| Summary: | In personalized medicine, two important tasks are predicting disease risk and selecting appropriate treatments for individuals based on their baseline information. The dissertation focuses on providing improved risk prediction for ordinal outcome data and proposing score-based test to identify informative markers for treatment selection. In Chapter 1, we take up the first problem and propose a disease risk prediction model for ordinal outcomes. Traditional ordinal outcome models leave out intermediate models which may lead to suboptimal prediction performance; they also don't allow for non-linear covariate effects. To overcome these, a continuation ratio kernel machine (CRKM) model is proposed both to let the data reveal the underlying model and to capture potential non-linearity effect among predictors, so that the prediction accuracy is maximized. In Chapter 2, we seek to develop a kernel machine (KM) score test that can efficiently identify markers that are predictive of treatment difference. This new approach overcomes the shortcomings of the standard Wald test, which is scale-dependent and only take into account linear effect among predictors. To do this, we propose a model-free score test statistics and implement the KM framework. Simulations and real data applications demonstrated the advantage of our methods over the Wald test. In Chapter 3, based on the procedure proposed in Chapter 2, we further add sparsity assumption on the predictors to take into account the real world problem of sparse signal. We incorporate the generalized higher criticism (GHC) to threshold the signals in a group and maintain a high detecting power. A comprehensive comparison of the procedures in Chapter 2 and Chapter 3 demonstrated the advantages and disadvantages of difference procedures under different scenarios. === Biostatistics
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