计厩╰簍量そ
 量 眎方玊  ╯ 
(いァ╯皘 参璸厩╯┮) 
量    肈Area under ROC curve type measures without binary gold standard
ら    戳10005る03ら琍戳と2:30  3:20
    翴计厩╰(厩繻S433)

篕    璶
The receiver operating characteristic (ROC) curve is a very useful tool in analyzing diagnostic/classification power of instruments/classification schemes as long as a binary-scale gold standard is available. The importance of ROC curve has been intensively studied by many authors, which can be easily found in the literatures and textbooks such as Pepe (2003) and Krzanowski and hand (2009). However, if the gold standard is continuous and there is no confirmative threshold for it is available, then the traditional ROC curve analysis cannot be applied. Hence, we propose a new measure, which extends the ROC curve based index, for identifying variables with good potential to be used in a diagnostic scheme.  The estimate of the proposed index and its asymptotic property is studied.  In addition, we propose a threshold gradient descend based algorithm for finding the best linear combination of variables that maximizes this new measure, which is applicable even when the number of variables is huge. Under the joint multivariate normality assumption, the algorithm for the linear combination can be relied on the LARS method. When this joint normality assumption is violated, we propose a threshold gradient descend based method (TGDM) to find the optimal linear combination. Thus, our algorithms also inherit the nice properties of LARS and TGDM when dealing with the high dimensional and variable selection problems. The performance of the proposed method is illustrated using both synthesized and real data sets.  

Co-authored with Professor Zhanfeng Wang

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