| Summary: | Hospital length of stay (LOS) is often used as a reliable proxy for measuring the consumption of hospital resources. However, the empirical distribution of LOS is established to be highly skewed with a heavy right tail. This makes the applications of simple statistics, such as averaging, to LOS for measuring and planning of hospital resources unrealistic.
This project seeks to find a sound and correct mathematical model of hospital LOS. Such a model would be the basis for a robust estimation of resource consumption, it will also assist the strategic planning of hospital facilities. In addition, the project also aims at identifying the significant factors that influence the probability of stay of a patient. Such knowledge will add more advantage to the health care administration. The project was carried out primarily using the R programming language and environment for statistical computing. It employed the the established methodologies of survival analysis to find out the significant factors of LOS. For the group of stroke patients discharged from the Singapore General Hospital (SGH) in the period of 2004–2007, the factors identified are: patient’s age, race, admission type and discharge class. A competing risks model was applied to reveal the different patterns of stay corresponding to different discharge groups.
Several models were tested on the data. Coxian phase-type model, a special type of Markov chain, was finally chosen to model the LOS data of this group of patients. This model fitted the data well based on high R2 and other information theoretic scores and could adequately explain the stochastic process of hospital stay. When using the model to fit yearly data, probability of discharge per phase for each year was calculated and compared with one another. In this study, a trend of LOS has emerged: the probabilities of discharge from early phases are getting smaller while the probabilities of discharge from later phases are growing over the years. This recent trend, however short, would be meaningful for the hospital planning.
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