Stochastic models and data driven simulations for healthcare operations

Abstract

This thesis considers problems in two areas in the healthcare operations: Kidney Paired Donation (KPD) and scheduling medical residents in hospitals. In both areas, we explore the implications of policy change through high fidelity simulations. We then build stochastic models to provide strategic insight into how policy decisions affect the operations of these healthcare systems. KPD programs enable patients with living but incompatible donors (referred to as patient-donor pairs) to exchange kidneys with other such pairs in a centrally organized clearing house. Exchanges involving two or more pairs are performed by arranging the pairs in a cycle, where the donor from each pair gives to the patient from the next pair. Alternatively, a so called altruistic donor can be used to initiate a chain of transplants through many pairs, ending on a patient without a willing donor. In recent years, the use of chains has become pervasive in KPD, with chains now accounting for the majority of KPD transplants performed in the United States. A major focus of our work is to understand why long chains have become the dominant method of exchange in KPD, and how to best integrate their use into exchange programs. In particular, we are interested in policies that KPD programs use to determine which exchanges to perform, which we refer to as matching policies. First, we devise a new algorithm using integer programming to maximize the number of transplants performed on a fixed pool of patients, demonstrating that matching policies which must solve this problem are implementable. Second, we evaluate the long run implications of various matching policies, both through high fidelity simulations and analytic models. Most importantly, we find that: (1) using long chains results in more transplants and reduced waiting time, and (2) the policy of maximizing the number of transplants performed each day is as good as any batching policy. Our theoretical results are based on introducing a novel model of a dynamically evolving random graph. The analysis of this model uses classical techniques from Erdos-Renyi random graph theory as well as tools from queueing theory including Lyapunov functions and Little's Law. In the second half of this thesis, we consider the problem of how hospitals should design schedules for their medical residents. These schedules must have capacity to treat all incoming patients, provide quality care, and comply with regulations restricting shift lengths. In 2011, the Accreditation Council for Graduate Medical Education (ACGME) instituted a new set of regulations on duty hours that restrict shift lengths for medical residents. We consider two operational questions for hospitals in light of these new regulations: will there be sufficient staff to admit all incoming patients, and how will the continuity of patient care be affected, particularly in a first day of a patients hospital stay, when such continuity is critical? To address these questions, we built a discrete event simulation tool using historical data from a major academic hospital, and compared several policies relying on both long and short shifts. The simulation tool was used to inform staffing level decisions at the hospital, which was transitioning away from long shifts. Use of the tool led to the following strategic insights. We found that schedules based on shorter more frequent shifts actually led to a larger admitting capacity. At the same time, such schedules generally reduce the continuity of care by most metrics when the departments operate at normal loads. However, in departments which operate at the critical capacity regime, we found that even the continuity of care improved in some metrics for schedules based on shorter shifts, due to a reduction in the use of overtime doctors. We develop an analytically tractable queueing model to capture these insights. The analysis of this model requires analyzing the steady-state behavior of the fluid limit of a queueing system, and proving a so called "interchange of limits" result.