This research focuses on developing new and computationally efficient statistical learning methods for multicategory classification and personalized medical decision making. Motivated by the challenge of multicategory classification problems, and the computational efficiency and theoretical properties of support vector machines (SVM), a novel learning algorithm is proposed. The method is then adapted to estimating multicategory individualized treatment by connecting with outcome weighted learning. At last, an application to Electronic Health Record data is explored.

The proposed algorithm, forward-backward SVM (FB-SVM) is based on a sequential binary classification algorithm and relies on support vector machines for each binary classification and utilizes only feasible data in each step. The method guarantees convergence and entails light computational burden. We prove the theoretical property of Fisher consistency of the classification rule derived from the FB-SVM and obtain the risk bound for the predicted misclassification rate. We conduct extensive simulation and application studies, using popular benchmarking data and data from a newly completed real-world study, to demonstrate that the proposed method has superior performance, in terms of low misclassification rates and significantly improved computational speed when compared to existing methods.

Furthermore, we generalize the proposed FB-SVM with outcome weighted learning to estimate optimal individualized treatment rule (ITR) with multiple options of treatment, namely sequential outcome-weighted learning (SOM). Theoretically, we show that the resulting ITR is Fisher consistent. We demonstrate the performance of proposed method with extensive simulations. An application to a three-arm randomized trial of treating major depressive disorder shows that an individualized treatment strategy tailored to individual characteristics such as patients' expectancy of treatment efficacy and baseline depression severity reduces depressive symptoms more than non-personalized treatment strategies.

Finally, we discuss how the proposed SOM learning can be used to estimate optimal ITRs with safety concerns in high dimensional data with patients' adverse reaction records who have taken statin medicine. We adopt sampling techniques, inverse probability weighting, propensity score adjustment, and variable clustering along with SOM learning in our analysis. Considering patients' demographics and medical history, we are able to recommend the best statin drug which has the lowest risk to cause myopathy or rhabdomyolysis.