FAN , AILIN . New Statistical Methods for Precision Medicine : Variable Selection for Optimal

FAN, AILIN. New Statistical Methods for Precision Medicine: Variable Selection for Optimal Dynamic Treatment Regimes and Subgroup Detection. (Under the direction of Dr. Wenbin Lu and Dr. Rui Song.) Due to patients’ heterogeneity and a growing number of specifically targeted treatments, precision medicine draws attentions for customization of therapies and medical decisions for individual patient. In this dissertation, we investigate statistical methods to address two problems in precision medicine. The first problem is variable selection for optimal dynamic treatment regime. Variable selection is gaining more attention because it plays an important role in deriving practical and reliable optimal treatment regimes, especially when there are a large number of predictors. The second problem is subgroup detection of patients with enhanced treatment effects. By assessing heterogeneous treatment effects based on a variety of covariates, subgroup detection helps narrow down the target population of a treatment. In Chapter 2, we develop a sequential advantage selection method for variable selection for optimal treatment regime. Variables that have qualitative interactions with treatment are of clinical importance for treatment decision-making. A qualitative interaction of a variable with treatment arises when the treatment effect changes direction as the value of the variable varies. Our sequential advantage selection method sequentially selects variables with a qualitative interaction and can be applied in multiple-decision-point settings. Numerical studies suggest that the proposed method is useful in identifying important variables under various underlying true models. In Chapter 3, we propose a penalized A-learning method for deriving the optimal dynamic treatment regime when the number of covariates is of the non-polynomial order of the sample size. To preserve the double robustness property of the A-learning method, we adopt the Dantzig selector which directly penalizes the A-learning estimating equations. Simulation studies show that the proposed method achieves good performance in terms of both variable selection and estimated optimal treatment regimes. In Chapter 4, we propose a systematic method for subgroup detection. Our method first tests the existence of a subgroup, and then identifies the subgroup if the null hypothesis on nonexistence of such a subgroup is rejected. A semiparametric model for response is considered for model flexibility, and a doubly-robust test statistic is constructed based on this model. Moreover, a sample size calculation method for subgroup detection is developed based on the proposed statistic. Simulation studies are provided to illustrate the empirical performance of the proposed methods for subgroup detection and sample size calculation.