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

Table 1

Means (standard deviations) of the partial area under the ROC curve for different combination methods based on the dataset consisted of ratings from multivariate normal distributions with equal variance-covariance matrices (scenario#1) with 1000 simulated datasets.

AUCs	Fpf range	Sample Size		MIN-MAX	SULIU	LIU	LOGISTIC
0.7-0.8	0-0.1	50:50	Re-Sub	0.036 (0.010)	0.038 (0.011)	0.024 (0.011)	0.038 (0.011)
			LOPO	0.028 (0.012)	0.030 (0.011)	0.016 (0.011)	0.030 (0.011)
		50:100	Re-Sub	0.036 (0.009)	0.038 (0.010)	0.024 (0.011)	0.037 (0.010)
			LOPO	0.028 (0.011)	0.031 (0.010)	0.016 (0.011)	0.031 (0.010)
		100:50	Re-Sub	0.034 (0.008)	0.036 (0.009)	0.021 (0.010)	0.036 (0.009)
			LOPO	0.028 (0.009)	0.031 (0.009)	0.015 (0.009)	0.030 (0.009)
		100:100	Re-Sub	0.033 (0.007)	0.036 (0.007)	0.021 (0.010)	0.036 (0.007)
			LOPO	0.028 (0.008)	0.031 (0.007)	0.015 (0.009)	0.031 (0.007)
	0-0.2	50:50	Re-Sub	0.094 (0.018)	0.101 (0.020)	0.064 (0.024)	0.101 (0.020)
			LOPO	0.081 (0.022)	0.086 (0.021)	0.049 (0.025)	0.086 (0.021)
		50:100	Re-Sub	0.092 (0.017)	0.099 (0.018)	0.064 (0.024)	0.099 (0.018)
			LOPO	0.081 (0.021)	0.087 (0.019)	0.049 (0.024)	0.087 (0.019)
		100:50	Re-Sub	0.091 (0.015)	0.097 (0.016)	0.059 (0.022)	0.098 (0.016)
			LOPO	0.082 (0.018)	0.087 (0.017)	0.047 (0.022)	0.087 (0.017)
		100:100	Re-Sub	0.089 (0.013)	0.096 (0.013)	0.058 (0.022)	0.096 (0.013)
			LOPO	0.081 (0.016)	0.089 (0.014)	0.047 (0.021)	0.089 (0.014)
0.6-0.9	0-0.1	50:50	Re-Sub	0.047 (0.010)	0.064 (0.011)	0.034 (0.018)	0.065 (0.011)
			LOPO	0.040 (0.012)	0.056 (0.013)	0.026 (0.017)	0.054 (0.012)
		50:100	Re-Sub	0.046 (0.010)	0.063 (0.010)	0.034 (0.018)	0.063 (0.010)
			LOPO	0.041 (0.012)	0.057 (0.012)	0.025 (0.016)	0.056 (0.011)
		100:50	Re-Sub	0.045 (0.009)	0.062 (0.009)	0.029 (0.016)	0.062 (0.009)
			LOPO	0.040 (0.010)	0.057 (0.010)	0.023 (0.014)	0.056 (0.010)
		100:100	Re-Sub	0.044 (0.008)	0.062 (0.008)	0.030 (0.016)	0.062 (0.008)
			LOPO	0.040 (0.009)	0.058 (0.008)	0.024 (0.014)	0.057 (0.008)
	0-0.2	50:50	Re-Sub	0.114 (0.017)	0.148 (0.017)	0.084 (0.037)	0.149 (0.017)
			LOPO	0.106 (0.020)	0.137 (0.019)	0.070 (0.036)	0.135 (0.019)
		50:100	Re-Sub	0.114 (0.017)	0.147 (0.015)	0.085 (0.037)	0.147 (0.015)
			LOPO	0.107 (0.019)	0.138 (0.017)	0.070 (0.034)	0.136 (0.017)
		100:50	Re-Sub	0.112 (0.015)	0.146 (0.014)	0.075 (0.033)	0.146 (0.014)
			LOPO	0.106 (0.017)	0.138 (0.015)	0.065 (0.032)	0.137 (0.015)
		100:100	Re-Sub	0.110 (0.013)	0.146 (0.012)	0.079 (0.035)	0.146 (0.012)
			LOPO	0.106 (0.014)	0.140 (0.012)	0.068 (0.032)	0.139 (0.012)