Table 1:
Comparisons of methods under mild censoring.
| Example | Method | (n, p) = (200,1000) | (n, p) = (400,1000) | ||||
|---|---|---|---|---|---|---|---|
| PIT | TP | FP | PIT | TP | FP | ||
| 1 (P0 = 4) | FR | 3.65 (0.52) | 3.61 (0.49) | 0.05 (0.21) | 3.99 (0.18) | 3.98 (0.14) | 0.01 (0.12) |
| FR+Lasso | 3.65 (0.52) | 3.02 (0.15) | 0.63 (0.48) | 3.99 (0.18) | 3.01 (0.12) | 0.98 (0.14) | |
| FR+MCP | 3.65 (0.52) | 3.02 (0.15) | 0.63 (0.48) | 3.99 (0.18) | 3.01 (0.12) | 0.98 (0.14) | |
| FR+SCAD | 3.65 (0.52) | 3.02 (0.15) | 0.63 (0.48) | 3.99 (0.18) | 3.01 (0.12) | 0.98 (0.14) | |
| FRx1 | 3.65 (0.52) | 3.61 (0.49) | 0.05 (0.21) | 3.99 (0.18) | 3.98 (0.14) | 0.01 (0.12) | |
| FRx10 | 4.64 (0.52) | 3.60 (0.49) | 1.04 (0.20) | 4.99 (0.19) | 3.98 (0.15) | 1.01 (0.12) | |
| FR(η1) | 5.04 (1.41) | 3.89 (0.32) | 1.16 (1.38) | 4.53 (0.85) | 4.00 (0.00) | 0.53 (0.85) | |
| FR(η2) | 3.95 (0.62) | 3.77 (0.42) | 0.18 (0.45) | 4.08 (0.33) | 3.99 (0.09) | 0.09 (0.31) | |
| PSIS | 38.00 (0.00) | 3.03 (0.55) | 34.97 (0.55) | 67.00 (0.00) | 3.39 (0.49) | 63.61 (0.49) | |
| PSIS+Lasso | 4.44 (2.71) | 2.43 (0.93) | 2.01 (2.12) | 6.82 (2.70) | 3.13 (0.48) | 3.69 (2.64) | |
| PSIS+MCP | 4.05 (2.14) | 2.47 (0.85) | 1.58 (1.67) | 4.81 (1.60) | 3.08 (0.47) | 1.74 (1.55) | |
| PSIS+SCAD | 4.22 (2.55) | 2.36 (0.89) | 1.86 (1.98) | 5.33 (1.96) | 3.06 (0.53) | 2.27 (1.85) | |
| CS | 38.00 (0.00) | 3.08 (0.48) | 34.92 (0.48) | 67.00 (0.00) | 3.23 (0.42) | 63.77 (0.42) | |
| CS+Lasso | 4.63 (2.49) | 2.51 (0.77) | 2.12 (2.09) | 6.50 (2.45) | 2.95 (0.43) | 3.54 (2.35) | |
| CS+MCP | 4.00 (1.86) | 2.44 (0.76) | 1.55 (1.47) | 4.78 (1.40) | 2.92 (0.37) | 1.86 (1.33) | |
| CS+SCAD | 4.30 (2.23) | 2.37 (0.75) | 1.93 (1.81) | 5.39 (1.82) | 2.90 (0.44) | 2.48 (1.67) | |
| 2 (p0 = 6) | FR | 0.91 (0.30) | 5.89 (0.40) | 1.34 (1.40) | 1.00 (0.00) | 6.00 (0.00) | 1.01 (1.20) |
| FR | 6.16 (0.47) | 6.00 (0.00) | 0.16 (0.47) | 6.02 (0.15) | 6.00 (0.00) | 0.02 (0.15) | |
| FR+Lasso | 6.16 (0.47) | 6.00 (0.00) | 0.16 (0.47) | 6.02 (0.15) | 6.00 (0.00) | 0.02 (0.15) | |
| FR+MCP | 6.16 (0.47) | 6.00 (0.00) | 0.16 (0.47) | 6.02 (0.15) | 6.00 (0.00) | 0.02 (0.15) | |
| FR+SCAD | 6.08 (0.35) | 5.91 (0.32) | 0.16 (0.47) | 6.02 (0.15) | 6.00 (0.00) | 0.02 (0.15) | |
| FRx1 | 6.08 (0.33) | 6.00 (0.00) | 0.08 (0.33) | 6.02 (0.15) | 6.00 (0.00) | 0.02 (0.15) | |
| FRx10 | 7.13 (0.42) | 6.00 (0.00) | 1.13 (0.42) | 7.01 (0.13) | 6.00 (0.00) | 1.01 (0.13) | |
| FR(η1) | 7.51 (1.78) | 6.00 (0.00) | 1.51 (1.78) | 6.78 (1.16) | 6.00 (0.00) | 0.78 (1.16) | |
| FR(η2) | 6.34 (0.72) | 6.00 (0.00) | 0.34 (0.72) | 6.11 (0.40) | 6.00 (0.00) | 0.11 (0.40) | |
| PSIS | 38.00 (0.00) | 3.42 (0.93) | 34.58 (0.93) | 67.00 (0.00) | 4.83 (0.53) | 62.17 (0.53) | |
| PSIS+Lasso | 8.54 (4.97) | 3.71 (0.97) | 4.84 (4.66) | 8.74 (5.33) | 4.82 (0.54) | 3.92 (5.21) | |
| PSIS+MCP | 5.75 (2.39) | 3.34 (1.01) | 2.42 (1.97) | 9.21 (3.05) | 4.80 (0.61) | 4.41 (2.77) | |
| PSIS+SCAD | 6.73 (3.29) | 3.51 (0.95) | 3.21 (3.08) | 8.80 (4.80) | 4.77 (0.63) | 4.03 (4.56) | |
| CS | 38.00 (0.00) | 4.45 (0.83) | 33.55 (0.83) | 67.00 (0.00) | 5.66 (0.53) | 61.34 (0.53) | |
| CS+Lasso | 8.68 (4.49) | 4.55 (0.93) | 4.13 (4.07) | 11.60 (4.50) | 5.67 (0.53) | 5.93 (4.22) | |
| CS+MCP | 6.41 (2.38) | 4.27 (1.09) | 2.14 (1.97) | 7.44 (2.20) | 5.64 (0.63) | 1.80 (2.46) | |
| CS+SCAD | 6.68 (2.92) | 4.34 (0.98) | 2.34 (2.69) | 6.83 (2.54) | 5.63 (0.63) | 1.20 (2.71) | |
| 3 (P0 = 6) | FR | 5.24 (0.95) | 5.02 (1.03) | 0.22 (0.49) | 5.75 (0.45) | 5.74 (0.44) | 0.01 (0.12) |
| FR+Lasso | 5.24 (0.95) | 5.19 (0.87) | 0.05 (0.25) | 5.75 (0.45) | 5.74 (0.44) | 0.01 (0.09) | |
| FR+MCP | 5.24 (0.95) | 5.19 (0.87) | 0.05 (0.25) | 5.75 (0.45) | 5.74 (0.44) | 0.01 (0.09) | |
| FR+SCAD | 5.21 (0.94) | 5.16 (0.87) | 0.05 (0.25) | 5.75 (0.45) | 5.74 (0.44) | 0.01 (0.09) | |
| FRx1 | 5.25 (0.85) | 5.10 (0.84) | 0.16 (0.40) | 5.75 (0.45) | 5.74 (0.44) | 0.01 (0.12) | |
| FRx10 | 6.05 (1.28) | 4.87 (1.28) | 1.17 (0.41) | 6.75 (0.45) | 5.73 (0.44) | 1.01 (0.12) | |
| FR(η1) | 6.84 (1.87) | 5.38 (0.93) | 1.45 (1.70) | 6.43 (0.87) | 5.93 (0.26) | 0.50 (0.84) | |
| FR(η2) | 5.60 (1.09) | 5.18 (1.00) | 0.41 (0.73) | 5.93 (0.48) | 5.85 (0.36) | 0.07 (0.33) | |
| PSIS | 38.00 (0.00) | 2.57 (0.72) | 35.43 (0.72) | 67.00 (0.00) | 3.35 (0.58) | 63.65 (0.58) | |
| PSIS+Lasso | 3.43 (2.69) | 2.06 (1.05) | 1.37 (1.96) | 6.18 (2.77) | 3.22 (0.56) | 2.96 (2.59) | |
| PSIS+MCP | 3.04 (1.64) | 2.21 (0.90) | 0.83 (1.16) | 3.51 (0.95) | 3.11 (0.49) | 0.40 (0.79) | |
| PSIS+SCAD | 3.64 (2.24) | 2.21 (0.99) | 1.43 (1.61) | 3.91 (1.18) | 3.13 (0.49) | 0.78 (1.04) | |
| CS | 38.00 (0.00) | 3.14 (0.68) | 34.86 (0.68) | 67.00 (0.00) | 4.17 (0.62) | 62.83 (0.62) | |
| CS+Lasso | 4.74 (3.02) | 2.67 (1.18) | 2.07 (2.21) | 7.97 (3.03) | 4.05 (0.65) | 3.93 (2.77) | |
| CS+MCP | 3.76 (1.67) | 2.84 (0.80) | 0.93 (1.39) | 4.31 (0.97) | 3.94 (0.58) | 0.38 (0.79) | |
| CS+SCAD | 4.62 (2.16) | 2.86 (0.95) | 1.76 (1.69) | 4.66 (1.08) | 3.95 (0.58) | 0.71 (0.98) | |
NOTE: FR, forward regression; PSIS, the principled sure independence screening; CS, the conditional screening with the given conditioning variable; PIT, estimated probability of including all true predictors in the selected predictors; TP, average number of true positives; FP, average number of false positives; p0 denotes the number of true signals; numbers in the parentheses are standard deviations. We used η1 = .5 and η2 = 1 – ln d/(3 ln p). When it is not noted, η = 1 was used. FRS0 denotes that FR was performed with the initial set of S0. We considered two initial sets x1 and x10.