Signature
C_adm = L_bar * c_bd
| Inputs | Definition | Unit |
|---|---|---|
L_bar | Mean length of stay of the admissions costed, the arithmetic mean | days per admission |
c_bd | Cost of one bed day, averaged over all days of a stay | currency per bed day |
C_adm | Cost of one admission | currency per admission, in a stated price year |
|---|
Function
Average length of stay calculation and bed-day costing function
Maps the bed-days and discharges of a period to the average length of stay (ALOS), and relates length of stay to bed capacity, payment trim points, a case-mix adjusted comparison and the cost of an admission or of a change in stay. The records follow the notation of the Average Length of Stay article, where L_bar is the average stay in days and N the number of discharges.
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Implementations
Excel
Top-down cost per admission in one cell
Excel multiplies the named ALOS cell by the named cost per bed day cell.
=ALOS*CostPerBedDay
Assumptions
Every day of the stay costs the same
The formula treats the first and last days of an admission as equally costly. Taheri and colleagues found the last full day averaged US$420, 2.4% of a mean total cost of US$17,734, so the product suits average costing, not the cost of a day more or less.
Worked examples
Illustrative stroke admission at Hospital B
Illustrative figures: a stroke ALOS of 14 days at an average £450 per bed day gives a top-down cost of £6,300 per admission.
L_bar = 14; c_bd = 450; C_adm = 6300
Common errors
Costing admissions with the median length of stay
Illustrative figures: five stays of 2, 3, 3, 4 and 18 days have a mean of 6 and a median of 3. At £450 a day, the mean gives £13,500 for the five, the true total for 30 bed-days, while the median gives £6,750, half of it. Only the mean scales to a budget.
Sources
Arithmetic mean for costing despite skewness
Thompson SG, Barber JA. How should cost data in pragmatic randomised trials be analysed? BMJ. 2000;320:1197-1200. Summary points: despite skewness the arithmetic mean is the most informative measure, because other measures do not give the cost of treating all patients.
Incremental cost of the last day of an admission
Taheri PA, Butz DA, Greenfield LJ. Length of stay has minimal impact on the cost of hospital admission. Journal of the American College of Surgeons. 2000;191(2):123-130. Abstract: cost-accounting records of 12,365 surviving patients, with the last full day averaging US$420, 2.4% of the mean total cost.
Canonical Identity
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