Modelling mortality and discharge of hospitalized stroke patients using a phase-type recovery model

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.