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. 2022 May 26;24(3):811–831. doi: 10.1093/biostatistics/kxac009

Table 3.

Bias, percentage bias, and coverage of estimates of log(Inline graphiclog(S(t))) when Inline graphic and Inline graphic

Time Model Scenario 1 Scenario 2 Scenario 3 Scenario 4
Bias Inline graphic Bias Cov. Inline graphic Conv. Bias Inline graphic Bias Cov. Inline graphic Conv. Bias Inline graphic Bias Cov. Inline graphic Conv. Bias Inline graphic Bias Cov. Inline graphic Conv.
1 Weibull 0.218 Inline graphic 9.5 19.6 1000 Inline graphic 0.020 . 92.2 1000 0.136 Inline graphic 13.0 36.2 1000 Inline graphic 0.009 0.4 95.2 1000
2 Weibull Inline graphic 0.154 39.8 15.7 1000 Inline graphic 0.134 Inline graphic 21.1 18.4 1000 0.185 Inline graphic 36.0 4.5 1000 Inline graphic 0.006 0.4 95.8 1000
3 Weibull Inline graphic 0.224 Inline graphic 38.2 1.4 1000 Inline graphic 0.065 Inline graphic 7.4 70.7 1000 0.106 Inline graphic 110.5 40.2 1000 Inline graphic 0.004 0.4 96.2 1000
4 Weibull 0.082 8.9 57.8 1000 0.035 3.5 86.7 1000 Inline graphic 0.019 Inline graphic 7.1 95.7 1000 Inline graphic 0.003 0.5 96.4 1000
5 Weibull 0.427 39.8 0.0 1000 0.118 11.0 39.1 1000 Inline graphic 0.104 Inline graphic 19.2 47.6 1000 Inline graphic 0.002 0.5 96.1 1000
1 Gamma 0.063 Inline graphic 2.7 87.3 1000 Inline graphic 0.056 . 79.9 1000 0.007 Inline graphic 0.7 87.7 929 Inline graphic 0.006 0.3 95.3 1000
2 Gamma Inline graphic 0.027 7.0 94.0 1000 Inline graphic 0.146 Inline graphic 22.9 14.6 1000 0.048 Inline graphic 9.3 77.2 929 Inline graphic 0.007 0.5 94.4 1000
3 Gamma Inline graphic 0.143 Inline graphic 24.4 14.4 1000 Inline graphic 0.051 Inline graphic 5.8 77.7 1000 0.018 Inline graphic 18.8 86.0 929 Inline graphic 0.007 0.7 93.9 1000
4 Gamma 0.056 6.1 72.4 1000 0.074 7.5 68.1 1000 Inline graphic 0.024 Inline graphic 8.9 83.2 929 Inline graphic 0.006 0.9 95.2 1000
5 Gamma 0.283 26.4 0.1 1000 0.180 16.7 16.1 1000 0.005 0.9 88.4 929 Inline graphic 0.002 0.5 96.1 1000
1 GenF 0.006 Inline graphic 0.3 92.9 990 0.001 . 67.4 707 0.007 Inline graphic 0.7 25.7 295 Inline graphic 0.006 0.3 69.4 779
2 GenF 0.004 Inline graphic 1.0 95.6 997 Inline graphic 0.018 Inline graphic 2.8 66.7 713 0.049 Inline graphic 9.5 31.3 380 0.000 0.0 71.0 801
3 GenF Inline graphic 0.037 Inline graphic 6.3 85.1 997 Inline graphic 0.003 Inline graphic 0.3 67.4 713 0.042 Inline graphic 43.8 52.1 628 0.005 Inline graphic 0.5 73.9 841
4 GenF 0.026 2.8 88.3 997 0.028 2.8 63.9 713 0.056 20.8 54.6 868 0.011 Inline graphic 1.7 75.2 873
5 GenF 0.103 9.6 48.7 997 0.043 4.0 60.5 713 0.055 10.2 55.9 907 0.000 0.0 76.2 874
1 FPAFT-df=2 0.032 Inline graphic 1.4 87.3 1000 Inline graphic 0.073 . 67.5 1000 0.041 Inline graphic 3.9 88.6 1000 Inline graphic 0.009 0.4 94.5 1000
2 FPAFT-df=2 0.050 Inline graphic 12.9 85.6 1000 Inline graphic 0.140 Inline graphic 22.0 17.4 1000 0.128 Inline graphic 24.9 29.7 1000 Inline graphic 0.003 0.2 95.7 1000
3 FPAFT-df=2 Inline graphic 0.104 Inline graphic 17.7 37.0 1000 Inline graphic 0.036 Inline graphic 4.1 83.1 1000 0.091 Inline graphic 94.9 52.7 1000 Inline graphic 0.002 0.2 96.4 1000
4 FPAFT-df=2 0.028 3.0 85.1 1000 0.091 9.2 57.1 1000 0.001 0.4 96.3 1000 Inline graphic 0.002 0.3 96.7 1000
5 FPAFT-df=2 0.209 19.5 12.7 1000 0.195 18.1 9.2 1000 Inline graphic 0.055 Inline graphic 10.2 83.3 1000 Inline graphic 0.002 0.5 96.0 1000
1 FPAFT-df=3 0.013 Inline graphic 0.6 95.0 1000 0.049 . 85.5 1000 Inline graphic 0.001 0.1 96.6 1000 Inline graphic 0.007 0.3 94.6 1000
2 FPAFT-df=3 Inline graphic 0.005 1.3 94.1 1000 Inline graphic 0.058 Inline graphic 9.1 78.9 1000 0.002 Inline graphic 0.4 94.1 1000 Inline graphic 0.003 0.2 95.5 1000
3 FPAFT-df=3 Inline graphic 0.000 0.0 95.0 1000 Inline graphic 0.026 Inline graphic 3.0 90.1 1000 Inline graphic 0.001 1.0 93.3 1000 Inline graphic 0.003 0.3 96.1 1000
4 FPAFT-df=3 0.011 1.2 93.9 1000 0.037 3.7 86.6 1000 Inline graphic 0.012 Inline graphic 4.5 92.9 1000 Inline graphic 0.003 0.5 95.8 1000
5 FPAFTdf=3 0.007 0.7 94.3 1000 0.090 8.4 65.5 1000 0.007 1.3 94.1 1000 Inline graphic 0.002 0.5 95.9 1000
1 FPAFT-df=4 0.002 Inline graphic 0.1 95.7 1000 Inline graphic 0.006 . 91.8 1000 Inline graphic 0.010 1.0 95.1 1000 Inline graphic 0.006 0.3 95.0 1000
2 FPAFT-df=4 0.001 Inline graphic 0.3 95.7 1000 Inline graphic 0.003 Inline graphic 0.5 93.8 1000 0.008 Inline graphic 1.6 95.4 1000 Inline graphic 0.003 0.2 95.6 1000
3 FPAFT-df=4 Inline graphic 0.005 Inline graphic 0.9 94.6 1000 Inline graphic 0.006 Inline graphic 0.7 95.0 1000 Inline graphic 0.001 1.0 95.6 1000 Inline graphic 0.004 0.4 96.1 1000
4 FPAFT-df=4 0.020 2.2 91.6 1000 0.004 0.4 94.2 1000 Inline graphic 0.015 Inline graphic 5.6 93.6 1000 Inline graphic 0.003 0.5 95.4 1000
5 FPAFT-df=4 0.010 0.9 94.4 1000 0.008 0.7 94.3 1000 0.008 1.5 94.4 1000 Inline graphic 0.003 0.8 96.1 1000
1 FPAFT-df=5 0.004 Inline graphic 0.2 95.4 1000 Inline graphic 0.002 . 94.7 1000 0.001 Inline graphic 0.1 95.6 1000 Inline graphic 0.007 0.3 94.9 1000
2 FPAFT-df=5 Inline graphic 0.001 0.3 95.5 1000 Inline graphic 0.001 Inline graphic 0.2 93.9 1000 0.000 0.0 95.0 1000 Inline graphic 0.005 0.3 95.0 1000
3 FPAFT-df=5 Inline graphic 0.003 Inline graphic 0.5 95.5 1000 Inline graphic 0.002 Inline graphic 0.2 94.4 1000 0.007 Inline graphic 7.3 94.8 1000 Inline graphic 0.005 0.5 94.5 1000
4 FPAFT-df=5 0.017 1.8 93.2 1000 0.004 0.4 94.4 1000 Inline graphic 0.006 Inline graphic 2.2 94.2 1000 Inline graphic 0.005 0.8 94.0 1000
5 FPAFT-df=5 0.009 0.8 94.6 1000 0.005 0.5 94.1 1000 0.004 0.7 94.9 1000 Inline graphic 0.004 1.1 95.2 1000
1 FPAFT-df=6 Inline graphic 0.005 0.2 94.6 1000 Inline graphic 0.001 . 95.0 1000 Inline graphic 0.001 0.1 96.0 1000 Inline graphic 0.007 0.3 94.7 1000
2 FPAFT-df=6 0.000 0.0 95.1 1000 Inline graphic 0.002 Inline graphic 0.3 94.4 1000 0.001 Inline graphic 0.2 94.7 1000 Inline graphic 0.005 0.3 93.9 1000
3 FPAFT-df=6 0.002 0.3 95.1 1000 0.001 0.1 95.1 1000 0.004 Inline graphic 4.2 94.6 1000 Inline graphic 0.005 0.5 93.4 1000
4 FPAFT-df=6 0.007 0.8 93.6 1000 0.005 0.5 94.6 1000 Inline graphic 0.001 Inline graphic 0.4 94.2 1000 Inline graphic 0.005 0.8 93.6 1000
5 FPAFT-df=6 0.005 0.5 94.1 1000 0.001 0.1 94.0 1000 0.003 0.6 94.8 1000 Inline graphic 0.004 1.1 95.4 1000
1 FPAFT-df=7 Inline graphic 0.008 0.3 93.9 1000 Inline graphic 0.002 . 93.6 1000 Inline graphic 0.003 0.3 95.6 1000 Inline graphic 0.007 0.3 93.5 1000
2 FPAFT-df=7 Inline graphic 0.001 0.3 95.4 1000 Inline graphic 0.002 Inline graphic 0.3 93.7 1000 Inline graphic 0.000 0.0 94.6 1000 Inline graphic 0.006 0.4 92.1 1000
3 FPAFT-df=7 0.003 0.5 95.1 1000 0.002 0.2 94.2 1000 0.000 0.0 93.8 1000 Inline graphic 0.006 0.6 92.9 1000
4 FPAFT-df=7 0.002 0.2 93.4 1000 0.006 0.6 94.8 1000 0.001 0.4 94.0 1000 Inline graphic 0.006 0.9 93.1 1000
5 FPAFT-df=7 0.003 0.3 94.3 1000 0.001 0.1 94.3 1000 0.002 0.4 94.6 1000 Inline graphic 0.005 1.3 93.9 1000
1 FPAFT-df=8 Inline graphic 0.010 0.4 93.9 1000 Inline graphic 0.001 . 94.3 1000 Inline graphic 0.002 0.2 95.7 1000 Inline graphic 0.009 0.4 92.9 1000
2 FPAFT-df=8 Inline graphic 0.002 0.5 94.4 1000 Inline graphic 0.002 Inline graphic 0.3 93.0 1000 Inline graphic 0.000 0.0 94.2 1000 Inline graphic 0.007 0.5 91.0 1000
3 FPAFT-df=8 0.002 0.3 94.6 1000 0.002 0.2 94.2 1000 Inline graphic 0.001 1.0 93.6 1000 Inline graphic 0.008 0.8 91.1 1000
4 FPAFT-df=8 0.001 0.1 92.6 1000 0.006 0.6 94.8 1000 0.003 1.1 93.8 1000 Inline graphic 0.008 1.3 91.3 1000
5 FPAFT-df=8 0.004 0.4 94.1 1000 0.002 0.2 93.9 1000 0.002 0.4 94.4 1000 Inline graphic 0.006 1.6 93.8 1000
1 FPAFT-df=9 Inline graphic 0.011 0.5 94.3 1000 Inline graphic 0.001 . 92.3 1000 Inline graphic 0.003 0.3 95.6 1000 Inline graphic 0.012 0.5 91.7 1000
2 FPAFT-df=9 Inline graphic 0.002 0.5 93.9 1000 Inline graphic 0.001 Inline graphic 0.2 93.5 1000 Inline graphic 0.001 0.2 94.2 1000 Inline graphic 0.010 0.7 89.8 1000
3 FPAFT-df=9 0.001 0.2 94.1 1000 0.002 0.2 94.2 1000 Inline graphic 0.001 1.0 93.3 1000 Inline graphic 0.010 1.0 90.7 1000
4 FPAFT-df=9 0.001 0.1 93.4 1000 0.006 0.6 95.2 1000 0.003 1.1 93.5 1000 Inline graphic 0.010 1.6 89.3 1000
5 FPAFT-df=9 0.004 0.4 94.4 1000 0.002 0.2 93.9 1000 0.002 0.4 94.3 1000 Inline graphic 0.008 2.2 91.9 1000