Table 4.
Simulation results (all the entries are multiplied by 100) under Setting 4. PL, the standard Cox regression with the partial likelihood; DEL and DEL-E, the double empirical likelihood method and its extension by Huang et al. (2016); ADEL, the proposed adaptive double empirical likelihood method.
| PC | Method | β 1 | β 2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bias | SD | SE | RMSE | CP | RE | Bias | SD | SE | RMSE | CP | RE | ||
| Sample Size=100 | |||||||||||||
| 0% | PL | −1.27 | 11.09 | 11.56 | 11.15 | 95.4 | – | 1.93 | 21.69 | 21.25 | 21.76 | 95.4 | – |
| DEL | 7.36 | 4.30 | 4.29 | 8.52 | 55.8 | 0.76 | −15.73 | 16.18 | 16.97 | 22.55 | 87.8 | 1.04 | |
| DEL-E | 6.81 | 4.50 | 4.42 | 8.16 | 59.8 | 0.73 | 0.30 | 20.72 | 20.98 | 20.70 | 96.4 | 0.95 | |
| ADEL | −1.68 | 10.79 | 10.82 | 10.91 | 92.2 | 0.98 | −3.27 | 19.48 | 20.43 | 19.73 | 95.8 | 0.91 | |
| 15% | PL | −1.53 | 12.28 | 12.43 | 12.36 | 95.2 | – | 1.17 | 26.29 | 23.05 | 26.29 | 92.0 | – |
| DEL | 7.84 | 4.34 | 4.23 | 8.95 | 51.8 | 0.72 | −16.65 | 18.64 | 18.17 | 24.98 | 85.2 | 0.95 | |
| DEL-E | 7.40 | 4.45 | 4.33 | 8.64 | 56.0 | 0.70 | −0.48 | 25.46 | 22.76 | 25.44 | 92.6 | 0.97 | |
| ADEL | −2.04 | 11.71 | 11.78 | 11.87 | 93.2 | 0.96 | −3.41 | 22.61 | 22.32 | 22.85 | 94.4 | 0.87 | |
| 30% | PL | −1.97 | 13.27 | 13.69 | 13.40 | 95.4 | – | 2.11 | 29.04 | 25.44 | 29.08 | 92.2 | – |
| DEL | 7.94 | 4.36 | 4.25 | 9.06 | 49.6 | 0.68 | −17.62 | 19.67 | 19.62 | 26.40 | 86.6 | 0.91 | |
| DEL-E | 7.55 | 4.47 | 4.35 | 8.77 | 54.0 | 0.65 | 0.37 | 28.00 | 25.11 | 27.98 | 92.4 | 0.96 | |
| ADEL | −2.39 | 12.44 | 13.11 | 12.66 | 95.0 | 0.94 | −2.92 | 23.70 | 24.63 | 23.85 | 95.6 | 0.82 | |
| Sample Size=200 | |||||||||||||
| 0% | PL | −0.18 | 8.15 | 8.00 | 8.15 | 95.4 | – | 0.44 | 15.17 | 14.78 | 15.16 | 95.2 | – |
| DEL | 7.62 | 3.04 | 3.01 | 8.20 | 30.2 | 1.01 | −15.91 | 11.44 | 11.90 | 19.60 | 73.0 | 1.29 | |
| DEL-E | 7.13 | 3.12 | 3.09 | 7.78 | 37.2 | 0.95 | −1.05 | 14.57 | 14.65 | 14.60 | 96.0 | 0.96 | |
| ADEL | −0.95 | 8.12 | 7.82 | 8.17 | 92.0 | 1.00 | −4.12 | 13.78 | 14.48 | 14.37 | 94.8 | 0.95 | |
| 15% | PL | −1.10 | 8.87 | 8.66 | 8.92 | 95.0 | – | −0.76 | 15.84 | 15.99 | 15.84 | 94.2 | – |
| DEL | 7.74 | 3.04 | 3.04 | 8.31 | 28.4 | 0.93 | −16.52 | 11.54 | 12.75 | 20.15 | 78.6 | 1.27 | |
| DEL-E | 7.35 | 3.10 | 3.10 | 7.97 | 33.2 | 0.89 | −2.25 | 15.29 | 15.86 | 15.44 | 95.2 | 0.97 | |
| ADEL | −1.71 | 8.77 | 8.42 | 8.93 | 91.8 | 1.00 | −4.88 | 14.15 | 15.57 | 14.95 | 94.4 | 0.94 | |
| 30% | PL | −1.12 | 9.60 | 9.49 | 9.66 | 95.4 | – | −0.71 | 18.11 | 17.59 | 18.11 | 93.6 | – |
| DEL | 7.88 | 3.09 | 3.06 | 8.46 | 26.2 | 0.88 | −17.70 | 13.14 | 13.76 | 22.04 | 78.4 | 1.22 | |
| DEL-E | 7.53 | 3.14 | 3.12 | 8.15 | 30.2 | 0.84 | −2.18 | 17.51 | 17.45 | 17.63 | 94.8 | 0.97 | |
| ADEL | −1.79 | 9.37 | 9.20 | 9.53 | 92.6 | 0.99 | −4.92 | 16.08 | 17.12 | 16.80 | 94.6 | 0.93 | |