ON DEVELOPMENT OF STATISTICAL LEARNING METHODS IN PRECISION MEDICINE

Precision medicine is an area that seeks to maximize clinical effectiveness by assigning treatment regimes tailored to individuals. In this dissertation, we present three topics that advance the methods and applications in the field of precision medicine.The first topic introduces a novel methodology termed random forest informed tree-based learning to discover underlying patient characteristics associated with differential improvement in knee osteoarthritis (OA) symptoms and to identify the individualized treatment regime (ITR) among three available treatments. The proposed algorithm suggests decision rules that divide participants into subgroups based on their characteristics. In our analysis, the estimated treatment rule yielded greater improvements in OA symptoms that could ultimately guide patients toward suitable treatment strategies.In the second topic, we propose a doubly robust estimator for patient-specific utilities and ITRs based on the inverse reinforcement framework from Luckett et al. (2021). This framework optimizes patient-utility for two outcomes by leveraging experts’ decisions on observational data. The suggested doubly robust estimator guarantees consistency even whenincorrect outcome models or incorrect propensity score models are applied, alleviating the need for exact formulation of the outcome model and improving the previous estimator. We also present asymptotic distributions for the estimators of boundary and utility functions using the newly developed indexed argmax theorem, which can be used for deriving weak convergence ofM-estimators with multiple layers.Lastly, we suggest an estimator for utilities when there are more than two treatments. Specifically, we utilize stabilized direct learning to estimate ITRs. Subsequently, we apply the inverse reinforcement framework once again to obtain an estimator for a composite outcome and the balance of the two outcomes. Also, the proposed estimator for utilities considers theheterogeneity in the variance of patients, leveraging the benefits of stabilized direct learning.Doctor of Philosoph

Six Statistical Senses

This article proposes a set of categories, each one representing a particular distillation of important statistical ideas. Each category is labeled a "sense" because we think of these as essential in helping every statistical mind connect in constructive and insightful ways with statistical theory, methodologies, and computation, toward the ultimate goal of building statistical phronesis. The illustration of each sense with statistical principles and methods provides a sensical tour of the conceptual landscape of statistics, as a leading discipline in the data science ecosystem

Doubly robust learning for estimating individualized treatment with censored data

Individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit. When the clinical outcome of interest is survival time, estimation is often complicated by censoring. We develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data. To adjust for censoring, we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model, but not both; the method is shown to be Fisher consistent when either model is correct. Furthermore, we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule. We illustrate the proposed methods using simulation study and data from a Phase III clinical trial on non-small cell lung cancer