Journal of Probability and Statistics / 2019 / Article / Tab 3

Research Article

On the Use of Min-Max Combination of Biomarkers to Maximize the Partial Area under the ROC Curve

Table 3

Means and standard deviation (SD) of the partial area under the ROC curve for different combination methods based on the dataset consisted of ratings from multivariate log-normal distributions with unequal variance-covariance matrices (scenario#3) with 1,000 simulated datasets.

AUCsFpf rangeSample SizeMIN-MAXSULIULIULOGISTIC

0.7-0.80-0.150:50Re-Sub0.059 (0.011)0.035 (0.009)0.040 (0.010)0.040 (0.010)
LOPO0.054 (0.012)0.026 (0.010)0.031 (0.011)0.028 (0.011)
50:100Re-Sub0.058 (0.009)0.035 (0.008)0.040 (0.009)0.039 (0.009)
LOPO0.054 (0.011)0.028 (0.009)0.032 (0.010)0.028 (0.010)
100:50Re-Sub0.057 (0.008)0.033 (0.008)0.037 (0.008)0.038 (0.008)
LOPO0.054 (0.009)0.027 (0.008)0.031 (0.009)0.030 (0.009)
100:100Re-Sub0.057 (0.007)0.033 (0.007)0.036 (0.007)0.037 (0.007)
LOPO0.054 (0.008)0.028 (0.007)0.031 (0.008)0.030 (0.007)

0-0.250:50Re-Sub0.136 (0.018)0.090 (0.018)0.095 (0.019)0.099 (0.019)
LOPO0.129 (0.020)0.074 (0.020)0.082 (0.020)0.079 (0.020)
50:100Re-Sub0.135 (0.015)0.091 (0.015)0.096 (0.017)0.097 (0.016)
LOPO0.129 (0.017)0.077 (0.017)0.084 (0.018)0.079 (0.018)
100:50Re-Sub0.133 (0.014)0.088 (0.015)0.091 (0.016)0.095 (0.016)
LOPO0.129 (0.015)0.077 (0.017)0.084 (0.016)0.084 (0.017)
100:100Re-Sub0.133 (0.012)0.087 (0.013)0.091 (0.014)0.094 (0.013)
LOPO0.130 (0.013)0.079 (0.014)0.084 (0.014)0.083 (0.014)

0.6-0.90-0.150:50Re-Sub0.050 (0.010)0.051 (0.012)0.056 (0.012)0.059 (0.012)
LOPO0.043 (0.012)0.043 (0.013)0.048 (0.014)0.048 (0.013)
50:100Re-Sub0.049 (0.008)0.050 (0.011)0.057 (0.011)0.058 (0.011)
LOPO0.043 (0.011)0.044 (0.012)0.050 (0.013)0.050 (0.012)
100:50Re-Sub0.114 (0.014)0.123 (0.020)0.128 (0.018)0.138 (0.016)
LOPO0.107 (0.016)0.115 (0.021)0.122 (0.019)0.129 (0.017)
100:100Re-Sub0.047 (0.007)0.049 (0.010)0.054 (0.009)0.056 (0.009)
LOPO0.044 (0.008)0.045 (0.010)0.050 (0.010)0.051 (0.009)

0-0.250:50Re-Sub0.116 (0.017)0.126 (0.021)0.130 (0.022)0.141 (0.019)
LOPO0.106 (0.021)0.114 (0.023)0.118 (0.024)0.125 (0.021)
50:100Re-Sub0.115 (0.014)0.125 (0.020)0.131 (0.020)0.140 (0.018)
LOPO0.107 (0.017)0.114 (0.021)0.121 (0.022)0.128 (0.019)
100:50Re-Sub0.048 (0.008)0.049 (0.011)0.054 (0.010)0.057 (0.010)
LOPO0.044 (0.009)0.044 (0.011)0.050 (0.011)0.051 (0.010)
100:100Re-Sub0.113 (0.012)0.124 (0.017)0.128 (0.016)0.138 (0.014)
LOPO0.108 (0.014)0.117 (0.018)0.122 (0.017)0.130 (0.015)

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