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The receiver operating characteristic (ROC) curve is a very useful tool foranalyzing the diagnostic/classification power of instruments/classificationschemes as long as a binary-scale gold standard is available. When the goldstandard is continuous and there is no confirmative threshold, ROC curvebecomes less useful. Hence, there are several extensions proposed forevaluating the diagnostic potential of variables of interest. However, due tothe computational difficulties of these nonparametric based extensions, theyare not easy to be used for finding the optimal combination of variables toimprove the individual diagnostic power. Therefore, we propose a new measure,which extends the AUC index for identifying variables with good potential to beused in a diagnostic scheme. In addition, we propose a threshold gradientdescent based algorithm for finding the best linear combination of variablesthat maximizes this new measure, which is applicable even when the number ofvariables is huge. The estimate of the proposed index and its asymptoticproperty are studied. The performance of the proposed method is illustratedusing both synthesized and real data sets.

Evaluating the diagnostic powers of variables and their linear combinations when the gold standard is continuous