Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - Nov 2019)
This thesis comprises three chapters with applications of stochastic optimization models to vascular access planning for patients with chronic kidney disease (CKD). Hemodialysis (HD) is the most common treatment for patients with end-stage renal disease, the last stage of CKD. There are two primary types of vascular accesses used for HD, arteriovenous fistula (AVF), and central venous catheter (CVC). An AVF, which is created via a surgical procedure, is often considered the gold standard for delivering HD due to better patient survival and higher quality of life. However, there exists a preparation lead-time for establishing a functional AVF since it takes several months to know whether the surgery was successful, and a majority of AVF surgeries end in failure. In this thesis, we address the question of whether and when to perform AVF surgery on patients with CKD with the aim of finding individualized policies that optimize patient outcomes. In Chapter 2 we focus on vascular access planning for HD dependent patients. Using a continuous-time dynamic programming model and under data-driven assumptions, we establish structural properties of optimal policies that maximize a patient's probability of survival and quality-adjusted life expectancy. We provide further insights for policy makers through our numerical experiments. In Chapter 3 we develop a Monte-Carlo simulation model to address the timing of AVF preparation for progressive CKD patients who have not yet initiated HD. We consider two types of strategies based on approaches suggested in recently published guidelines. We evaluate these strategies over a range of values for each strategy, compare them with respect to different performance metrics (e.g., percentage of patients with an unnecessary AVF creation), and provide policy recommendations. Our simulation results suggest that the timing of AVF referral should be guided by the individual rate of CKD progression. Motivated by our findings in Chapter 3, we develop a dynamic programming model in Chapter 4 that incorporates patient heterogeneity in disease progression when making clinical decisions. We then apply this modeling framework to the case of the AVF preparation timing problem introduced in Chapter 3 and provide recommendations that consider patient heterogeneity in CKD progression.
This thesis comprises three chapters with applications of the stochastic optimization models in healthcare as a central theme. The first chapter considers a patient screening problem. Patients on the kidney transplant waiting list are at higher risk for developing cardiovascular disease (CVD), which makes them ineligible for transplant. Therefore, transplant centers screen waiting patients to identify patients with severe CVD. We propose a model for finding screening strategies, with the objective of minimizing sum of the expected screening cost and the expected penalty cost associated with transplanting an organ to an ineligible patient. Our results suggest that current screening guidelines, which are only based on patients' risk for developing CVD, are significantly dominated by policies that also consider factors related to patients' waiting time.In the second chapter, we extend our results from the first chapter to the case of inspecting a vital component which is needed at a random future time when an emergency occurs. If the component is not operational at that time, the system incurs a large penalty, which we want to avoid through inspections and replacements. We propose a model and solution algorithm for finding an inspection policy that minimizes the infinite horizon discounted expected penalty, replacement, and inspection costs. We also discuss other structural properties of the solution, as well as insights based on numerical results. In the third chapter, we consider inventory decisions regarding issuing blood in a hospital. This research is motivated by recent findings in medicine that the age of transfused blood can affect health outcomes, with older blood contributing to more complications. Current practice at hospital blood banks is to issue blood in order from oldest to youngest inventory, so as to minimize shortage. However, the conflicting objective of reducing the age of blood transfused requires an issuing policy that also depends on the inventory of units of different ages. We propose a model that balances the trade-off between the average age of blood transfused and the shortage rate. Our numerical results suggest we can significantly reduce the age of transfused blood with a relatively small increase in the shortage rate.
Master's Student Supervision (2010 - 2018)
Red blood cells (RBCs) are the most common type of blood cells and the primary means of delivering oxygen throughout the body. They are perishable with a permitted storage time of forty-two days in Canada and in the United States. RBCs undergo a series of pathological changes while in storage. These pathological changes are known as storage lesions, and they have a negative impact on the amount of oxygen delivered to the tissue during transfusion. As a result, many studies have been conducted on the age of blood used in transfusion to patient outcomes over the past two decades. Although conflicting results have been found, most studies find that the age of blood used in transfusion plays a role in disease recurrence and mortality. Therefore, we are interested in studying hospital blood issuing policies, and in finding ones that can minimize hospital blood shortages and wastages while reducing the age of blood used in transfusion. In this thesis, we first formulate our problem as a Markov Decision Process (MDP) model, and find optimal policies that minimize blood shortages, wastages, and age of blood used in transfusion, individually. We then use simulation to compare eleven policies, including a Myopic policy derived from the MDP model. We find policies that minimize the average expected total cost of blood shortages, wastages, and age of blood used in transfusion for various shortage and wastage costs. We also perform sensitivity analyses of total costs with respect to varying threshold and cost parameters.