Precision medicine has undergone substantial theoretical advancements spanning various levels of human health, from cellular subtyping to the development of individualized dynamic treatment regimes (DTRs), decision rules that map patient states to treatments optimized for desired health outcomes. Dr. Zikry will describe methodologies created for precision medicine in both micro and macro domains: (1) the characterization of proteomic signatures driving resistance in ER+/HER2- breast cancer treatments, and (2) the learning of optimal DTRs under resource constraints. In domain (1), Dr. Zikry first details a novel framework for characterizing subpopulations of cells that evade treatment-mediated cell cycle arrest. Identifying regulators of cell cycle plasticity could enhance therapies targeting fractionally resistant cells and improve patient outcomes. In the second project, Dr. Zikry leverages spherical manifold approximations to represent the cell cycle in a new paradigm, suggesting that significant changes in manifold structures correspond to distinct cell cycle responses to cancer treatments. He establishes an empirical hypothesis testing method to directly quantify differences in these manifolds across treatments. In domain (2), Dr. Zikry estimates optimal DTRs under resource constraints via the approximation of surrogate action-value and cost functions. Crucially, this work accounts for the impact of resource allocation on the health and disease progression of patients treated in the future and proves optimal properties using empirical process theory. Collectively, the proposed projects seek to further the inherent goals of precision medicine and the advancement of public health.