Fitting a Stochastic Model of Intensive Care Occupancy to Noisy Hospitalization Time Series
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Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. To reliably forecast this occupancy, the rate at which patients are admitted to hospitals and intensive care units (ICUs) and the rate at which patients leave ICUs are crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to be able to estimate these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data, and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find through rigorous model selection that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics, and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.
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