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

Table 6.

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 0.042 Inline graphic 4.6 87.5 1000 Inline graphic 0.156 Inline graphic 32.5 9.7 1000 0.153 Inline graphic 22.6 18.2 1000 Inline graphic 0.007 0.4 94.2 1000
2 Weibull Inline graphic 0.301 Inline graphic 40.9 0.1 1000 Inline graphic 0.089 Inline graphic 9.7 52.1 1000 0.062 314.2 73.7 1000 Inline graphic 0.004 0.5 94.8 1000
3 Weibull 0.137 12.9 29.1 1000 0.047 4.4 79.1 1000 Inline graphic 0.092 Inline graphic 17.4 48.9 1000 Inline graphic 0.002 0.5 95.7 1000
4 Weibull 0.450 34.7 0.0 1000 0.144 12.2 24.7 1000 Inline graphic 0.085 Inline graphic 11.0 58.3 1000 Inline graphic 0.001 2.6 95.0 1000
5 Weibull 0.657 43.5 0.0 1000 0.216 17.0 3.9 1000 Inline graphic 0.029 Inline graphic 3.2 93.0 1000 0.000 0.0 95.1 1000
1 Gamma 0.111 Inline graphic 12.1 55.0 1000 Inline graphic 0.163 Inline graphic 34.0 7.4 1000 0.044 Inline graphic 6.5 86.5 1000 Inline graphic 0.005 0.3 94.7 1000
2 Gamma Inline graphic 0.176 Inline graphic 23.9 2.9 1000 Inline graphic 0.087 Inline graphic 9.5 53.4 1000 Inline graphic 0.024 Inline graphic 121.6 92.9 1000 Inline graphic 0.003 0.3 95.2 1000
3 Gamma 0.111 10.4 34.7 1000 0.058 5.4 74.8 1000 Inline graphic 0.118 Inline graphic 22.3 31.1 1000 Inline graphic 0.002 0.5 95.0 1000
4 Gamma 0.258 19.9 0.7 1000 0.162 13.7 21.6 1000 Inline graphic 0.040 Inline graphic 5.2 85.2 1000 Inline graphic 0.001 2.6 94.9 1000
5 Gamma 0.310 20.5 0.3 1000 0.241 19.0 3.5 1000 0.089 9.8 66.4 1000 Inline graphic 0.000 0.0 94.5 1000
1 GenF Inline graphic 0.026 2.8 91.8 991 Inline graphic 0.013 Inline graphic 2.7 65.6 692 0.041 Inline graphic 6.1 23.0 257 Inline graphic 0.009 0.5 80.7 914
2 GenF Inline graphic 0.059 Inline graphic 8.0 67.4 993 Inline graphic 0.004 Inline graphic 0.4 65.3 692 0.019 96.3 36.6 384 0.001 Inline graphic 0.1 81.2 914
3 GenF 0.066 6.2 64.9 993 0.029 2.7 61.8 692 Inline graphic 0.013 Inline graphic 2.5 38.5 407 0.009 Inline graphic 2.3 81.5 918
4 GenF 0.066 5.1 69.0 993 0.034 2.9 61.2 692 0.007 0.9 38.8 407 0.007 Inline graphic 17.9 82.0 922
5 GenF Inline graphic 0.001 Inline graphic 0.1 92.8 993 0.026 2.0 63.4 692 0.034 3.7 37.6 407 Inline graphic 0.003 Inline graphic 1.3 82.1 923
1 FPAFT-df=2 0.105 Inline graphic 11.4 58.9 1000 Inline graphic 0.168 Inline graphic 35.0 7.4 1000 0.066 Inline graphic 9.7 75.7 1000 Inline graphic 0.005 0.3 94.9 1000
2 FPAFT-df=2 Inline graphic 0.210 Inline graphic 28.5 0.2 1000 Inline graphic 0.067 Inline graphic 7.3 65.9 1000 0.027 136.8 90.2 1000 Inline graphic 0.002 0.2 95.2 1000
3 FPAFT-df=2 0.025 2.3 84.4 1000 0.091 8.5 56.2 1000 Inline graphic 0.088 Inline graphic 16.6 53.9 1000 Inline graphic 0.001 0.3 95.2 1000
4 FPAFT-df=2 0.174 13.4 23.7 1000 0.203 17.2 7.8 1000 Inline graphic 0.051 Inline graphic 6.6 82.4 1000 Inline graphic 0.001 2.6 94.8 1000
5 FPAFT-df=2 0.254 16.8 12.4 1000 0.288 22.7 0.6 1000 0.028 3.1 90.5 1000 Inline graphic 0.000 0.0 94.8 1000
1 FPAFT-df=3 Inline graphic 0.005 0.5 92.3 1000 Inline graphic 0.130 Inline graphic 27.1 14.3 1000 0.008 Inline graphic 1.2 96.3 1000 Inline graphic 0.003 0.2 94.7 1000
2 FPAFT-df=3 Inline graphic 0.124 Inline graphic 16.9 8.1 1000 Inline graphic 0.102 Inline graphic 11.2 37.7 1000 Inline graphic 0.029 Inline graphic 147.0 90.7 1000 Inline graphic 0.004 0.5 95.2 1000
3 FPAFT-df=3 Inline graphic 0.002 Inline graphic 0.2 92.2 1000 Inline graphic 0.003 Inline graphic 0.3 87.9 1000 Inline graphic 0.086 Inline graphic 16.3 55.4 1000 Inline graphic 0.003 0.8 95.1 1000
4 FPAFT-df=3 0.046 3.5 85.7 1000 0.065 5.5 76.2 1000 Inline graphic 0.001 Inline graphic 0.1 93.5 1000 Inline graphic 0.001 2.6 95.0 1000
5 FPAFT-df=3 0.047 3.1 87.1 1000 0.116 9.1 59.2 1000 0.114 12.5 44.0 1000 Inline graphic 0.000 0.0 95.1 1000
1 FPAFT-df=4 Inline graphic 0.061 6.6 81.6 1000 Inline graphic 0.034 Inline graphic 7.1 90.6 1000 Inline graphic 0.000 0.0 93.7 1000 Inline graphic 0.005 0.3 94.5 1000
2 FPAFT-df=4 Inline graphic 0.070 Inline graphic 9.5 56.2 1000 Inline graphic 0.047 Inline graphic 5.1 76.9 1000 Inline graphic 0.025 Inline graphic 126.7 93.5 1000 Inline graphic 0.003 0.3 95.4 1000
3 FPAFT-df=4 0.007 0.7 94.3 1000 Inline graphic 0.009 Inline graphic 0.8 92.3 1000 Inline graphic 0.087 Inline graphic 16.4 55.4 1000 Inline graphic 0.002 0.5 95.0 1000
4 FPAFT-df=4 0.015 1.2 94.3 1000 0.013 1.1 93.0 1000 Inline graphic 0.008 Inline graphic 1.0 91.9 1000 Inline graphic 0.001 2.6 94.4 1000
5 FPAFT-df=4 Inline graphic 0.014 Inline graphic 0.9 92.3 1000 0.027 2.1 91.3 1000 0.102 11.2 55.1 1000 Inline graphic 0.000 0.0 95.0 1000
1 FPAFT-df=5 Inline graphic 0.045 4.9 87.9 1000 Inline graphic 0.013 Inline graphic 2.7 96.2 1000 Inline graphic 0.026 3.8 90.6 1000 Inline graphic 0.004 0.2 94.5 1000
2 FPAFT-df=5 Inline graphic 0.044 Inline graphic 6.0 82.9 1000 Inline graphic 0.029 Inline graphic 3.2 88.6 1000 Inline graphic 0.018 Inline graphic 91.2 94.9 1000 Inline graphic 0.002 0.2 94.6 1000
3 FPAFT-df=5 0.015 1.4 93.7 1000 Inline graphic 0.005 Inline graphic 0.5 93.8 1000 Inline graphic 0.085 Inline graphic 16.1 53.7 1000 Inline graphic 0.002 0.5 94.3 1000
4 FPAFT-df=5 0.005 0.4 95.7 1000 0.007 0.6 93.6 1000 Inline graphic 0.020 Inline graphic 2.6 90.2 1000 Inline graphic 0.001 2.6 94.2 1000
5 FPAFT-df=5 Inline graphic 0.039 Inline graphic 2.6 88.0 1000 0.014 1.1 93.4 1000 0.079 8.7 70.2 1000 0.000 0.0 94.3 1000
1 FPAFT-df=6 Inline graphic 0.018 2.0 95.1 1000 Inline graphic 0.002 Inline graphic 0.4 95.0 1000 Inline graphic 0.023 3.4 92.9 1000 Inline graphic 0.004 0.2 94.4 1000
2 FPAFT-df=6 Inline graphic 0.029 Inline graphic 3.9 90.1 1000 Inline graphic 0.016 Inline graphic 1.8 93.9 1000 Inline graphic 0.016 Inline graphic 81.1 94.3 1000 Inline graphic 0.002 0.2 94.1 1000
3 FPAFT-df=6 0.021 2.0 92.8 1000 Inline graphic 0.001 Inline graphic 0.1 94.7 1000 Inline graphic 0.079 Inline graphic 14.9 58.4 1000 Inline graphic 0.002 0.5 93.0 1000
4 FPAFT-df=6 0.001 0.1 96.0 1000 0.004 0.3 94.4 1000 Inline graphic 0.027 Inline graphic 3.5 88.6 1000 Inline graphic 0.001 2.6 92.6 1000
5 FPAFT-df=6 Inline graphic 0.050 Inline graphic 3.3 86.1 1000 0.006 0.5 94.3 1000 0.064 7.0 77.7 1000 Inline graphic 0.000 0.0 93.8 1000
1 FPAFT-df=7 Inline graphic 0.004 0.4 94.5 1000 0.003 0.6 93.8 1000 Inline graphic 0.020 3.0 92.6 1000 Inline graphic 0.004 0.2 93.4 1000
2 FPAFT-df=7 Inline graphic 0.019 Inline graphic 2.6 93.6 1000 Inline graphic 0.007 Inline graphic 0.8 95.3 1000 Inline graphic 0.018 Inline graphic 91.2 91.7 1000 Inline graphic 0.002 0.2 93.2 1000
3 FPAFT-df=7 0.026 2.4 91.0 1000 0.003 0.3 94.8 1000 Inline graphic 0.072 Inline graphic 13.6 62.3 1000 Inline graphic 0.003 0.8 90.9 1000
4 FPAFT-df=7 Inline graphic 0.001 Inline graphic 0.1 96.2 1000 0.004 0.3 94.2 1000 Inline graphic 0.030 Inline graphic 3.9 86.4 1000 Inline graphic 0.001 2.6 92.9 1000
5 FPAFT-df=7 Inline graphic 0.057 Inline graphic 3.8 84.7 1000 0.002 0.2 94.2 1000 0.053 5.8 82.6 1000 Inline graphic 0.000 0.0 93.8 1000
1 FPAFT-df=8 0.001 Inline graphic 0.1 94.0 1000 0.004 0.8 93.5 1000 Inline graphic 0.022 3.2 92.0 1000 Inline graphic 0.006 0.4 92.2 1000
2 FPAFT-df=8 Inline graphic 0.013 Inline graphic 1.8 94.5 1000 Inline graphic 0.003 Inline graphic 0.3 95.4 1000 Inline graphic 0.022 Inline graphic 111.5 89.5 1000 Inline graphic 0.005 0.6 91.0 1000
3 FPAFT-df=8 0.029 2.7 89.8 1000 0.005 0.5 94.6 1000 Inline graphic 0.066 Inline graphic 12.5 66.4 1000 Inline graphic 0.005 1.3 88.7 1000
4 FPAFT-df=8 Inline graphic 0.001 Inline graphic 0.1 96.1 1000 0.004 0.3 94.4 1000 Inline graphic 0.031 Inline graphic 4.0 85.2 1000 Inline graphic 0.003 7.7 89.8 1000
5 FPAFT-df=8 Inline graphic 0.060 Inline graphic 4.0 83.5 1000 0.000 0.0 93.9 1000 0.046 5.0 85.6 1000 Inline graphic 0.002 Inline graphic 0.9 92.4 1000
1 FPAFT-df=9 0.002 Inline graphic 0.2 93.7 1000 0.004 0.8 92.5 1000 Inline graphic 0.023 3.4 91.8 1000 Inline graphic 0.009 0.5 91.8 1000
2 FPAFT-df=9 Inline graphic 0.010 Inline graphic 1.4 94.6 1000 0.000 0.0 95.5 1000 Inline graphic 0.025 Inline graphic 126.7 86.6 1000 Inline graphic 0.008 0.9 89.6 1000
3 FPAFT-df=9 0.030 2.8 89.4 1000 0.006 0.6 95.1 1000 Inline graphic 0.061 Inline graphic 11.5 71.9 1000 Inline graphic 0.008 2.1 85.7 1000
4 FPAFT-df=9 Inline graphic 0.001 Inline graphic 0.1 96.2 1000 0.003 0.3 94.8 1000 Inline graphic 0.031 Inline graphic 4.0 84.5 1000 Inline graphic 0.006 15.4 89.3 1000
5 FPAFT-df=9 Inline graphic 0.062 Inline graphic 4.1 84.0 1000 Inline graphic 0.001 Inline graphic 0.1 94.8 1000 0.041 4.5 85.1 1000 Inline graphic 0.004 Inline graphic 1.7 91.7 1000