application of covid-simr function to data from an unnamed hospital as used for covid-19 response planning
R
covid-simr
simple script to generate a projection of deaths arising from insufficent acute/ICU capacity for a given trajectory of covid19 cases requiring hospitalisation, and to model the effect of various user-defined mitigating scenarios
This function outputs per day and cumulative estimates of hospital admissions, occupancy, and deaths arising from insufficient capacity given i) expected number of hospitalisations over time, and ii) detail on expected length of stay distribution
Separate use of this tool is envisaged for the impact of given capacity and hospitalisation estimates for ICU and general acute beds, as well as resources like ventilators
For each use, provide the demand (i.e. number of hospitalisations) and information pertaining to LOS for that service being considered
It is complemented by a separate tool (INSERT NAME/LINK HERE - covid19_reqd_beds_projection https://github.com/nhs-bnssg-analytics/covid19-reqd-beds-projection) which can be used to estimate how many beds are required to meet given estimates of the same input parameters
INPUTS
The user must input the expected hospitalisations over time
These can relate to ICU beds, general beds, community beds, etc
The corresponding expected length of stay detail is also entered
This consists of median length of stay and the 95th quantile
A given hospital capacity is also entered (as a non-negative integer)
As is a probabilty that patients who cannot be admitted will die (as a number in the range 0 [all survive] to 1 [all die])
Additionally an optional tolerance can be placed around the expected hospitalisations in order to represent uncertainty
The effect of this on the expected hospitalisations can be seen in the bands on the outputs plot (see later)
ENGINE
Simulates the arrival and lengths of stay through sampling from the Poisson and lognormal distributions respectively
Note the Poisson rate parameter (taken from expected hospitalisations by day) is scaled normally according to selected tolerance (if optionally configured). At a maximum tolerance value of 100 (representing the greatest uncertaintly in the orignal point estimates), the daily arrivals will be scaled within approximately a range between 1/10 times and 2 times (with the majority of the results within half and 1.5 times) the original estimate.
The lognormal ditribution parameters are from (automatically) matching quantiles using the exact formulae
The effect of capacity constraint is estiamted by using the Poisson arrival estimates to create a continuous schedule of attempted arrivals over the simulated period, tracking the current occupancy of the hospital during that period, and "rejecting" attempted arrivals if all hospital beds (the user-input hospital capacity) are occupied at that time. "Rejected" patients die at the rate specified by the user.
OUTPUTS
A table of results for expected number of deaths arising from insufficent capacity by day is output, including mean, median and various quantiles
The table also includes outputs in the same format for pateints refused a bed who survived, and occupancy
A PDF containg a grid of six plots showing (i) cases per day requiring hospitalisation, (ii) occupied beds per day, (iii) deaths resulting from insufficient capacity per day, (iv) cumulative number of admitted patients, (v) cumulative total of patients who could not be admitted but survived, and (vi) cumulative total of patients who died because they could not be admitted
Each of these plots includes shaded bands showing confidence estimates for these values
The also includes the bands for the normally-distributed tolerance on the (inputted) expected hospitalisations (if optionally configured)
Bands represent a 40% chance of being in the central band and 30%, 20%, 5% and 3% in the (paired) outer bands (with 2% not displayed)
FUNCTION ARGUMENTS
'cases' must be a data.frame containing daily hospitalisation numbers (column 2 'hospitalisations') over the considered date range (column 1 'dates')
'los_median' is the median length of stay (LOS) for hospitalised cases (in days)
'los_95' is the 95th quantile of LOS, i.e. the LOS (in days) such that only 1 in 20 of patients experience a greater duration
'cap' is the number of beds (acute or ICU) for which occupancy cannot be exceeded
'pfat' is the probabilty that a patient who cannot be admitted dies (a number in the range 0 to 1, e.g. 0.5 corresponds to a 50% chance, 0.75 to a 75% chance, 1 to all patients who cannot be admitted dying)
'tol' is an optional tolerance parameter (default 25) which can be flexed to represent a level of uncertainty around the case projection (range 0 to 100)
'nreps' is the number of simulation replications (more reps, greater accuracy, but takes longer)