In medical research, it is common to collect information of multiple continuous biomarkers to improve the accuracy of diagnostic tests. Combining the measurements of these biomarkers into one single score is a popular practice to integrate the collected information, where the accuracy of the resultant diagnostic test is usually improved. To measure the accuracy of a diagnostic test, the Youden index has been widely used in literature. Various parametric and nonparametric methods have been proposed to linearly combine biomarkers so that the corresponding Youden index can be optimized. Yet there seems to be little justification of enforcing such a linear combination. This paper proposes a flexible approach that allows both linear and nonlinear combinations of biomarkers. The proposed approach formulates the problem in a large margin classification framework, where the combination function is embedded in a flexible reproducing kernel Hilbert space. Advantages of the proposed approach are demonstrated in a variety of simulated experiments as well as a real application to a liver disorder study.
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