Table 4.
Mean concordance index error for competing learning methods, aggregated over 100 replicates of bootstrap cross-validation in five independent data sets. The minimum concordance error value for each analysis is written in bold text.
| Ensemble Survival Trees§ | Proportional Hazards | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Scenario† | ORSF | ORSFCV | CIF | RSF | Xgboost | CoxBoost | Lasso | Ridge | Step |
| Concordance error: 100 · | |||||||||
| GEBC | 24.98 | 25.08 | 25.79 | 31.19 | 27.08 | 28.62 | 28.59 | 26.47 | – |
| GBSG2 | 28.10 | 27.86 | 28.40 | 28.71 | 28.09 | 30.24 | 30.30 | 29.99 | 29.88 |
| JHS1 | 17.67 | 17.58 | 17.74 | 19.31 | 17.84 | 18.69 | 18.68 | 18.37 | 18.74 |
| JHS3 | 17.61 | 17.57 | 17.91 | 18.40 | 17.63 | 18.54 | 18.90 | 19.66 | 18.07 |
| JHS2 | 13.13 | 13.16 | 13.42 | 13.45 | 13.61 | 17.51 | 18.86 | 14.43 | 14.83 |
| PBC | 12.25 | 12.29 | 12.80 | 13.90 | 12.87 | 13.53 | 13.72 | 12.82 | 15.15 |
| REGARDS1 | 21.81 | 21.83 | 21.84 | 22.69 | 22.15 | 22.68 | 22.57 | 22.35 | 24.58 |
| REGARDS3 | 18.69 | 18.80 | 18.82 | 19.01 | 18.55 | 19.27 | 20.33 | 30.62 | 19.32 |
| REGARDS2 | 13.91 | 13.86 | 14.21 | 16.08 | 14.01 | 15.64 | 17.87 | 29.38 | 16.93 |
| MBC | 29.41 | 29.27 | 27.99 | 32.47 | 31.28 | 40.62 | 39.79 | 35.14 | – |
| Percent increase in , relative to minimum (0.00) | |||||||||
| GEBC | 0.0 | 0.4 | 3.3 | 24.9 | 8.4 | 14.6 | 14.5 | 6.0 | – |
| GBSG2 | 0.9 | 0.0 | 1.9 | 3.0 | 0.8 | 8.5 | 8.7 | 7.6 | 7.2 |
| JHS1 | 0.5 | 0.0 | 0.9 | 9.8 | 1.5 | 6.3 | 6.3 | 4.5 | 6.6 |
| JHS3 | 0.2 | 0.0 | 1.9 | 4.7 | 0.3 | 5.5 | 7.5 | 11.9 | 2.8 |
| JHS2 | 0.0 | 0.2 | 2.2 | 2.5 | 3.7 | 33.4 | 43.7 | 10.0 | 13.0 |
| PBC | 0.0 | 0.3 | 4.5 | 13.5 | 5.1 | 10.5 | 12.0 | 4.7 | 23.7 |
| REGARDS1 | 0.0 | 0.1 | 0.1 | 4.1 | 1.6 | 4.0 | 3.5 | 2.5 | 12.7 |
| REGARDS3 | 0.7 | 1.4 | 1.5 | 2.5 | 0.0 | 3.9 | 9.6 | 65.0 | 4.2 |
| REGARDS2 | 0.4 | 0.0 | 2.6 | 16.1 | 1.1 | 12.8 | 29.0 | 112.0 | 22.2 |
| MBC | 5.1 | 4.6 | 0.0 | 16.0 | 11.7 | 45.1 | 42.2 | 25.5 | – |
| Rankings based on | |||||||||
| GEBC | 1 | 2 | 3 | 8 | 5 | 7 | 6 | 4 | – |
| GBSG2 | 3 | 1 | 4 | 5 | 2 | 8 | 9 | 7 | 6 |
| JHS1 | 2 | 1 | 3 | 9 | 4 | 7 | 6 | 5 | 8 |
| JHS3 | 2 | 1 | 4 | 6 | 3 | 7 | 8 | 9 | 5 |
| JHS2 | 1 | 2 | 3 | 4 | 5 | 8 | 9 | 6 | 7 |
| PBC | 1 | 2 | 3 | 8 | 5 | 6 | 7 | 4 | 9 |
| REGARDS1 | 1 | 2 | 3 | 8 | 4 | 7 | 6 | 5 | 9 |
| REGARDS3 | 2 | 3 | 4 | 5 | 1 | 6 | 8 | 9 | 7 |
| REGARDS2 | 2 | 1 | 4 | 6 | 3 | 5 | 8 | 9 | 7 |
| MBC | 3 | 2 | 1 | 5 | 4 | 8 | 7 | 6 | – |
| Mean | 1.80 | 1.70 | 3.20 | 6.40 | 3.60 | 6.90 | 7.40 | 6.40 | 7.25 |
§
RSF = random survival forest; CIF = conditional inference forest; ORSF = oblique random survival forest; ORSFCV = oblique random survival forest with internal cross-validation (see Section 3.2).
†
GEBC = gene expression breast cancer; MBC = microarray breast cancer; GBSG2 = German breast cancer study group; PBC = primary biliary cirrhosis; JHS = Jackson heart study; REGARDS = REasons for Geographic And Racial Differences in Stroke.
‡
Apparent ties in concordance errors are a result of rounding errors.