Linear combinations of biomarkers to improve diagnostic accuracy with three ordinal diagnostic categories

Many researchers have addressed the problem of finding the optimal linear combination of biomarkers to maximize the area under receiver operating characteristic (ROC) curves for scenarios with binary disease status. In practice, many disease processes such as Alzheimer can be naturally classified into three diagnostic categories such as normal, mild cognitive impairment and Alzheimer's disease (AD), and for such diseases the volume under the ROC surface (VUS) is the most commonly used index of diagnostic accuracy. In this article, we propose a few parametric and nonparametric approaches to address the problem of finding the optimal linear combination to maximize the VUS. We carried out simulation studies to investigate the performance of the proposed methods. We apply all of the investigated approaches to a real data set from a cohort study in early stage AD.