Title: Statistical and Machine Learning Methods for Precision Medicine
Description: Heterogeneous treatment responses are commonly observed in patients with mental disorders. Thus, a universal treatment strategy may not be adequate, and tailored treatments adapted to individual characteristics could improve treatment responses. The theme of the dissertation is to develop statistical and machine learning methods to address patients heterogeneity and derive robust and generalizable individualized treatment strategies by integrating evidence from multi-domain data and multiple studies to achieve precision medicine. Unique challenges arising from the research of mental disorders need to be addressed in order to facilitate personalized medical decision-making in clinical practice. This dissertation contains four projects to achieve these goals while addressing the challenges: (i) a statistical method to learn dynamic treatment regimes (DTRs) by synthesizing independent trials over different stages when sequential randomization data is not available; (ii) a statistical method to learn optimal individualized treatment rules (ITRs) for mental disorders by modeling patients' latent mental states using probabilistic generative models; (iii) an integrative learning algorithm to incorporate multi-domain and multi-treatment-phase measures for optimizing individualized treatments; (iv) a statistical machine learning method to optimize ITRs that can benefit subjects in a target population for mental disorders with improved learning efficiency and generalizability.

DTRs adaptively prescribe treatments based on patients' intermediate responses and evolving health status over multiple treatment stages. Data from sequential multiple assignment randomization trials (SMARTs) are recommended to be used for learning DTRs. However, due to the re-randomization of the same patients over multiple treatment stages and a prolonged follow-up period, SMARTs are often difficult to implement and costly to manage, and patient adherence is always a concern in practice. To lessen such practical challenges, in the first part of the dissertation, we propose an alternative approach to learn optimal DTRs by synthesizing independent trials over different stages without using data from SMARTs. Specifically, at each stage, data from a single randomized trial along with patients' natural medical history and health status in previous stages are used. We use a backward learning method to estimate optimal treatment decisions at a particular stage, where patients' future optimal outcome increment is estimated using data observed from independent trials with future stages' information.

Under some conditions, we show that the proposed method yields consistent estimation of the optimal DTRs, and we obtain the same learning rates as those from SMARTs. We conduct simulation studies to demonstrate the advantage of the proposed method. Finally, we learn DTRs for treating major depressive disorder (MDD) by stage-wise synthesis of two randomized trials. We perform a validation study on independent subjects and show that the synthesized DTRs lead to the greatest MDD symptom reduction compared to alternative methods. The second part of the dissertation focuses on optimizing individualized treatments for mental disorders. Due to disease complexity, substantial diversity in patients' symptomatology within the same diagnostic category is widely observed. Leveraging the measurement model theory in psychiatry and psychology, we learn patient's intrinsic latent mental status from psychological or clinical symptoms under a probabilistic generative model, restricted Boltzmann machine (RBM), through which patients' heterogeneous symptoms are represented using an economic number of latent variables and yet remains flexible.

These latent mental states serve as a better characterization of the underlying disorder status than a simple summary score of the symptoms. They also serve as more reliable and representative features to differentiate treatment responses. We then optimize a value function defined by the latent states after treatment by exploiting a transformation of the observed symptoms based on the RBM without modeling the relationship between the latent mental states before and after treatment. The optimal treatment rules are derived using a weighted large margin classifier. We derive the convergence rate of the proposed estimator under the latent models. Simulation studies are conducted to test the performance of the proposed method. Finally, we apply the developed method to real-world studies. We demonstrate the utility and advantage of our method in tailoring treatments for patients with major depression and identify patient subgroups informative for treatment recommendations. In the third part of the dissertation, based on the general framework introduced in the previous part, we propose an integrated learning algorithm that can simultaneously learn patients' underlying mental states and recommend optimal treatments for each individual with improved learning efficiency.

It allows incorporation of both the pre- and post-treatment outcomes in learning the invariant latent structure and allows integration of outcome measures from different domains to characterize patients' mental health more comprehensively. A multi-layer neural network is used to allow complex treatment effect heterogeneity. Optimal treatment policy can be inferred for future patients by comparing their potential mental states under different treatments given the observed multi-domain pre-treatment measurements. Experiments on simulated data and real-world clinical trial data show that the learned treatment polices compare favorably to alternative methods on heterogeneous treatment effects and have broad utilities which lead to better patient outcomes on multiple domains. The fourth part of the dissertation aims to infer optimal treatments of mental disorders for a target population considering the potential distribution disparities between the patient data in a study we collect and the target population of interest.

To achieve that, we propose a learning approach that connects measurement theory, efficient weighting procedure, and flexible neural network architecture through latent variables. In our method, patients' underlying mental states are represented by a reduced number of latent state variables allowing for incorporating domain knowledge, and the invariant latent structure is preserved for interpretability and validity. Subject-specific weights to balance population differences are constructed using these compact latent variables, which capture the major variations and facilitate the weighting procedure due to the reduced dimensionality. Data from multiple studies can be integrated to learn the latent structure to improve learning efficiency and generalizability. Extensive simulation studies demonstrate consistent superiority of the proposed method and the weighting scheme to alternative methods when applying to the target population. Application of our method to real-world studies is conducted to recommend treatments to patients with major depressive disorder and has shown a broader utility of the ITRs learned from the proposed method in improving the mental states of patients in the target population.