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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
  1. Ln: natural logarithm; WHR: Weighted all-cause hazard ratio; sd: Standard deviation;
  2. *It is assumed that the Weibull model used to estimate the cause-specific hazards is the correct one;
  3. #It is assumed that the cause-specific baseline hazards are equal.