Identifying Optimal Biomarker Combinations for Treatment Selection via a Robust Kernel Method

Treatment-selection markers predict an individual's response to different therapies, thus allowing for the selection of a therapy with the best predicted outcome. A good marker-based treatment-selection rule can significantly impact public health through the reduction of the disease burden in a cost-effective manner. Our goal in this article is to use data from randomized trials to identify optimal linear and nonlinear biomarker combinations for treatment selection that minimize the total burden to the population caused by either the targeted disease or its treatment. We frame this objective into a general problem of minimizing a weighted sum of 0-1 loss and propose a novel penalized minimization method that is based on the difference of convex functions algorithm (DCA). The corresponding estimator of marker combinations has a kernel property that allows flexible modeling of linear and nonlinear marker combinations. We compare the proposed methods with existing methods for optimizing treatment regimens such as the logistic regression model and the weighted support vector machine. Performances of different weight functions are also investigated. The application of the proposed method is illustrated using a real example from an HIV vaccine trial: we search for a combination of Fc receptor genes for recommending vaccination in preventing HIV infection.