The Linear Combinations of Markers That Maximize the Partial Area Under the ROC Curves

• Activity Number: 342
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Man-Jen Hsu*+ and Huey-Miin Hsueh
• Companies: National Chengchi University and National Chengchi University
• Keywords: Partial area under curve ; pAUC ; ROC curve ; Sensitivity ; Specificity

Abstract

As biotechnology has remarkable progress nowadays, there is a great improvement in data collecting procedure with lower cost and higher quality. When multiple potential markers are available in constructing a diagnostic tool of a disease, an effective approach is to combine the information to build one single summarizing indicator. For continuous-scaled data, the linear combination is popular due to its easy interpretability. Su and Liu (1993) derived the best linear combination under the criterion of maximal area under the ROC curve. In many investigations, the emphasis is placed only on limited extent, instead of the whole curve. The goal of this study is to find the best linear combination that maximizes the partial area under a ROC curve (pAUC). To find the solution analytically, the first derivative of the pAUC under normal assumption is derived. Because the pAUC maximizer may not be unique in some cases, the existing algorithm is inadequate and thus we propose a revised algorithm by adopting several initial points. Intensive numerical studies are perform and the results justify the adequacy of the proposed algorithm. Real examples are also provided for illustration.