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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
  1. *Defined as proportion of times the 95%-confidence interval for the estimator includes the true effect.