Statistical Learning Methods for Personalized Medicine

de Xin Qiu

The theme of this dissertation is to develop simple and interpretable individualized treatment rules (ITRs) using statistical learning methods to assist personalized decision making in clinical practice. Considerable heterogeneity in treatment response is observed among individuals with mental disorders. Administering an individualized treatment rule according to patient-specific characteristics offers an opportunity to tailor treatment strategies to improve response. Black-box machine learning methods for estimating ITRs may produce treatment rules that have optimal benefit but lack transparency and interpretability. Barriers to implementing personalized treatments in clinical psychiatry include a lack of evidence-based, clinically interpretable, individualized treatment rules, a lack of diagnostic measure to evaluate candidate ITRs, a lack of power to detect treatment modifiers from a single study, and a lack of reproducibility of treatment rules estimated from single studies. This dissertation contains three parts to tackle these barriers: (1) methods to estimate the best linear ITR with guaranteed performance among the class of linear rules; (2) a tree-based method to improve the performance of a linear ITR fitted from the overall sample and identify subgroups with a large benefit; and (3) an integrative learning combining information across trials to provide an integrative ITR with improved efficiency and reproducibility. In the first part of the dissertation, we propose a machine learning method to estimate optimal linear individualized treatment rules for data collected from single stage randomized controlled trials (RCTs). In clinical practice, an informative and practically useful treatment rule should be simple and transparent. However, because simple rules are likely to be far from optimal, effective methods to construct such rules must guarantee performance, in terms of yielding the best clinical outcome (highest reward) among the class of simple rules under consideration. Furthermore, it is important to evaluate the benefit of the derived rules on the whole sample and in pre-specified subgroups (e.g., vulnerable patients). To achieve both goals, we propose a robust machine learn- ing algorithm replacing zero-one loss with an authentic approximation loss (ramp loss) for value maximization, referred to as the asymptotically best linear O-learning (ABLO), which estimates a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules. We then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods. We provide theoretical justification for the proposed method and its inference procedure, and we demonstrate via simulations its superior performance when compared to existing methods. Lastly, we apply the proposed method to the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial on major depressive disorder (MDD) and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack-of-fit for moderately depressed patients. The second part of the dissertation is motivated by the results of real data analysis in the first part, where the global linear rule estimated by ABLO from the overall sample performs inadequately on the subgroup of moderately depressed patients. Therefore, we aim to derive a simple and interpretable piece-wise linear ITR to maintain certain optimality that leads to improved benefit in subgroups of patients, as well as the overall sample. In this work, we propose a tree-based robust learning method to estimate optimal piece-wise linear ITRs and identify subgroups of patients with a large benefit. We achieve these goals by simultaneously identifying qualitative and quantitative interactions through a tree model, referred to as the composite interaction tree (CITree). We show that it has improved performance compared to existing methods on both overall sample and subgroups via extensive simulation studies. Lastly, we fit CITree to Research Evaluating the Value of Augmenting Medication with Psychotherapy (REVAMP) trial for treating major depressive disorders, where we identified both qualitative and quantitative interactions and subgroups of patients with a large benefit. The third part deals with the difficulties in the low power of identifying ITRs and replicating ITRs due to small sample sizes of single randomized controlled trials. In this work, a novel integrative learning method is developed to synthesize evidence across trials and provide an integrative ITR that improves efficiency and reproducibility. Our method does not require all studies to collect a common set of variables and thus allows information to be combined from ITRs identified from randomized controlled trials with heterogeneous sets of baseline covariates collected from different