Title: Impact of linear constraints on a multivariate binary classification problem
Authors: Sonia Perez-Fernandez - University of Oviedo (Spain) [presenting]
Abstract: The classification accuracy of a continuous variable - frequently called a marker - to distinguish between two groups is usually measured in terms of the sensitivity and the specificity, which are the probabilities of correctly classifying a subject from each group. When classification rules are based on a unique threshold for the marker, those resulting probabilities for every possible cut-off point are frequently displayed on a single graphic, called the Receiver Operating Characteristic (ROC) curve. There are some generalizations of the ROC curve to accommodate scenarios where using a unique cut-off point is far from the optimal classification rule. One example is the so-called general ROC (gROC) curve, where two thresholds are considered. A reformulation of the definition of the ROC curve is combined with the idea underlying the gROC curve, with the goal of constructing interpretable classification regions which report the maximum sensitivity for a particular specificity. The study is carried out in a conditionally normal bivariate scenario. The resulting decision rules and ROC curves are compared to the optimal ones without imposing any restrictions.