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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