Costs and consequences of using average demand to plan baseline nurse staffing levels: a computer simulation study

Background Planning numbers of nursing staff allocated to each hospital ward (the ‘staffing establishment’) is challenging because both demand for and supply of staff vary. Having low numbers of registered nurses working on a shift is associated with worse quality of care and adverse patient outcomes, including higher risk of patient safety incidents. Most nurse staffing tools recommend setting staffing levels at the average needed but modelling studies suggest that this may not lead to optimal levels. Objective Using computer simulation to estimate the costs and understaffing/overstaffing rates delivered/caused by different approaches to setting staffing establishments. Methods We used patient and roster data from 81 inpatient wards in four English hospital Trusts to develop a simulation of nurse staffing. Outcome measures were understaffed/overstaffed patient shifts and the cost per patient-day. We compared staffing establishments based on average demand with higher and lower baseline levels, using an evidence-based tool to assess daily demand and to guide flexible staff redeployments and temporary staffing hires to make up any shortfalls. Results When baseline staffing was set to meet the average demand, 32% of patient shifts were understaffed by more than 15% after redeployment and hiring from a limited pool of temporary staff. Higher baseline staffing reduced understaffing rates to 21% of patient shifts. Flexible staffing reduced both overstaffing and understaffing but when used with low staffing establishments, the risk of critical understaffing was high, unless temporary staff were unlimited, which was associated with high costs. Conclusion While it is common practice to base staffing establishments on average demand, our results suggest that this may lead to more understaffing than setting establishments at higher levels. Flexible staffing, while an important adjunct to the baseline staffing, was most effective at avoiding understaffing when high numbers of permanent staff were employed. Low staffing establishments with flexible staffing saved money because shifts were unfilled rather than due to efficiencies. Thus, employing low numbers of permanent staff (and relying on temporary staff and redeployments) risks quality of care and patient safety.

BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s) hours (proportion of staff deployed in the morning/afternoon/evening/night), the directorate number, whether the ward is an acute admissions unit and some purely descriptive information (directorate, medical or surgical).
The probabilities of requests for temporary staff being fulfilled is imported from an Excel file into another database template table. The template allows probabilities to differ between bank and agency, up to three staff types, weekend and weekday, and time period (morning, afternoon, evening, night, and over a 24-hour period).
Next, further parameter values that apply globally to the whole hospital Trust (the system) are set. These parameters relate to: (1) nursing staff requirements -acuity/dependency multipliers, specials multiplier, standard deviation of multipliers, minimum number of registered nurses needed (constraint), demand for registered nurses with a particular skill (2) permanent staff -the baseline staffing level, the data sample used to calculate the staffing level, the staff types, absence chance for each staff type, absence length, proportion of registered nurses with a particular skill (3) redeployed staff -redeployment rules, priority sequences for providing and receiving redeployed staff, efficiency of redeployed staff, redeployed staff shift length (4) temporary staff -rules for requesting temporary staff, efficiency of bank and agency staff, temporary staff shift length (5) display settings -the understaffing criterion to plot in charts, e.g. 15% or more under requirement (6) general settings -step length, round down bound used when converting required hours to requested hours.

At start of run
At the start of a run, variables tracking time (the step number and the shift number) are reset to zero. The wards, staff types and sharing groups are counted. Occupancy distributions are created from the occupancy data table. Data are placed in arrays, which are convenient structures for working with multi-dimensional data.
Then, the establishment (number of staff employed in WTE) is converted to the number of planned deployed hours per time step (6-hour-shift or day), including applying the skill mix, rounding to whole people and dealing with minimum constraints, as follows. Note that the establishment does not need to be a whole number since staff may work part-time, but the planned number of staff to deploy each six-hour shift should be a whole number. As in our other analyses we use equation 3 for converting the planned staffing in WTE to the planned total care hours per day (see Equation 3, Appendix 1, main report 1 ).
The planned skill mix (proportion of staff that are registered nurses) and distribution of staff over the day in each ward is set as the average observed for that ward. There is a constraint that there must be at least one registered nurse present on each ward, so if the registered nurse hours is under 6, this is rounded up to 6. Otherwise, the registered nurse hours are rounded up or down to the nearest six hours. The remaining planned hours are assigned to nursing support workers, and again rounded up or down to the nearest 6 hours. For example, suppose the planned nursing hours for a morning shift on a particular ward are 18, and the skill mix is 50%. This is equivalent to 9 hours of registered nurse time, which is rounded up to 12 hours. There are 6 hours left to cover which are assigned to nursing support workers.
The planned deployed hours per day (sum over the four shifts) are converted back into WTE to enable calculation of the cost of employing this number of permanent staff.

Before time-step
Before each time-step, i.e. before the simulation switches to the next period (six-hour shift or day), the variables for this period are updated. These variables are the time step, the shift (1 to 4), the day type (weekday, Saturday of Sunday/bank holiday) and the planned staffing level for this shift. The deployment array (numbers of staff from each source and of each staff type deployed on each ward in what capacity) is reset at zero ready to be filled in the next stages.

Before time-step, in each ward
Next, the required staffing for this period is calculated for each ward in turn. For this, firstly the number of patients on the ward is sampled from the occupancy distribution for that ward, day of week and shift (morning, afternoon, evening or night).
Secondly, the acuity/dependency profile is sampled from the acuity/dependency data. This is done by selecting a random observation for that ward (we assumed there were no day of week or time of day patterns). For each patient, the probability of being in each acuity/dependency category and the probability of requiring specialing are the corresponding observed proportions. The required staffing per patient (in WTE) is sampled based on the patient's acuity/dependency category and specialing requirements. This is converted into the required staffing level for this period using the skill mix, distribution of staff over the day and minimum constraints (as for the planned staffing levels), but is not rounded.

On time-step, in each ward
On the time-step, i.e. immediately when the period begins, the number of hours of staffing provided by permanent staff in this period is calculated for each ward. For this, the number of planned staff who are not unexpectedly absent (i.e. at short notice) is calculated. The chance of being unexpectedly absent can differ between staff types in the model. All these staff are allocated to their home ward to start with. The (absolute) shortfall for each staff type is calculated as required minus allocated hours. Where applicable, the simulation checks which of the registered nurses working are IV-trained (sampled probabilistically).
Similarly the spare hours (hours that could be redeployed to another ward) for each staff type is calculated. This is the allocated minus the required hours, rounded down to the nearest multiple of 'redeployed hours chunk', since staff can only be redeployed for fixed time periods.

On time-step
Next, staff are redeployed within sharing groups (directorates) to attempt to cover shortfalls for each staff type, as shown in FIGURE 2. The shortfall is rounded up or down (depending on the round down bound) to the nearest multiple of 'redeployment chunks'. Requests for extra staff are triggered if the rounded shortfall for that staff type is more than zero, and if either the total shortfall or the staff type shortfall are more than the trigger (6 hours). In order to decide the priority of redeploying extra staff to wards, lists of wards are sorted using the bubble sort algorithm 2 , which BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s) works by comparing the shortfall as a proportion of the requirement (or spare hours as a proportion of requirement) for adjacent wards in the list and swapping them if they are in the wrong order.

FIGURE 2 Summary process flow of staff redeployment
Following this, for the wards that are still requesting extra staff, for each staff type, first bank and then agency staff are requested, as shown in FIGURE 3. The hours requested are the shortfall rounded up or down (depending on the round down bound) to the nearest multiple of 'external work time'. The probability of a request for temporary staff being fulfilled depends on the staff source, staff type, whether it is a weekday or weekend and the time period.
Label first ward requesting extra staff of this staff type as "u", and first ward with enough spare nursing hours (NH) to reallocate as "s" Does "s" have at least as many spare NH as requested by "u"?
Yes. Allocate enough spare NH from "s" to "u" so that "u" reaches adequate staffing No. Allocate all spare NH from "s" to "u"

FIGURE 3 Process flow of hiring temporary staff
Then, the effective staffing on each ward, given that redeployed and temporary staff are less efficient than permanent staff, is calculated. The effective shortfall on each ward is calculated. The staffing adequacy (understaffed, adequately staffed or overstaffed) on each ward according to a range of criteria is assessed, e.g. understaffing can be measured as 'more than 15% under the requirement', 'more than one person short', etc. Depending which staffing adequacy criterion was chosen to be displayed; the state chart for each ward is updated (see Figure 1, main report 1 ). The running totals of understaffed, adequately staffed and overstaffed time periods per ward are updated, as well as the charts tracking their relative numbers. The array of the total number of staff deployed on wards from different sources and of different types is updated.

At the end of run (1 year)
At the end of each run, the total permanent staff employed (in WTE) and the number of agency and bank hours worked across the whole hospital are summed up by staff type.
The total yearly costs are calculated. For this, first the costs of employing staff and hiring temporary staff at the standard rates are calculated. Then bonuses for unsocial hours for substantive, bank and agency staff are added on.
The results of the run at both the ward and hospital level are exported to Excel.  Like-for-like. Bank before agency. Experts (hospital Trust PIs) advised that these are reasonable general rules (although will not always be true).

Efficiency
The productivity of redeployed/temporary staff Efficiency of redeployed/bank staff -90%.
Assumption. Recognises that agency staff, who work across different hospitals, will be less familiar with ward processes than BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance  Sampled with replacement from observed acuity/dependency proportions for that ward and observed specials proportions for that ward.

PLANNED SKILL MIX
The planned proportion of registered nurses for the morning, afternoon, evening and night six-hour shifts The average observed skill mix in each ward for each time period. Note that planned registered nurse/nursing support worker hours are subject to a minimum constraint of one registered nurse and rounded to the nearest six hours

REQUIRED SKILL MIX
Of the required staffing each six-hour shift on each ward, how much is required to be done by registered nurses.
The average observed skill mix in each ward for each time period but the required registered nurse/nursing support worker hours are also subject to a minimum constraint of one registered nurse (no rounding).

OVER THE DAY
The proportion of planned staffing that occurs in each sixhour shift (morning, afternoon, evening and night).
The average observed proportion of worked hours in each time period for each ward.

OVER THE DAY
The proportion of daily staffing required in each six-hour shift (morning, afternoon, evening and night).
As for planned distribution of staff over day.

Variability within acuity/dependency levels
We have no information about the shape and variability of nursing requirement distributions within acuity/dependency levels. Even with relatively small variability within acuity/dependency levels (standard deviation set at 10% of the mean) and assuming they follow symmetric distributions, the required staffing for patients in levels 1a, 1b, and 2 would overlap substantially, as shown in FIGURE 4 and even more so for a standard deviation at 25% of the mean, as shown in FIGURE 5.   Table 3 shows the empirical percentages of all requested temporary shifts (both bank and agency) that were filled by bank staff at hospital Trust B, i.e. assumes that bank staff were asked first. Morning shifts are those that start between 7am-1pm, afternoon between 1pm-7pm, evening/night between 7pm-7am. Table 4 shows the percentage of empirical percentages of agency requests that were filled at hospital Trust B. We did not have equivalent data for the other hospital Trusts.  This allows a buffer of 15 per cent either side of the estimated requirement within which staffing is considered adequate, as is also done in the RAFAELA tool. 5 We consider patient shifts rather than shifts in order to estimate how many understaffed shifts individual patients are exposed to. We express the understaffed patient shifts (the sum of the occupancies at the start of each understaffed shift) as a percentage of the total patient shifts (the sum of the occupancies at the start of each shift).

Cost per patient day
The annual staffing cost divided by the number of patient shifts, multiplied by four (in our model there are four six-hour shifts in a day).

Other performance measures Ward establishments
The number of staff employed on each ward under a particular scenario. Measured in whole time equivalents. Percentage of hours worked by redeployed/bank/ agency staff Percentage overstaffed patient shifts We say a shift is 'overstaffed' if the total effective staffing (i.e. accounting for the lower efficiencies of temporary and redeployed staff) is more than 15% over the estimated requirement according to the SNCT for the shift. Percentage of patient shifts with no intravenous-trained registered nurse Used only for the scenario looking at intravenous (IV)-trained nurses.

Alternative understaffing criteria
Percentage patient shifts with absolute understaffing 'Absolute understaffing' means the total effective staffing is less than the estimated requirement for the shift.
Percentage patient shifts with at least one person short 'At least one person short' means the total effective staffing is at least six hours below the estimated requirement for the shift. Percentage patient shifts with registered nurse shortfall 'Registered nurse shortfall' means the effective registered nurse staffing is less than 85% of the estimated registered nurse requirement for the shift. Percentage patient shifts with nursing support worker shortfall 'Nursing support worker shortfall' means the effective nursing support worker staffing is less than 85% of the estimated nursing support worker requirement for the shift. Percentage patient shifts with both 'Both' means there is both 'registered nurse shortfall' and 'nursing support worker shortfall' on this shift. Percentage patient shifts with either 'Either' means there is either 'registered nurse shortfall 'or 'nursing support worker shortfall' on this shift.

Trace
Used a simulation language so simulation debugger picked up most errors in the language. CS checked for problems with e.g. array sizes by tracing through calculations.

MODEL PROGRAMMED CORRECTLY
Animation, operational graphics, trace Animation of numbers of staff from each source used to show whether redeployments working correctly.
Operational graphics of understaffed/overstaffed wards over time used to quickly spot errors, e.g. all wards understaffed.
Put in actual staffing levels, occupancy and acuities. Compared understaffed shifts output of simulation with actual understaffed shifts.

Trace
Used standard Anylogic in-built RNG so has already been tested for correctness, so just needed to check that sampling was working correctly in our model.

Yes High
BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Face validity was tested and variability between run results was low.

DATA VALIDITY
Data sufficiently valid -improving data validity further unlikely to impact conclusions Outliers were removed, although it is hard to distinguish between valid and invalid outliers. Inter-rater-reliability between SNCT ratings was high.