Abstract
We model the length of in-patient hospital stays due to stroke and the mode of discharge using a phase-type stroke recovery model. The model allows for three different types of stroke: haemorrhagic (the most severe, caused by ruptured blood vessels that cause brain bleeding), cerebral infarction (less severe, caused by blood clots) and transient ischemic attack or TIA (the least severe, a mini-stroke caused by a temporary blood clot). A four-phase recovery process is used, where the initial phase depends on the type of stroke, and transition from one phase to the next depends on the age of the patient. There are three differing modes of absorption for this phase-type model: from a typical recovery phase, a patient may die (mode 1), be transferred to a nursing home (mode 2) or be discharged to the individual’s usual residence (mode 3). The first recovery phase is characterized by a very high rate of mortality and very low rates of discharge by the other two modes. The next two recovery phases have progressively lower mortality rates and higher mode 2 and 3 discharge rates. The fourth recovery phase is visited only by those who experience a very mild TIA, and they are discharged to home after a short stay. The novelty of our approach to phase representation is two-fold: first, it aligns the phases with labelled diagnosis states, representing stages of illness severity; second, the model allows us to obtain expressions for Key Performance Indicators that are of use to healthcare professionals. This allows us to use a backward estimation process where we leverage the fact that we know the phase of admission (the diagnosis), but not which phases are subsequently entered or when this happens; this strategy improves both computational efficiency and accuracy. The model has clear practical value as it yields length of stay distributions by age and type of stroke, which are useful in resource planning. Also, inclusion of the three modes of discharge permits analyses of outcomes.
Highlights
Due to the debilitating nature of a stroke and complex makeup of the disease there is an urgent need for stochastic models that can be used for bed occupancy analysis, capacity planning, performance modeling and prediction, with a view to decreasing patient delays, better use of resources, and improved adherence to targets.Department of Statistical & Actuarial Sciences, Western University, London, Ontario, N6A 5B7, CanadaSchool of Computing & Information Engineering, Ulster University, Coleraine BT52 1SA, UKModeling length-of-stay (LOS) in hospital is an important aspect of characterising patient stay in hospital and outcomes in the form of discharge destinations
For TIA patients, we see that the likelihoods of death and discharge to nursing home increase with age, and the likelihood of discharge to usual residence decreases with age
We have developed a phase-type modelling approach with particular applicability to stroke patient care
Summary
Due to the debilitating nature of a stroke and complex makeup of the disease there is an urgent need for stochastic models that can be used for bed occupancy analysis, capacity planning, performance modeling and prediction, with a view to decreasing patient delays, better use of resources, and improved adherence to targets.Modeling length-of-stay (LOS) in hospital is an important aspect of characterising patient stay in hospital and outcomes in the form of discharge destinations. We focus on using accessible administrative data routinely collected at discharge Such data, which include information on patient date of birth, date of admission, diagnosis and discharge date, are not appropriate for patient prognostication but can rather be aimed towards supporting planning, service organization, and allocation of resources (see, for example, Shahani et al [20], Faddy and McClean [5], Marshall and McClean [12] and McClean and Millard [14]). Heterogeneity of patient pathways and LOS characteristics have been investigated by a number of authors Such heterogeneity arises from a number of sources, for example, method of admission, diagnosis, severity of illness, age, gender, and treatment (see, for example, [6, 9, 10, 13]). Such covariates have previously been incorporated into phasetype models via conditional phase-type models by Marshall and McClean [12], a Coxian proportional hazards approach [5] and classification trees [9]
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