Decision-Making in Radiation Therapy in the Presence of Uncertainties

Uncertainties degrade outcomes from decision-making models. In intensity modulated radiation therapy (IMRT) for cancer treatments, uncertainties lead to treatment failures, directly impacting a patient\u27s life. Robust methods mitigate the chances of treatment failures by producing clinically acceptable treatments, even under worst-case scenarios. In this thesis, we develop robust and adaptive optimization models to overcome spatiotemporal and biological uncertainties in a patient\u27s anatomy, that occur during IMRT treatments. The set of developed robust decision-making methodologies are independent of application, and, therefore, can be readily translated to other fields. First, we report significant variations in treatment outcomes as a result of subjective preferences in decision-making. Using robust statistical estimators, we quantify the direct impact of violating or satisfying clinical constraints. Furthermore, we observe competing objectives in clinical protocols established internationally and institutionally. This study demonstrates a need for a unifying set protocols in IMRT plan evaluation, alleviating subjective preferences, and thus making the clinical decision-making process more certain. Second, we developed a robust methodology that can incorporate uncertainties in quality of data, to address spatiotemporal changes in a patient\u27s anatomy during IMRT treatments. Specifically, the robust model optimally employs high-quality, low-quantity spatiotemporal data and low-quality, high-quantity spatiotemporal data, based on the expert\u27s knowledge, empirical models, or historical cases. At times, the robust method improved organ sparing by $18\%$ and $29\%$, for two distinctive lung cancer cases, compared to conventional methods. When uncertainties were encountered, the robust method remained within $19\%$ of nominal dose to target, even in the worst-case. Finally, we address evolving uncertainties through an adaptive optimization framework. Considering uncertainties on evolving processes, we construct time-dependent uncertainty sets on a generic linear program. The uncertainty set description is adapted during the process through the proposed conic two-stage robust linear program. We apply this method to overcome uncertainties in biological changes within the tumor. The robust method improved dose to tumor by $9\%$ on average under nominal and extreme conditions. In the very worst-case, the robust method outperformed other methods by $4\%$ on average. Additionally, through numerical computations we identify optimal adaptation strategies to best improve organ sparing