Table 1.
Percent reduction in θ using marker-based rule compared to the best treatment strategy in the absence of marker information, for δ = 0, training size n = 100. Five-fold CV is used for selecting tuning parameters.
| Scenario | ρ0 | ρ1 | Method | Weights for Ramp and SVM | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Case-only | Control-only | CCa | DRb | ||||||||
| Mean | SE | Mean | SE | Mean | SE | Mean | SE | ||||
| I-A | 0.244 | 0.236 | Linear logistic | 21.15 | (0.25) | ||||||
| W-GENOUD, Linear | 10.81 | (0.34) | 3.89 | (0.34) | 8.31 | (0.34) | 18.52 | (0.34) | |||
| W-Ramp, Linear | 14.12 | (0.43) | 13.90 | (0.42) | 14.94 | (0.42) | 14.73 | (0.44) | |||
| W-SVM, Linear | 7.09 | (0.44) | 0.98 | (0.25) | 2.40 | (0.29) | 12.08 | (0.48) | |||
| W-Ramp, RBF | 8.80 | (0.38) | 5.59 | (0.33) | 6.72 | (0.31) | 11.01 | (0.39) | |||
| W-SVM, RBF | 8.78 | (0.39) | 6.06 | (0.34) | 6.66 | (0.32) | 9.82 | (0.37) | |||
| I-B | 0.318 | 0.307 | Linear logistic | 1.56 | (0.35) | ||||||
| W-GENOUD, Linear | 4.71 | (0.37) | 2.15 | (0.37) | 4.38 | (0.37) | 4.95 | (0.37) | |||
| W-Ramp, Linear | 5.23 | (0.35) | 4.59 | (0.36) | 5.11 | (0.38) | 5.19 | (0.36) | |||
| W-SVM, Linear | −0.58 | (0.16) | −0.09 | (0.18) | −0.59 | (0.16) | −0.43 | (0.17) | |||
| W-Ramp, RBF | 4.53 | (0.27) | 3.12 | (0.24) | 4.35 | (0.24) | 5.04 | (0.26) | |||
| W-SVM, RBF | 4.33 | (0.26) | 3.10 | (0.24) | 4.36 | (0.24) | 4.63 | (0.25) | |||
| II-A | 0.185 | 0.175 | Linear logistic | 30.81 | (0.65) | ||||||
| W-GENOUD, Linear | 31.14 | (0.53) | 16.03 | (0.53) | 26.92 | (0.53) | 33.22 | (0.53) | |||
| W-Ramp, Linear | 31.19 | (0.67) | 30.41 | (0.65) | 32.27 | (0.62) | 31.44 | (0.67) | |||
| W-SVM, Linear | 24.17 | (0.83) | 12.07 | (0.74) | 17.43 | (0.77) | 23.45 | (0.83) | |||
| W-Ramp, RBF | 32.62 | (0.68) | 23.30 | (0.7) | 30.86 | (0.67) | 32.42 | (0.69) | |||
| W-SVM, RBF | 32.47 | (0.68) | 22.75 | (0.71) | 30.45 | (0.68) | 32.64 | (0.66) | |||
| II-B | 0.192 | 0.19 | Linear logistic | 15.57 | (0.68) | ||||||
| W-GENOUD, Linear | 21.99 | (0.53) | 10.85 | (0.53) | 19.72 | (0.53) | 23.49 | (0.53) | |||
| W-Ramp, Linear | 21.06 | (0.57) | 19.30 | (0.62) | 21.08 | (0.59) | 21.77 | (0.58) | |||
| W-SVM, Linear | 12.76 | (0.62) | 7.55 | (0.53) | 9.12 | (0.54) | 12.51 | (0.60) | |||
| W-Ramp, RBF | 31.31 | (0.64) | 23.94 | (0.68) | 29.47 | (0.63) | 32.62 | (0.61) | |||
| W-SVM, RBF | 31.46 | (0.64) | 23.81 | (0.67) | 29.55 | (0.64) | 32.11 | (0.60) | |||
| III | 0.269 | 0.256 | Linear logistic | −0.54 | (0.23) | ||||||
| W-GENOUD, Linear | 1.94 | (0.25) | −0.06 | (0.25) | 1.79 | (0.25) | 2.31 | (0.25) | |||
| W-Ramp, Linear | 1.19 | (0.22) | 0.10 | (0.21) | 0.76 | (0.22) | 1.16 | (0.22) | |||
| W-SVM, Linear | −0.24 | (0.19) | −1.01 | (0.21) | −1.20 | (0.18) | −0.87 | (0.18) | |||
| W-Ramp, RBF | 5.19 | (0.31) | 1.53 | (0.25) | 3.38 | (0.26) | 4.04 | (0.28) | |||
| W-SVM, RBF | 5.17 | (0.31) | 1.48 | (0.26) | 3.39 | (0.26) | 4.28 | (0.26) | |||
CCa: Case-control weights; DRb: double-robustness weights