)	2 (2, 2)	1 (0, 2)	1 (1, 2)	2 (1, 2)	4 (4, 5)
L2 - data splitting	6 (5, 6)	3 (2, 4)	4 (3, 6)	4 (2, 5)	2 (2, 2)	3 (2, 4)	2 (1, 2)	4 (2, 6)	7 (6, 8)
L2 - permutation test	6 (5, 7)	3 (2, 4)	5 (3, 6)	4 (2, 5)	2 (2, 2)	2 (1, 3)	2 (1, 2)	3 (2, 6)	7 (6, 8)
Inflated Type I error
WQS - no data splitting	6 (5, 6)	2 (1, 3)	4 (3, 4)	3 (2, 3)	2 (2, 2)	2 (2, 3)	2 (1, 2)	3 (2, 4)	6 (5, 7)
One at a time	9 (7, 10)	6 (4, 7)	10 (10, 10)	10 (10, 10)	2 (2, 2)	2 (1, 3)	2 (2, 2)	8 (8, 8)	8 (8, 9)

Note: Scenario 1 involved a mixture of 20 components, 10 of which were equally associated with the outcome. Scenario 2 had 10 mixture components, two of which were associated with the outcome, one more than the other. Scenario 3 had nine components, all equally associated with the outcome and generated using the observed correlation matrix from the applied example. Selection was defined as weights ≥ 0.05 for the weighted sum regressions and p-values < 0.05 for the linear regressions.