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

Table 4.

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 0.586 Inline graphic 25.4 0.0 1000 Inline graphic 0.007 . 94.6 1000 0.092 Inline graphic 8.8 59.8 1000 Inline graphic 0.008 0.3 94.7 1000
2 Weibull Inline graphic 0.018 4.6 92.6 1000 Inline graphic 0.142 Inline graphic 22.3 13.6 1000 0.167 Inline graphic 32.5 9.0 1000 Inline graphic 0.006 0.4 96.3 1000
3 Weibull Inline graphic 0.224 Inline graphic 38.2 0.7 1000 Inline graphic 0.086 Inline graphic 9.8 55.4 1000 0.103 Inline graphic 107.4 42.3 1000 Inline graphic 0.004 0.4 96.3 1000
4 Weibull Inline graphic 0.015 Inline graphic 1.6 87.4 1000 0.005 0.5 92.7 1000 Inline graphic 0.010 Inline graphic 3.7 96.3 1000 Inline graphic 0.003 0.5 96.4 1000
5 Weibull 0.256 23.9 1.1 1000 0.081 7.5 63.9 1000 Inline graphic 0.086 Inline graphic 15.9 62.9 1000 Inline graphic 0.002 0.5 96.4 1000
1 Gamma 0.187 Inline graphic 8.1 45.5 1000 Inline graphic 0.013 . 94.5 1000 0.064 Inline graphic 6.1 75.7 1000 Inline graphic 0.009 0.4 94.6 1000
2 Gamma 0.031 Inline graphic 8.0 92.1 1000 Inline graphic 0.143 Inline graphic 22.5 13.4 1000 0.119 Inline graphic 23.1 28.7 1000 Inline graphic 0.005 0.3 96.1 1000
3 Gamma Inline graphic 0.169 Inline graphic 28.8 2.8 1000 Inline graphic 0.081 Inline graphic 9.3 59.9 1000 0.077 Inline graphic 80.3 63.0 1000 Inline graphic 0.003 0.3 95.7 1000
4 Gamma Inline graphic 0.039 Inline graphic 4.2 82.9 1000 0.016 1.6 91.1 1000 0.000 0.0 95.8 1000 Inline graphic 0.003 0.5 95.9 1000
5 Gamma 0.132 12.3 23.4 1000 0.097 9.0 57.6 1000 Inline graphic 0.032 Inline graphic 5.9 91.2 1000 Inline graphic 0.002 0.5 96.3 1000
1 GenF 0.007 Inline graphic 0.3 92.4 984 0.000 . 65.9 686 Inline graphic 0.004 0.4 18.8 196 Inline graphic 0.022 1.0 81.5 914
2 GenF 0.004 Inline graphic 1.0 95.1 993 Inline graphic 0.025 Inline graphic 3.9 63.9 692 0.046 Inline graphic 8.9 25.2 293 Inline graphic 0.016 1.1 82.4 915
3 GenF Inline graphic 0.052 Inline graphic 8.9 76.3 993 Inline graphic 0.013 Inline graphic 1.5 65.0 692 0.027 Inline graphic 28.2 33.8 365 Inline graphic 0.010 1.0 82.4 915
4 GenF Inline graphic 0.002 Inline graphic 0.2 93.0 993 0.015 1.5 63.8 692 Inline graphic 0.002 Inline graphic 0.7 38.8 404 Inline graphic 0.004 0.6 81.9 915
5 GenF 0.069 6.4 64.5 993 0.030 2.8 60.4 692 Inline graphic 0.016 Inline graphic 3.0 38.4 406 0.000 0.0 82.3 922
1 FPAFT-df=2 0.171 Inline graphic 7.4 54.0 1000 Inline graphic 0.039 . 87.3 1000 0.021 Inline graphic 2.0 92.8 1000 Inline graphic 0.012 0.5 95.2 1000
2 FPAFT-df=2 0.131 Inline graphic 33.8 26.0 1000 Inline graphic 0.147 Inline graphic 23.1 12.9 1000 0.121 Inline graphic 23.5 32.2 1000 Inline graphic 0.005 0.3 96.3 1000
3 FPAFT-df=2 Inline graphic 0.125 Inline graphic 21.3 17.5 1000 Inline graphic 0.070 Inline graphic 8.0 67.8 1000 0.090 Inline graphic 93.8 52.6 1000 Inline graphic 0.003 0.3 96.1 1000
4 FPAFT-df=2 Inline graphic 0.045 Inline graphic 4.9 78.6 1000 0.037 3.7 86.5 1000 0.004 1.5 96.2 1000 Inline graphic 0.002 0.3 96.4 1000
5 FPAFT-df=2 0.101 9.4 45.7 1000 0.125 11.6 37.6 1000 Inline graphic 0.049 Inline graphic 9.1 85.7 1000 Inline graphic 0.002 0.5 96.4 1000
1 FPAFT-df=3 Inline graphic 0.104 4.5 85.1 1000 0.066 . 73.0 1000 0.031 Inline graphic 3.0 93.2 1000 Inline graphic 0.009 0.4 94.2 1000
2 FPAFT-df=3 0.140 Inline graphic 36.2 22.0 1000 Inline graphic 0.079 Inline graphic 12.4 60.6 1000 0.046 Inline graphic 8.9 84.7 1000 Inline graphic 0.004 0.3 96.3 1000
3 FPAFT-df=3 Inline graphic 0.050 Inline graphic 8.5 81.5 1000 Inline graphic 0.052 Inline graphic 6.0 78.5 1000 0.030 Inline graphic 31.3 90.5 1000 Inline graphic 0.004 0.4 95.8 1000
4 FPAFT-df=3 Inline graphic 0.032 Inline graphic 3.5 87.8 1000 0.013 1.3 91.9 1000 Inline graphic 0.019 Inline graphic 7.1 93.4 1000 Inline graphic 0.003 0.5 95.9 1000
5 FPAFT-df=3 0.039 3.6 84.3 1000 0.068 6.3 73.9 1000 Inline graphic 0.037 Inline graphic 6.8 88.9 1000 Inline graphic 0.002 0.5 96.3 1000
1 FPAFT-df=4 0.005 Inline graphic 0.2 94.5 1000 0.072 . 64.2 1000 0.013 Inline graphic 1.2 94.5 1000 Inline graphic 0.007 0.3 94.3 1000
2 FPAFT-df=4 0.074 Inline graphic 19.1 67.0 1000 Inline graphic 0.017 Inline graphic 2.7 93.6 1000 0.054 Inline graphic 10.5 82.1 1000 Inline graphic 0.006 0.4 96.2 1000
3 FPAFT-df=4 Inline graphic 0.022 Inline graphic 3.8 92.8 1000 Inline graphic 0.024 Inline graphic 2.7 91.4 1000 0.041 Inline graphic 42.8 88.3 1000 Inline graphic 0.004 0.4 95.9 1000
4 FPAFT-df=4 0.017 Inline graphic 1.8 93.9 1000 Inline graphic 0.000 0.0 94.6 1000 Inline graphic 0.011 Inline graphic 4.1 94.7 1000 Inline graphic 0.003 0.5 95.3 1000
5 FPAFT-df=4 0.026 2.4 89.7 1000 0.019 1.8 90.7 1000 Inline graphic 0.033 Inline graphic 6.1 90.2 1000 Inline graphic 0.002 0.5 96.3 1000
1 FPAFT-df=5 0.004 Inline graphic 0.2 94.4 1000 0.044 . 82.2 1000 0.024 Inline graphic 2.3 94.0 1000 Inline graphic 0.007 0.3 94.6 1000
2 FPAFT-df=5 0.023 Inline graphic 5.9 90.4 1000 Inline graphic 0.007 Inline graphic 1.1 94.2 1000 0.037 Inline graphic 7.2 88.0 1000 Inline graphic 0.006 0.4 95.7 1000
3 FPAFT-df=5 Inline graphic 0.012 Inline graphic 2.0 94.3 1000 Inline graphic 0.017 Inline graphic 1.9 93.0 1000 0.059 Inline graphic 61.5 80.2 1000 Inline graphic 0.005 0.5 95.4 1000
4 FPAFT-df=5 Inline graphic 0.006 Inline graphic 0.7 94.9 1000 Inline graphic 0.000 0.0 94.9 1000 0.008 3.0 93.6 1000 Inline graphic 0.004 0.6 94.9 1000
5 FPAFT-df=5 0.024 2.2 90.6 1000 0.011 1.0 93.0 1000 Inline graphic 0.023 Inline graphic 4.3 92.3 1000 Inline graphic 0.003 0.8 95.9 1000
1 FPAFT-df=6 Inline graphic 0.007 0.3 94.7 1000 0.018 . 91.6 1000 0.026 Inline graphic 2.5 92.7 1000 Inline graphic 0.007 0.3 94.7 1000
2 FPAFT-df=6 Inline graphic 0.001 0.3 94.0 1000 Inline graphic 0.001 Inline graphic 0.2 94.0 1000 0.026 Inline graphic 5.1 91.7 1000 Inline graphic 0.006 0.4 95.5 1000
3 FPAFT-df=6 Inline graphic 0.009 Inline graphic 1.5 94.2 1000 Inline graphic 0.009 Inline graphic 1.0 94.3 1000 0.064 Inline graphic 66.7 76.4 1000 Inline graphic 0.005 0.5 95.0 1000
4 FPAFT-df=6 0.001 0.1 94.5 1000 0.002 0.2 94.1 1000 0.022 8.2 91.3 1000 Inline graphic 0.004 0.6 94.0 1000
5 FPAFT-df=6 0.025 2.3 90.7 1000 0.008 0.7 93.7 1000 Inline graphic 0.017 Inline graphic 3.1 92.8 1000 Inline graphic 0.003 0.8 94.5 1000
1 FPAFT-df=7 Inline graphic 0.006 0.3 94.4 1000 0.004 . 93.8 1000 0.020 Inline graphic 1.9 93.4 1000 Inline graphic 0.007 0.3 94.9 1000
2 FPAFT-df=7 Inline graphic 0.008 2.1 94.4 1000 0.001 0.2 93.9 1000 0.025 Inline graphic 4.9 90.6 1000 Inline graphic 0.006 0.4 94.9 1000
3 FPAFT-df=7 Inline graphic 0.009 Inline graphic 1.5 94.5 1000 Inline graphic 0.006 Inline graphic 0.7 94.9 1000 0.059 Inline graphic 61.5 77.1 1000 Inline graphic 0.005 0.5 93.1 1000
4 FPAFT-df=7 0.006 0.7 93.5 1000 0.003 0.3 93.5 1000 0.031 11.5 88.9 1000 Inline graphic 0.003 0.5 92.3 1000
5 FPAFT-df=7 0.026 2.4 90.4 1000 0.006 0.6 93.1 1000 Inline graphic 0.013 Inline graphic 2.4 92.9 1000 Inline graphic 0.003 0.8 92.0 1000
1 FPAFT-df=8 Inline graphic 0.012 0.5 94.1 1000 Inline graphic 0.002 . 92.7 1000 0.020 Inline graphic 1.9 93.5 1000 Inline graphic 0.006 0.3 94.2 1000
2 FPAFT-df=8 Inline graphic 0.009 2.3 95.3 1000 0.000 0.0 93.3 1000 0.030 Inline graphic 5.8 89.7 1000 Inline graphic 0.004 0.3 93.0 1000
3 FPAFT-df=8 Inline graphic 0.010 Inline graphic 1.7 93.2 1000 Inline graphic 0.003 Inline graphic 0.3 94.0 1000 0.050 Inline graphic 52.1 81.9 1000 Inline graphic 0.002 0.2 92.5 1000
4 FPAFT-df=8 0.009 1.0 92.9 1000 0.004 0.4 93.7 1000 0.037 13.7 85.8 1000 Inline graphic 0.001 0.2 91.1 1000
5 FPAFT-df=8 0.026 2.4 90.3 1000 0.006 0.6 93.1 1000 Inline graphic 0.011 Inline graphic 2.0 91.7 1000 Inline graphic 0.000 0.0 89.6 1000
1 FPAFT-df=9 Inline graphic 0.014 0.6 94.8 1000 Inline graphic 0.002 . 93.9 1000 0.020 Inline graphic 1.9 93.3 1000 Inline graphic 0.004 0.2 93.6 1000
2 FPAFT-df=9 Inline graphic 0.008 2.1 94.4 1000 Inline graphic 0.000 0.0 93.5 1000 0.030 Inline graphic 5.8 89.3 1000 Inline graphic 0.000 0.0 91.7 1000
3 FPAFT-df=9 Inline graphic 0.012 Inline graphic 2.0 92.1 1000 Inline graphic 0.002 Inline graphic 0.2 94.4 1000 0.041 Inline graphic 42.8 83.7 1000 0.001 Inline graphic 0.1 90.1 1000
4 FPAFT-df=9 0.011 1.2 92.6 1000 0.005 0.5 93.0 1000 0.041 15.2 82.2 1000 0.002 Inline graphic 0.3 87.8 1000
5 FPAFT-df=9 0.027 2.5 90.0 1000 0.006 0.6 92.9 1000 Inline graphic 0.009 Inline graphic 1.7 90.9 1000 0.004 Inline graphic 1.1 86.9 1000