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.

AUCs	Fpf range	Sample Size		MIN-MAX	SULIU	LIU	LOGISTIC
0.7-0.8	0-0.1	50:50	Re-Sub	0.059 (0.011)	0.035 (0.009)	0.040 (0.010)	0.040 (0.010)
			LOPO	0.054 (0.012)	0.026 (0.010)	0.031 (0.011)	0.028 (0.011)
		50:100	Re-Sub	0.058 (0.009)	0.035 (0.008)	0.040 (0.009)	0.039 (0.009)
			LOPO	0.054 (0.011)	0.028 (0.009)	0.032 (0.010)	0.028 (0.010)
		100:50	Re-Sub	0.057 (0.008)	0.033 (0.008)	0.037 (0.008)	0.038 (0.008)
			LOPO	0.054 (0.009)	0.027 (0.008)	0.031 (0.009)	0.030 (0.009)
		100:100	Re-Sub	0.057 (0.007)	0.033 (0.007)	0.036 (0.007)	0.037 (0.007)
			LOPO	0.054 (0.008)	0.028 (0.007)	0.031 (0.008)	0.030 (0.007)
	0-0.2	50:50	Re-Sub	0.136 (0.018)	0.090 (0.018)	0.095 (0.019)	0.099 (0.019)
			LOPO	0.129 (0.020)	0.074 (0.020)	0.082 (0.020)	0.079 (0.020)
		50:100	Re-Sub	0.135 (0.015)	0.091 (0.015)	0.096 (0.017)	0.097 (0.016)
			LOPO	0.129 (0.017)	0.077 (0.017)	0.084 (0.018)	0.079 (0.018)
		100:50	Re-Sub	0.133 (0.014)	0.088 (0.015)	0.091 (0.016)	0.095 (0.016)
			LOPO	0.129 (0.015)	0.077 (0.017)	0.084 (0.016)	0.084 (0.017)
		100:100	Re-Sub	0.133 (0.012)	0.087 (0.013)	0.091 (0.014)	0.094 (0.013)
			LOPO	0.130 (0.013)	0.079 (0.014)	0.084 (0.014)	0.083 (0.014)
0.6-0.9	0-0.1	50:50	Re-Sub	0.050 (0.010)	0.051 (0.012)	0.056 (0.012)	0.059 (0.012)
			LOPO	0.043 (0.012)	0.043 (0.013)	0.048 (0.014)	0.048 (0.013)
		50:100	Re-Sub	0.049 (0.008)	0.050 (0.011)	0.057 (0.011)	0.058 (0.011)
			LOPO	0.043 (0.011)	0.044 (0.012)	0.050 (0.013)	0.050 (0.012)
		100:50	Re-Sub	0.114 (0.014)	0.123 (0.020)	0.128 (0.018)	0.138 (0.016)
			LOPO	0.107 (0.016)	0.115 (0.021)	0.122 (0.019)	0.129 (0.017)
		100:100	Re-Sub	0.047 (0.007)	0.049 (0.010)	0.054 (0.009)	0.056 (0.009)
			LOPO	0.044 (0.008)	0.045 (0.010)	0.050 (0.010)	0.051 (0.009)
	0-0.2	50:50	Re-Sub	0.116 (0.017)	0.126 (0.021)	0.130 (0.022)	0.141 (0.019)
			LOPO	0.106 (0.021)	0.114 (0.023)	0.118 (0.024)	0.125 (0.021)
		50:100	Re-Sub	0.115 (0.014)	0.125 (0.020)	0.131 (0.020)	0.140 (0.018)
			LOPO	0.107 (0.017)	0.114 (0.021)	0.121 (0.022)	0.128 (0.019)
		100:50	Re-Sub	0.048 (0.008)	0.049 (0.011)	0.054 (0.010)	0.057 (0.010)
			LOPO	0.044 (0.009)	0.044 (0.011)	0.050 (0.011)	0.051 (0.010)
		100:100	Re-Sub	0.113 (0.012)	0.124 (0.017)	0.128 (0.016)	0.138 (0.014)
			LOPO	0.108 (0.014)	0.117 (0.018)	0.122 (0.017)	0.130 (0.015)