Applications of Decision Analysis to Health Care
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This dissertation deals with three problems in health care. In the first, we consider the incentives to change prices and capital levels at hospitals, using optimal control under the assumption that private payers charge higher prices if patients consume more hospital services. The main results are that even with fixed technology, investment and prices exhibit explosive growth, and that prices and capital stock grow in proportion to one another. In the second chapter, we study the flow of nosocomial infections in an intensive care unit. We use data from Cook County Hospital, along with numerous results from the literature, to construct a discrete event simulation. This model highlights emergent properties from treating the flow of patients and pathogens in one interconnected system, and sheds light on how nosocomial infections relate to hospital costs. We find that the system is not decomposable to individual systems, exhibiting behavior that would be difficult to explain in isolation. In the third chapter, we analyze a proposed change in diversion policies at hospitals, in order to increase the number of patients served, without an increase in resources. Overcrowding in hospital emergency departments is caused in part by the inability to send patients to main hospital wards, due to limited capacity. When a hospital is completely full, the hospital often goes on ambulance diversion, until some spare capacity has opened up. Diversion is costly, and often leads to waves of diversions in systems of hospitals, a situation that is regarded as highly problematic in public health. We construct and analyze a continuous-time Markov chain model for one hospital. The intuition behind the model is that load-balancing between various hospitals in a metro area may hinder full congestion. We find that a more flexible contract may benefit all parties, through the partial diversion of federally insured patients, when a hospital is very close to full. Discrete event simulation models are run to assess the effect, using data from DeKalb Medical Center, and also to show that in a two-hospital system, more federally insured patients are served using this mechanism.