Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Engineering (PhD)

Degree Level



Industrial Engineering


Shengfan Zhang

Committee Member

Haitao Liao

Second Committee Member

Chase E. Rainwater

Third Committee Member

Qingyang Zhang


Health Care, Markov Decision Process, Prediabetes, Quantile Regression, Statin, Transition Probabilities


This dissertation develops quantitative models to support medical decision making of statininitiation considering the uncertainty in disease progression for prediabetes patients. A mathematical model is built to help medical decision-makers take action of statin initiation under uncertainty in future prediabetes progressions. The association between cholesterol drug use, such as statin, and elevating glucose level attracted considerable amounts of attention in the literature. Statin effects on glucose vary with respect to different levels of glucose. The first chapter of this dissertation introduces the problem and an overview of the tools that will be used to solve it. In the second chapter of this dissertation, we use quantile regression to investigate the statin effects on different glucose quantiles. The third chapter is devoted to address the problem of estimating transition probabilities for the prediabetes populations for different levels of lipid ratios (i.e., ratios of total cholesterol to high-density lipoprotein) from cross-sectional data. We also show the risk of prediabetes as a function of age using a Bayesian approach. These parameters are used in the implementation of the Markov Decision Process (MDP) to estimate the best point in time, i.e., age to start statin treatment, which is discussed in the fourth chapter of the dissertation. Parameter estimation plays a crucial role in our model. Therefore, our fifth problem to tackle is to provide the optimal policy for statin initiation by considering stochastic progression under uncertainty for lipid ratio transition probabilities. A robust MDP problem is formulated and an optimal policy for statin initiation is provided. Structural properties of the robust MDP problem are proved. Additionally, sufficient conditions for the existent of robust MDP are introduced.