Fit a length of stay survival curve from observed admissions and census

Recovers P(LOS > d) by deconvolving an observed admissions and census time series. Use this when you have last season's admissions and census time series and want a data driven LOS for fcast_census(). If you do not have such data, use spec_los() with literature priors instead.

Usage

fit_los(data, family = "negbin", max_stay = 50, skip = max_stay)

Arguments

data: Data frame with one row per time step and two numeric columns: admissions (observed admissions at that time step) and census (observed census at that time step).
family: Character. LOS distribution family to fit. One of "negbin", "normal", "lognormal", "geometric" (same set as spec_los()). Default "negbin".
max_stay: Integer. Longest LOS modelled, in time step units of the data. The returned survival vector has length max_stay + 1. Default 50.
skip: Integer. Number of time steps at the start of the series to ignore in the loss. Their census depends on admissions before the observation window, which we do not see. Default max_stay.

Value

A numeric vector of length max_stay + 1 giving P(LOS > d) for d = 0..max_stay, of class los_fit. Drops directly into fcast_census(). Fitted parameters and family are attached as attributes.

Details

If instead you have a line list (one observed length of stay per patient), you do not need fit_los(). Build the empirical survival from the vector directly and pass it to fcast_census(): surv <- 1 - stats::ecdf(los_values)(0:max_stay).

Examples

set.seed(1)
true_surv <- spec_los("negbin", mu = 3, k = 2, max_stay = 30)
admissions <- rpois(120, 20)
census <- stats::convolve(admissions, rev(true_surv), type = "open")[
  seq_along(admissions)
]
fit <- fit_los(
  data.frame(admissions = admissions, census = census),
  family = "negbin", max_stay = 30
)
attr(fit, "params")
#>       mu        k 
#> 2.999999 1.999998