Table 2 Selection performance of biomarker-treatment interactions and main effects corresponding to the selected interactions
AL(LRT) | AL(SW) | AL(ridge) | SGL | cMCP | gel | |||
|---|---|---|---|---|---|---|---|---|
Scenario 1 \(q_{Pe} = 0\) \(q_{Po} = 0\) | Interactions | \(n_{Pe}\) | 9.96 | 13.02 | 1.95 | 0.00 | 0.68 | 0.44 |
FP | 9.96 | 13.02 | 1.95 | 0.00 | 0.68 | 0.44 | ||
FDR | 0.95 | 0.97 | 0.95 | - | 0.24 | 0.20 | ||
Main effects | \(n_{Po}\) \((n_{Po}/n_{Pe})\) | 3.96 (40%) | 5.68 (44%) | 0.24 (12%) | 0.00 | 0.01 (1%) | 0.01 (2%) | |
FP | 3.96 | 5.68 | 0.24 | 0.00 | 0.01 | 0.01 | ||
FDR | 0.85 | 0.88 | 0.17 | - | 0.01 | 0.01 | ||
Scenario 2 \(q_{Pe} = 1\) \(q_{Po} = 0\) | Interactions | \(n_{Pe}\) | 8.89 | 6.71 | 4.31 | 1.37 | 2.28 | 1.54 |
TP / FP | 1.00/7.89 | 1.00/5.71 | 1.00/3.31 | 1.00/0.37 | 1.00/1.28 | 1.00/0.54 | ||
FDR / FNR | 0.72/0.00 | 0.44/0.00 | 0.53/0.00 | 0.15/0.00 | 0.26/0.00 | 0.15/0.00 | ||
Main effects | \(n_{Po}\) \((n_{Po}/n_{Pe})\) | 4.79 (54%) | 3.67 (55%) | 0.48 (11%) | 0.11 (8%) | 0.05 (2%) | 0.34 (52%) | |
TP / FP | 0.87/3.93 | 0.73/2.94 | 0.07/0.41 | 0.05/0.06 | 0.03/0.02 | 0.33/0.01 | ||
FDR / FNR | 0.63/0.13 | 0.37/0.27 | 0.24/0.93 | 0.06/0.95 | 0.02/0.97 | 0.01/0.67 | ||
Scenario 3 \(q_{Pe} = 10\) \(q_{Po} = 0\) | Interactions | \(n_{Pe}\) | 15.51 | 15.18 | 22.40 | 20.20 | 13.68 | 10.48 |
TP / FP | 10.00/5.51 | 10.00/5.18 | 10.00/12.40 | 10.00/10.20 | 10.00/3.68 | 10.00/0.48 | ||
FDR / FNR | 0.33/0.00 | 0.32/0.00 | 0.51/0.00 | 0.48/0.00 | 0.24/0.00 | 0.04/0.00 | ||
Main effects | \(n_{Po}\) \((n_{Po}/n_{Pe})\) | 9.54 (61%) | 9.15 (60%) | 2.28 (1%) | 4.09 (20%) | 1.02 (7%) | 5.73 (55%) | |
TP / FP | 6.74/2.80 | 6.61/2.54 | 0.93/1.35 | 1.69/2.40 | 0.96/0.07 | 5.72/0.01 | ||
FDR / FNR | 0.27/0.33 | 0.26/0.34 | 0.43/0.91 | 0.55/0.83 | 0.04/0.90 | 0.00/0.43 | ||
Scenario 4 \(q_{Pe} = 10\) \(q_{Po} = 10\) | Interactions | \(n_{Pe}\) | 15.15 | 70.88 | 19.93 | 26.27 | 14.57 | 19.67 |
TP / FP | 9.97/5.18 | 9.99/60.89 | 10.00/9.93 | 10.00/16.27 | 10.00/4.57 | 9.99/9.69 | ||
FDR / FNR | 0.32/0.00 | 0.85/0.00 | 0.46/0.00 | 0.60/0.00 | 0.29/0.00 | 0.49/0.00 | ||
Main effects | \(n_{Po}\) \((n_{Po}/n_{Pe})\) | 8.43 (56%) | 52.40 (74%) | 2.04 (10%) | 6.88 (26%) | 2.73 (19%) | 15.56 (78%) | |
TP / FP | 5.80/2.63 | 8.99/43.41 | 0.91/1.13 | 2.07/4.82 | 1.11/1.62 | 6.05/9.51 | ||
FDR / FNR | 0.29/0.42 | 0.82/0.10 | 0.42/0.91 | 0.68/0.79 | 0.56/0.89 | 0.62/0.39 |