Works out how many admissions a given average daily population and average length of stay imply over a period. Published statistics often give the population held and the average stay but not the number admitted (or the other way round); this recovers the missing quantity from the identity that links all three.
Value
A numeric scalar: the implied number of admissions over the
period, \(\mathrm{adp} \times t / \mathrm{alos}\). It is not rounded.
It has class c("rmbl_admits", "rmbl_measure", "numeric") and an
attribute "lakner" (adp, alos and t), so it
prints as a box with its inputs, formula and caveats; arithmetic,
round(), sum(), mean(), [, c() and
as.numeric() give a plain number.
Details
Rearranging the identity \(\bar{X}_{hc} = N_a \bar{X}_t / t\) (Lakner 1976, p.18-20) for \(N_a\). Useful when two of the three quantities are published and the third is not. The identity holds exactly only in a steady state (admissions and stays roughly constant across the period); with a population that is growing or shrinking quickly the result is an approximation.
Errors when any argument is not numeric, is NA or Inf, is
not positive, or has more than one value.
Examples
# Lakner (p.20) runs this the other way: t = 365, an average daily
# population of 25 and 1,750 admissions imply a stay of 5.2 days.
alosimplied <- 25 * 365 / 1750
round(alosimplied, 1)
#> [1] 5.2
# and back again
admits(25, alosimplied)
#> ╭── Admissions implied by stock and stay ─────────────────────────────────────╮
#> │ Admissions 1,750 over the period │
#> │ Average daily population 25 │
#> │ Average stay 5.214 days │
#> │ Period 365 days │
#> │ Formula admits = adp x t / alos = 25 x 365 / 5.214 │
#> │ │
#> │ 25 held on an average day, staying 5.214 days each, imply 1,750 │
#> │ admissions over 365 days. │
#> │ │
#> │ Lakner (1976, p.18-20): adp = admissions x alos / t is exact only in │
#> │ a steady state; with a population growing or shrinking quickly the │
#> │ result is an approximation. It is not rounded. │
#> ╰─────────────────────────────────────────────────────────────────────────────╯
# a 90-day quarter with 40 held on average and a 12-day average stay
admits(40, 12, t = 90)
#> ╭── Admissions implied by stock and stay ─────────────────────────────────────╮
#> │ Admissions 300 over the period │
#> │ Average daily population 40 │
#> │ Average stay 12 days │
#> │ Period 90 days │
#> │ Formula admits = adp x t / alos = 40 x 90 / 12 │
#> │ │
#> │ 40 held on an average day, staying 12 days each, imply 300 admissions │
#> │ over 90 days. │
#> │ │
#> │ Lakner (1976, p.18-20): adp = admissions x alos / t is exact only in │
#> │ a steady state; with a population growing or shrinking quickly the │
#> │ result is an approximation. It is not rounded. │
#> ╰─────────────────────────────────────────────────────────────────────────────╯
# an average stay of zero is refused
try(admits(25, 0))
#> Error : admits: `alos` must be positive