Table 1.
Simulation results (all the entries are multiplied by 100) under Setting 1. 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 | β2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | −0.68 | 4.92 | 4.90 | 4.96 | 95.4 | 0.44 | −0.76 | 17.62 | 17.48 | 17.62 | 94.8 | 0.81 | |
| DEL-E | −0.80 | 5.02 | 4.96 | 5.08 | 95.0 | 0.46 | 1.61 | 21.07 | 21.02 | 21.11 | 95.4 | 0.97 | |
| ADEL | −1.29 | 9.65 | 8.73 | 9.73 | 95.0 | 0.87 | 0.72 | 18.96 | 18.91 | 18.96 | 94.6 | 0.87 | |
| 15% | PL | −1.53 | 12.28 | 12.43 | 12.36 | 95.2 | – | 1.17 | 26.29 | 23.05 | 26.29 | 92.0 | – |
| DEL | −0.31 | 5.03 | 4.87 | 5.04 | 95.2 | 0.41 | −0.95 | 20.33 | 18.72 | 20.33 | 92.4 | 0.77 | |
| DEL-E | −0.38 | 5.07 | 4.91 | 5.08 | 95.2 | 0.41 | 0.72 | 25.95 | 22.80 | 25.93 | 92.0 | 0.99 | |
| ADEL | −1.65 | 10.68 | 9.67 | 10.80 | 96.6 | 0.87 | 0.33 | 22.42 | 20.55 | 22.40 | 93.0 | 0.85 | |
| 30% | PL | −1.97 | 13.27 | 13.68 | 13.40 | 95.4 | – | 2.11 | 29.04 | 25.44 | 29.08 | 92.2 | – |
| DEL | −0.32 | 5.09 | 4.94 | 5.10 | 95.0 | 0.38 | −0.80 | 21.44 | 20.20 | 21.43 | 92.8 | 0.74 | |
| DEL-E | −0.41 | 5.14 | 4.98 | 5.15 | 95.6 | 0.38 | 1.51 | 28.67 | 25.15 | 28.68 | 91.8 | 0.99 | |
| ADEL | −2.04 | 11.34 | 10.90 | 11.51 | 96.6 | 0.86 | 0.84 | 23.35 | 22.81 | 23.34 | 93.8 | 0.80 | |
| 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 | −0.35 | 3.48 | 3.44 | 3.49 | 94.4 | 0.43 | −1.09 | 12.50 | 12.26 | 12.54 | 95.2 | 0.83 | |
| DEL-E | −0.42 | 3.51 | 3.47 | 3.53 | 94.0 | 0.43 | 0.23 | 14.92 | 14.68 | 14.91 | 94.6 | 0.98 | |
| ADEL | −0.44 | 7.19 | 6.29 | 7.20 | 93.8 | 0.88 | −0.28 | 13.52 | 13.06 | 13.51 | 94.8 | 0.89 | |
| 15% | PL | −1.10 | 8.87 | 8.66 | 8.92 | 95.0 | – | −0.76 | 15.84 | 15.99 | 15.84 | 94.2 | – |
| DEL | −0.39 | 3.53 | 3.51 | 3.55 | 95.0 | 0.40 | −1.05 | 12.59 | 13.14 | 12.62 | 95.2 | 0.80 | |
| DEL-E | −0.39 | 3.53 | 3.52 | 3.55 | 94.8 | 0.40 | −1.17 | 15.62 | 15.88 | 15.65 | 95.0 | 0.99 | |
| ADEL | −1.17 | 7.98 | 6.89 | 8.05 | 94.2 | 0.90 | −0.54 | 13.85 | 14.14 | 13.85 | 95.0 | 0.87 | |
| 30% | PL | −1.12 | 9.60 | 9.49 | 9.66 | 95.4 | – | −0.71 | 18.11 | 17.59 | 18.11 | 93.6 | – |
| DEL | −0.37 | 3.60 | 3.56 | 3.61 | 95.8 | 0.37 | −1.22 | 14.25 | 14.17 | 14.28 | 94.4 | 0.79 | |
| DEL-E | −0.38 | 3.61 | 3.57 | 3.62 | 95.4 | 0.37 | −1.17 | 17.86 | 17.47 | 17.88 | 93.4 | 0.99 | |
| ADEL | −1.09 | 8.73 | 7.10 | 8.80 | 94.6 | 0.91 | −0.65 | 15.91 | 15.50 | 15.91 | 94.8 | 0.88 | |