Topics in ROC analysis: Joint Inference, Combination of Biomarkers, and Confidence Bands
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In the field of diagnostic studies, the Receiver Operating Characteristic ( ROC ) and its summary indices are often used to evaluate biomarker/diagnostic test's accuracy. We propose to consider several popular indices of ROC curve jointly in order to evaluate biomarker more comprehensively. Usually multiple biomarkers are measured on the same subjects and combining these biomarkers could improve diagnostic accuracy. We propose to use the Youden index as an objective function for searching the optimal linear combination. The combined score achieves the maximum overall correct classification rate at the diagnostic threshold, in other words, it is the optimal combined score for making diagnosis. It is not uncommon to make inference about the ROC curve itself, that is, to estimate the confidence band of the ROC curve. We propose a parametric generalized confidence band for binormal ROC curve and the proposed confidence band is expected to provide more satisfactory coverage about the true ROC curve under small samples.