Data-Driven Optimization for Individualized Medical Decision-Making in Cancer

Abstract

Cancer is one of the leading causes of death in many countries, including the United States. Medical decision-making in cancer detection and treatment is often a challenging engineering problem for three reasons: the unobservable nature of the cancer state, the trade-off between alternative detection and treatment policies, and the patient heterogeneity in disease progression and clinical effectiveness. In this thesis, we take a holistic approach on data-driven optimization methods for individualized medical decision-making in cancer via three studies, in the context of active surveillance for prostate cancer.

In the first study, we develop a hidden Markov model to describe the stochastic process of cancer progression and diagnosis tests dynamics in four major studies. The model is subsequently used as the basis for simulation models to evaluate different published biopsy protocols. In the second study, we propose a finite-horizon partially observable Markov decision process (POMDP) to optimize the timing of biopsies for each individual patient. We develop two fast approximation algorithms to solve the proposed model, and show some important properties of the optimal biopsy policy. This study also considers the impact of parameter ambiguity caused by the variation across different clinical studies and patients' preferences. In the third study, we propose a new multi-model POMDP to address the issue of parameter ambiguity in POMDPs. We analyze the mathematical structure of the model, solution algorithms, and we present numerical results demonstrating the benefits of the Multi-model partially observable Markov decision processes (MPOMDP). Finally, we summarize the most important findings from this dissertation.