Table 2.
Comparison of four support vector learning methods for right censored data using a linear kernel, with censoring times following the Cox proportional hazards model
| Censoring | # of Noises | Method |
n =
100 |
n =
200 |
||||
|---|---|---|---|---|---|---|---|---|
| CORRa | RMSEb(SDc) | Ratiod | CORR | RMSE (SD) | Ratio | |||
| 40% | 0 | Modified SVR | 0.59 | 5.15 (0.59) | 1.11 | 0.62 | 5.09 (0.54) | 1.12 |
| IPCW-KMe | 0.53 | 5.16 (0.42) | 1.11 | 0.55 | 5.08 (0.31) | 1.12 | ||
| IPCW-Coxf | 0.52 | 5.31 (0.57) | 1.14 | 0.56 | 5.09 (0.46) | 1.12 | ||
| SVHM | 0.61g | 4.66 (0.25) | 1.00 | 0.63 | 4.53 (0.16) | 1.00 | ||
| 5 | Modified SVR | 0.56 | 5.28 (0.51) | 1.08 | 0.61 | 5.09 (0.50) | 1.12 | |
| IPCW-KM | 0.46 | 5.58 (0.42) | 1.14 | 0.52 | 5.27 (0.34) | 1.13 | ||
| IPCW-Cox | 0.44 | 5.73 (0.52) | 1.17 | 0.51 | 5.41 (0.51) | 1.16 | ||
| SVHM | 0.58 | 4.89 (0.29) | 1.00 | 0.62 | 4.65 (0.18) | 1.00 | ||
| 15 | Modified SVR | 0.47 | 5.43 (0.40) | 1.04 | 0.55 | 5.14 (0.38) | 1.06 | |
| IPCW-KM | 0.36 | 5.79 (0.34) | 1.11 | 0.44 | 5.49 (0.30) | 1.13 | ||
| IPCW-Cox | 0.34 | 6.00 (0.40) | 1.15 | 0.42 | 5.70 (0.43) | 1.18 | ||
| SVHM | 0.49 | 5.21 (0.33) | 1.00 | 0.57 | 4.84 (0.20) | 1.00 | ||
| 95h | Modified SVR | 0.21 | 6.43 (0.92) | 1.04 | 0.33 | 6.03 (0.54) | 1.04 | |
| IPCW-KM | 0.17 | 6.16 (0.21) | 1.00 | 0.24 | 6.06 (0.18) | 1.05 | ||
| IPCW-Cox | 0.16 | 6.32 (0.23) | 1.02 | 0.22 | 6.21 (0.22) | 1.07 | ||
| SVHM | 0.23 | 6.18 (0.40) | 1.00 | 0.34 | 5.78 (0.24) | 1.00 | ||
| 60% | 0 | Modified SVR | 0.56 | 5.43 (0.56) | 1.08 | 0.59 | 5.43 (0.47) | 1.12 |
| IPCW-KM | 0.44 | 5.68 (0.43) | 1.13 | 0.46 | 5.62 (0.33) | 1.16 | ||
| IPCW-Cox | 0.42 | 5.83 (0.56) | 1.16 | 0.47 | 5.67 (0.48) | 1.17 | ||
| SVHM | 0.57 | 5.01 (0.37) | 1.00 | 0.60 | 4.85 (0.25) | 1.00 | ||
| 5 | Modified SVR | 0.50 | 5.61 (0.48) | 1.07 | 0.57 | 5.40 (0.46) | 1.09 | |
| IPCW-KM | 0.36 | 6.02 (0.38) | 1.15 | 0.43 | 5.79 (0.35) | 1.17 | ||
| IPCW-Cox | 0.34 | 6.25 (0.44) | 1.20 | 0.41 | 5.96 (0.47) | 1.20 | ||
| SVHM | 0.53 | 5.23 (0.37) | 1.00 | 0.59 | 4.96 (0.27) | 1.00 | ||
| 15 | Modified SVR | 0.40 | 5.77 (0.42) | 1.05 | 0.50 | 5.44 (0.38) | 1.06 | |
| IPCW-KM | 0.27 | 6.07 (0.31) | 1.10 | 0.35 | 5.94 (0.26) | 1.16 | ||
| IPCW-Cox | 0.25 | 6.39 (0.40) | 1.16 | 0.32 | 6.16 (0.33) | 1.20 | ||
| SVHM | 0.42 | 5.51 (0.40) | 1.00 | 0.52 | 5.13 (0.29) | 1.00 | ||
| 95 | Modified SVR | 0.18 | 6.47 (0.87) | 1.05 | 0.27 | 6.31 (0.80) | 1.05 | |
| IPCW-KM | 0.12 | 6.22 (0.29) | 1.01 | 0.18 | 6.19 (0.21) | 1.03 | ||
| IPCW-Cox | 0.12 | 6.54 (0.26) | 1.07 | 0.16 | 6.50 (0.23) | 1.08 | ||
| SVHM | 0.20 | 6.14 (0.38) | 1.00 | 0.28 | 6.00 (0.35) | 1.00 | ||
CORR, average value of correlations.
RMSE, average value of root mean square errors.
Empirical standard deviation of the RMSE across 500 repetitions
Ratio, ratio of average root mean square errors between the method used and our method.
IPCW-KM, IPCW using the Kaplan-Meier estimator for the censoring distribution.
IPCW-Cox, IPCW using the Cox model for the censoring distribution.
Entries in boldface highlight the best performance method.
For the cases of 95 noises, the calculation of inverse weights in the IPCW-Cox method uses only five signal variables to fit the Cox model for the censoring times.