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Another popular ROC index could be the Youden index (J), which corresponds to the optimum sum of sensitivity and specificity minus one. Since the AUC and J describe different factors of diagnostic overall performance, we suggest to evaluate if a biomarker beats the pre-specified targeting values of AUC0 and J0 simultaneously with H0   AUC ≤ AUC0 or J ≤ J0 against Ha   AUC  AUC0 and J  J0 . This can be a multivariate order restrictive theory with a non-convex space i

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