Table 3 Simulation results: Performance
From: Introducing a new estimator and test for the weighted all-cause hazard ratio
Sc. | Amount of Simulations | Bias | Standardized Bias | \(\sqrt {\text {Mean Square Error}}\) | Relative Efficiency | Coverage ∗ | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | \(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | \(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | \(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | \(\frac {MSE\left (ln(\hat {\theta }^{w}_{CE}(\tau))\right)}{MSE\left (ln(\tilde {\theta }^{w}_{CE}(\tau))\right)}\) | \(ln(\hat {\theta }^{w}_{CE}(\tau))\) | \(ln(\tilde {\theta }^{w}_{CE}(\tau))\) | |
1a | 991 | 1000 | -0.01 | 0.03 | -0.05 | 0.11 | 0.27 | 0.29 | 0.91 | 93.14 | 92.70 |
1b | 997 | 1000 | -0.01 | 0.07 | -0.04 | 0.30 | 0.20 | 0.23 | 0.76 | 94.68 | 93.10 |
1c | 997 | 1000 | -0.02 | 0.04 | -0.07 | 0.19 | 0.23 | 0.22 | 1.12 | 95.29 | 94.80 |
2a | 1000 | 1000 | -0.15 | -0.14 | -0.51 | -0.49 | 0.32 | 0.32 | 1.02 | 90.60 | 91.00 |
2b | 999 | 1000 | -0.15 | -0.15 | -0.63 | -0.63 | 0.28 | 0.28 | 1.02 | 89.09 | 88.80 |
3a | 1000 | 1000 | -0.02 | -0.12 | -0.07 | -0.37 | 0.30 | 0.33 | 0.79 | 93.50 | 91.40 |
3b | 1000 | 1000 | -0.00 | -0.04 | -0.01 | -0.15 | 0.30 | 0.29 | 1.06 | 94.20 | 95.20 |
3c | 1000 | 1000 | 0.00 | -0.12 | 0.02 | -0.58 | 0.20 | 0.24 | 0.68 | 93.10 | 88.70 |
4a | 993 | 1000 | 0.17 | 0.16 | 0.26 | 0.39 | 0.66 | 0.31 | 4.57 | 90.07 | 89.53 |
4b | 993 | 1000 | 0.20 | 0.09 | 0.21 | 0.21 | 0.98 | 0.46 | 4.85 | 94.44 | 95.47 |
4c | 996 | 1000 | 0.19 | 0.18 | 0.93 | 0.84 | 0.29 | 0.28 | 1.03 | 82.90 | 84.87 |
4d | 996 | 1000 | 0.24 | 0.21 | 0.60 | 0.65 | 0.46 | 0.39 | 1.43 | 90.14 | 89.48 |
5a | 995 | 1000 | -0.26 | -0.25 | -0.91 | -1.46 | 0.38 | 0.31 | 1.55 | 71.80 | 68.07 |
5b | 995 | 1000 | -0.01 | -0.11 | -0.01 | -0.35 | 0.57 | 0.32 | 3.21 | 93.56 | 93.99 |
6a | 998 | 998 | 0.00 | 0.00 | 0.01 | 0.01 | 0.21 | 0.23 | 0.86 | 94.79 | 94.60 |
6b | 998 | 998 | -0.00 | -0.00 | -0.01 | -0.01 | 0.25 | 0.24 | 1.11 | 95.69 | 95.90 |
7a | 984 | 1000 | 0.01 | 0.02 | 0.04 | 0.07 | 0.30 | 0.28 | 1.16 | 94.60 | 95.20 |
7b | 984 | 1000 | 0.01 | 0.01 | 0.04 | 0.03 | 0.16 | 0.17 | 0.99 | 94.70 | 94.99 |
8a | 1000 | 1000 | -0.14 | 0.00 | -0.64 | 0.01 | 0.25 | 0.19 | 1.78 | 89.20 | 93.70 |
8b | 1000 | 1000 | -0.17 | -0.01 | -0.70 | -0.05 | 0.30 | 0.21 | 1.97 | 85.00 | 93.30 |
9a | 998 | 998 | -0.22 | -0.05 | -0.53 | -0.18 | 0.47 | 0.32 | 2.22 | 90.68 | 96.09 |
9b | 990 | 1000 | -0.15 | -0.01 | -0.81 | -0.04 | 0.23 | 0.15 | 2.29 | 86.97 | 94.20 |
9c | 990 | 1000 | -0.60 | -0.18 | -1.25 | -0.59 | 0.77 | 0.35 | 4.74 | 62.93 | 87.10 |
10a | 1000 | 1000 | 0.06 | 0.04 | 0.28 | 0.21 | 0.21 | 0.21 | 1.00 | 93.70 | 93.80 |
10b | 1000 | 1000 | -0.09 | -0.10 | -0.38 | -0.44 | 0.24 | 0.25 | 0.94 | 92.70 | 92.10 |
10c | 1000 | 1000 | 0.17 | 0.11 | 0.99 | 0.60 | 0.24 | 0.22 | 1.27 | 83.80 | 89.30 |
10d | 1000 | 1000 | -0.16 | -0.23 | -0.81 | -1.10 | 0.25 | 0.32 | 0.63 | 87.20 | 75.90 |