Table 2 Simulation results
From: Introducing a new estimator and test for the weighted all-cause hazard ratio
Sc. | Assumptions for | Assumptions for | τ | Weights | Ln of | Mean number | Mean of estimated | Power for | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
original parametric | new non-parametric | True | of events (sd) | Ln(WHR) (sd) | permutation | weight-based | ||||||
estimator* | estimator# | WHR | test | log-rank test | ||||||||
\(w_{EP_{1}}\) | \(w_{EP_{2}}\) | \(ln(\theta _{CE}^{w}(\tau))\) | E P 1 | E P 2 | \(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | \(\hat {\theta }^{w}_{CE}(\tau)\) | \(\tilde {\theta }^{w}_{CE}(\tau)\) | ||||
1a | \(\checkmark \) | ✗ | 1 | 1 | 0.1 | -0.60 | 50.21 (6.51) | 35.16 (5.21) | -0.61 (0.27) | -0.57 (0.28) | 0.66 | 0.72 |
1b | 2 | 1 | 0.1 | -0.67 | 72.60 (6.74) | 80.13 (6.73) | -0.67 (0.20) | -0.60 (0.24) | 0.94 | 0.90 | ||
1c | 2 | 0.1 | 1 | -1.18 | -1.20 (0.22) | -1.14 (0.21) | 1.00 | 1.00 | ||||
2a | ✗ | ✗ | 1 | 1 | 0.1 | -0.44 | 48.22 (6.08) | 37.15 (5.33) | -0.59 (0.29) | -0.58 (0.29) | 0.58 | 0.75 |
2b | 2 | 1 | 0.1 | -0.38 | 67.79 (6.75) | 51.93 (5.60) | -0.54 (0.23) | -0.53 (0.23) | 0.64 | 0.81 | ||
3a | \(\checkmark \) | ✗ | 1 | 1 | 0.1 | -0.88 | 39.97 (5.63) | 47.94 (5.87) | -0.90 (0.29) | -1.00 (0.31) | 0.90 | 0.96 |
3b | 1 | 0.1 | 1 | 0.43 | 0.42 (0.29) | 0.38 (0.28) | 0.00 | 0.00 | ||||
3c | 2 | 1 | 0.1 | -0.68 | 69.84 (6.39) | 124.63 (6.40) | -0.67 (0.20) | -0.80 (0.21) | 0.96 | 1.00 | ||
4a | ✗ | ✗ | 1 | 1 | 0.1 | -0.39 | 62.84 (6.39) | 6.49 (2.50) | -0.22 (0.64) | -0.23 (0.26) | 0.14 | 0.29 |
4b | 1 | 0.1 | 1 | -0.08 | 0.12 (0.96) | 0.01 (0.44) | 0.02 | 0.05 | ||||
4c | 2 | 1 | 0.1 | -0.46 | 86.66 (6.95) | 24.29 (4.57) | -0.27 (0.21) | -0.28 (0.21) | 0.27 | 0.44 | ||
4d | 2 | 0.1 | 1 | -0.36 | -0.12 (0.40) | -0.15 (0.32) | 0.05 | 0.17 | ||||
5a | ✗ | ✗ | 1 | 1 | 0.1 | -0.56 | 133.27 (6.26) | 19.31 (4.05) | -0.82 (0.28) | -0.82 (0.17) | 1.00 | 1.00 |
5b | 1 | 0.1 | 1 | -0.03 | -0.04 (0.57) | -0.14 (0.30) | 0.03 | 0.34 | ||||
6a | \(\checkmark \) | ✗ | 2 | 1 | 0.1 | 0.00 | 67.04 (6.74) | 56.49 (6.37) | 0.00 (0.21) | 0.00 (0.23) | 0.02 | 0.08 |
6b | 2 | 0.1 | 1 | 0.00 | -0.00 (0.25) | -0.00 (0.24) | 0.02 | 0.06 | ||||
7a | \(\checkmark \) | \(\checkmark \) | 2 | 1 | 0.1 | 0.00 | 15.83 (3.84) | 141.89 (6.18) | 0.01 (0.30) | 0.02 (0.28) | 0.02 | 0.02 |
7b | 2 | 0.1 | 1 | 0.68 | 0.68 (0.16) | 0.68 (0.17) | 0.00 | 0.00 | ||||
8a | ✗ | \(\checkmark \) | 2 | 1 | 0.1 | -0.56 | 108.25 (6.93) | 78.79 (6.69) | -0.69 (0.21) | -0.56 (0.19) | 0.92 | 0.96 |
8b | 2 | 0.1 | 1 | -1.12 | -1.29 (0.24) | -1.13 (0.21) | 1.00 | 1.00 | ||||
9a | ✗ | ✗ | 1 | 0.1 | 1 | -0.88 | 132.78 (6.43) | 15.22 (3.56) | -1.10 (0.42) | -0.93 (0.31) | 0.77 | 0.97 |
9b | 2 | 1 | 0.1 | -0.51 | 178.24 (4.21) | 21.76 (4.21) | -0.66 (0.18) | -0.52 (0.15) | 0.96 | 0.97 | ||
9c | 2 | 0.1 | 1 | -0.71 | -1.31 (0.48) | -0.89 (0.30) | 0.90 | 0.99 | ||||
10a | ✗ | ✗ | 1 | 1 | 0.1 | -0.64 | 84.95 (7.02) | 62.44 (6.34) | -0.58 (0.21) | -0.59 (0.21) | 0.81 | 0.94 |
10b | 1 | 0.1 | 1 | -0.95 | -1.04 (0.23) | -1.05 (0.23) | 1.00 | 1.00 | ||||
10c | 2 | 1 | 0.1 | -0.72 | 113.64 (6.92) | 80.58 (6.55) | -0.55 (0.17) | -0.61 (0.18) | 0.89 | 0.98 | ||
10d | 2 | 0.1 | 1 | -0.79 | -0.95 (0.19) | -1.03 (0.21) | 1.00 | 1.00 | ||||