Q:

Why are risk days calculated differently for "Admissions" (patients are at risk only for the time not spent in the hospital) and "Unadjusted average days in the hospital per patient year" (patients are at risk whether or not they are in the hospital)?

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For the "Admissions" figure, patients are considered to be at risk only when they are not in the hospital because while the patient is in the hospital, they cannot be at risk for entering the hospital (theyre already there!). However, time in the hospital are counted as days at risk for "Unadjusted average days in the hospital per patient year" because while a patient is in the hospital, they are at risk for staying in the hospital for an additional day.  more
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