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Title: The length of the ROC curve and the two cutoff Youden through a biomarker discovery framework Authors:  John Tsimikas - University of the Aegean (Greece)
Leonidas Bantis - University of Kansas Medical Center (United States) [presenting]
Gregory Chambers - Rice Unviersity (United States)
Michela Capello - MD Anderson Cancer Center (United States)
Samir Hanash - MD Anderson Cancer Center (United States)
Ziding Feng - The University of Texas MD Anderson Cancer Center (United States)
Abstract: During biomarker discovery, high throughput technologies allow for simultaneous input of thousands of biomarkers that attempt to discriminate between healthy and diseased subjects. In such cases, proper ranking of biomarkers is highly important. Common measures, such as the area under the receiver operating characteristic (ROC) curve (AUC), as well as affordable sensitivity and specificity levels, are often taken into consideration. Strictly speaking, such measures are appropriate under a stochastic ordering assumption, which implies that higher (or lower) measurements are more indicative of the disease. Such an assumption is not always plausible and may lead to the rejection of extremely useful biomarkers at this early discovery stage. We explore the length of a smooth ROC curve as a measure for biomarker ranking, which is not subject to a single directionality. We show that the length corresponds to a divergence, is identical to the corresponding length of the optimal (likelihood ratio) ROC curve, and is an appropriate measure for ranking biomarkers. We explore the relationship between the length measure and the AUC of the optimal ROC curve. We then provide a complete framework for the evaluation of a biomarker in terms of sensitivity and specificity through a proposed ROC analogue for use in improper settings. We consider broad parametric families as well as non-parametric estimates. We apply our approaches on real data sets related to pancreatic and esophageal cancer.