Table 6 The related pAUCs and the global test for three and four dimensions
From: Biomarker selection for medical diagnosis using the partial area under the ROC curve
Full biomarker Set | Reduced biomarker Set | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mean difference | Correlation | Forward selection | Backward selection | ||||||||||||
Case | ∆1 | ∆2 | ∆3 | ∆4 | ρ 0 | ρ 1 | True | Ave | SE | Power (Tg) | Ave | SE | Ave | SE | |
p = 3 | 1 | 0.0 | 0.0 | 0.0 | - | 0.0 | 0.0 | 0.005 | 0.010 | 0.002 | 0.052 | 0.011 | 0.002 | 0.013 | 0.002 |
2 | 0.5 | 0.0 | 0.0 | - | 0.0 | 0.0 | 0.012 | 0.015 | 0.004 | 0.576 | 0.014 | 0.003 | 0.015 | 0.003 | |
3 | 0.5 | 0.5 | 0.0 | - | 0.0 | 0.0 | 0.017 | 0.019 | 0.004 | 0.870 | 0.016 | 0.005 | 0.016 | 0.005 | |
4 | 0.5 | 0.5 | 0.5 | - | 0.0 | 0.0 | 0.021 | 0.023 | 0.005 | 0.977 | 0.018 | 0.006 | 0.018 | 0.007 | |
5 | 0.5 | 1.0 | 0.0 | - | 0.0 | 0.0 | 0.028 | 0.030 | 0.006 | 1.000 | 0.028 | 0.007 | 0.027 | 0.008 | |
6 | 0.5 | 0.5 | 0.0 | - | 0.1 | 0.1 | 0.016 | 0.018 | 0.004 | 0.845 | 0.015 | 0.004 | 0.016 | 0.004 | |
7 | 0.5 | 0.5 | 0.0 | - | 0.5 | 0.5 | 0.014 | 0.016 | 0.004 | 0.713 | 0.015 | 0.004 | 0.016 | 0.004 | |
8 | 0.5 | 0.5 | 0.0 | - | 0.9 | 0.9 | 0.013 | 0.015 | 0.004 | 0.616 | 0.014 | 0.004 | 0.016 | 0.004 | |
9 | 0.5 | 1.0 | 0.0 | - | 0.1 | 0.1 | 0.027 | 0.029 | 0.006 | 0.998 | 0.027 | 0.006 | 0.027 | 0.007 | |
10 | 0.5 | 1.0 | 0.0 | - | 0.5 | 0.5 | 0.025 | 0.026 | 0.006 | 0.995 | 0.025 | 0.006 | 0.025 | 0.006 | |
11 | 0.5 | 1.0 | 0.0 | - | 0.9 | 0.9 | 0.036 | 0.038 | 0.006 | 1.000 | 0.034 | 0.010 | 0.021 | 0.017 | |
p = 4 | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.005 | 0.011 | 0.002 | 0.051 | 0.011 | 0.002 | 0.012 | 0.002 |
2 | 0.5 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.012 | 0.016 | 0.004 | 0.520 | 0.014 | 0.004 | 0.015 | 0.003 | |
3 | 0.5 | 0.5 | 0.0 | 0.0 | 0.0 | 0.0 | 0.017 | 0.020 | 0.004 | 0.862 | 0.016 | 0.005 | 0.016 | 0.005 | |
4 | 0.5 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.028 | 0.031 | 0.006 | 1.000 | 0.028 | 0.007 | 0.026 | 0.008 | |
5 | 0.5 | 1.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.041 | 0.043 | 0.007 | 1.000 | 0.042 | 0.008 | 0.042 | 0.008 | |
6 | 0.5 | 1.0 | 0.0 | 0.0 | 0.1 | 0.1 | 0.027 | 0.029 | 0.006 | 0.995 | 0.027 | 0.007 | 0.026 | 0.007 | |
7 | 0.5 | 1.0 | 0.0 | 0.0 | 0.5 | 0.5 | 0.025 | 0.027 | 0.005 | 0.993 | 0.025 | 0.006 | 0.025 | 0.006 | |
8 | 0.5 | 1.0 | 0.0 | 0.0 | 0.9 | 0.9 | 0.036 | 0.038 | 0.006 | 1.000 | 0.035 | 0.009 | 0.021 | 0.017 | |
9 | 0.5 | 1.0 | 1.0 | 0.0 | 0.1 | 0.1 | 0.040 | 0.042 | 0.007 | 1.000 | 0.041 | 0.008 | 0.041 | 0.008 | |
10 | 0.5 | 1.0 | 1.0 | 0.0 | 0.5 | 0.5 | 0.038 | 0.040 | 0.006 | 1.000 | 0.039 | 0.007 | 0.039 | 0.008 | |
11 | 0.5 | 1.0 | 1.0 | 0.0 | 0.9 | 0.9 | 0.048 | 0.050 | 0.007 | 1.000 | 0.047 | 0.009 | 0.049 | 0.008 | |