Table 1. Simulation results under sparse cases with p = 100 and n = 100 based on 50 replications.
, q = 2 | , q = 4 | ||||||||
CC | CS | Ridge | Lasso | CC | CS | Ridge | Lasso | ||
Scenario1, s = 4 | LR-test | −5.89 | −5.88 | −4.99 | −10.59 | −4.71 | −4.55 | −4.75 | −8.76 |
Cox-test | −8.41 | −8.26 | −7.32 | −13.80 | −6.76 | −7.06 | −6.95 | −11.73 | |
Devi | 66.63 | 45.62 | −29.48 | −76.92 | 75.34 | 56.30 | −25.75 | −60.50 | |
c-index | 0.772 | 0.768 | 0.752 | 0.859 | 0.750 | 0.751 | 0.750 | 0.825 | |
/ | 0.25 | 74.54 | 7.06 | / | 0.28 | 68.81 | 6.59 | ||
Scenario2 | LR-test | −8.88 | −9.35 | −7.01 | −12.39 | −6.38 | −6.74 | −6.30 | −11.40 |
Cox-test | −12.16 | −12.35 | −9.64 | −14.51 | −9.27 | −9.94 | −8.77 | −14.21 | |
Devi | −17.25 | −26.02 | −43.04 | −95.39 | −4.63 | −11.32 | −36.79 | −84.14 | |
c-index | 0.828 | 0.833 | 0.790 | 0.879 | 0.785 | 0.790 | 0.770 | 0.864 | |
/ | 0.30 | 37.88 | 6.90 | / | 0.30 | 50.91 | 6.17 | ||
, q = 5 | , q = 10 | ||||||||
CC | CS | Ridge | Lasso | CC | CS | Ridge | Lasso | ||
Scenario1, s = 4 | LR-test | −3.88 | −4.31 | −4.21 | −6.64 | −2.28 | −2.45 | −2.40 | −1.90 |
Cox-test | −6.18 | −6.19 | −6.04 | −9.47 | −3.03 | −3.03 | −3.01 | −2.86 | |
Devi | 80.59 | 56.87 | −21.44 | −43.22 | 145.95 | 97.88 | −9.28 | −7.85 | |
c-index | 0.725 | 0.722 | 0.722 | 0.790 | 0.659 | 0.656 | 0.652 | 0.649 | |
/ | 0.28 | 79.85 | 6.89 | / | 0.275 | 101.77 | 8.44 | ||
Scenario2 | LR-test | −13.71 | −13.69 | −11.38 | −14.52 | −9.67 | −9.34 | −8.86 | −9.65 |
Cox-test | −15.18 | −15.22 | −14.04 | −15.48 | −12.68 | −12.65 | −11.34 | −12.24 | |
Devi | −23.91 | −34.13 | −77.63 | −107.14 | 8.563 | −0.559 | −55.62 | −67.93 | |
c-index | 0.886 | 0.885 | 0.862 | 0.889 | 0.843 | 0.835 | 0.822 | 0.838 | |
/ | 0.33 | 33.34 | 6.66 | / | 0.29 | 47.22 | 6.86 |
NOTE: For Scenario 1, each informative covariate is correlated with s non-informative covariates. For Scenario 2, the covariates for the right panel have two gene pathways and those for the left panel have one gene pathway. In each setting, q is the number of informative covariates (covariates with non-zero coefficients).