Using Discrete Event Simulation to explore "what-if" waiting list scenarios in NHS Scotland
This publication explores the usability of the discrete event simulation method for modelling NHS Scotland planned care waiting lists, given the data available. As an initial case study the focus was on ophthalmology, and in particular cataract surgery.
Annex
Model input distributions
The Simul8 software employed in this modelling uses variables in the format of “inter-arrival times” i.e. the time there is in between new patients arriving at different points in the system. The unit used is days. As an example, if 10 patients arrive for an NOP consultation on average per day. Then the inter-arrival time would be 1/10 = 0.1 days. A list of the model input distributions is included below:
- NOP list inter-arrival times
- NOP attendance inter-arrival times
- NOP removals inter-arrival times
- NOP to TTG conversion rate
- IP inter-arrival times
- TTG removals inter-arrival times
- DC inter-arrival times
| Model input data | Simul8 distribution name | Range | Notes |
|---|---|---|---|
| NOP inter-arrival time | NOParrival | MIN: 0.000959 MAX: 0.004 MODE: 0.001398 | This is the time between patients arriving in the simulation and is based on the volume of additions to the NOP list. Triangular distribution used, set so average is average of data. |
| NOP attendance inter-arrival time | NOPConsultationDist | MIN: 0.00125 MAX: 0.00498 MODE: 0.00218 | This is the time between patients attending a consultation and is based on the volume of NOP attendances. Triangular distribution used, set so average is average of data. |
| NOP other removal rate | Average | Average: 0.00899 | The NOP other removal rate has been trending upwards consistently over the data period. Use the rate from Q2 2024 with the built-in Simul8 distribution |
| Inpatient inter-arrival time | IP attendance dist | MIN: 0.17614 MAX: 0.32718 MODE: 0.80357 | This is the time between patients attending an inpatient appointment and is based on the volume of IP attendances. Triangular distribution used, set so average is average of data. |
| Day case inter-arrival time | DC attendance dist | MIN: 0.003115 MAX: 0.0158 MODE: 0.004636 | This is the time between patients attending an inpatient appointment and is based on the volume of DC attendances. Triangular distribution used, set so average is average of data |
| TTG other removal rate | Average | Average: 0.0437 | Same principle applied to this removal rate as for NOP removal rate. |
Linear regression models for conversion rates
Linear regression models in R were used to build the conversion rate and direct TTG rate distributions for the two model versions: with and without direct TTG additions. In both cases intercepts are set to 0 as it is assumed that if there are no NOP attendances then no patients would be referred to the TTG list. It is important to note that the below conversion rates and direct TTG rates are theoretical constructs developed to explore this simulation modelling method.
Without direct TTG additions, the assumption is that TTG additions directly correlate to NOP attendances:
Only using timeseries data from March 2022 results in an estimated conversion rate of 43.7 1.3%, p<0.001. Using all available timeseries data from March 2019 results in an estimated conversion rate of 40.9 0.9%, p<0.001.
With direct TTG additions, the assumption is that TTG additions are correlated with both NOP attendances and TTG attendances:
Only using timeseries data from March 2022 results in an estimated conversion rate of 17.9 5.7% p = 0.01354, and a direct TTG rate of 74.5 16.3%, p = 0.00179. Using all available timeseries data from March 2019 results in an estimated conversion rate of 19.2 5.1% p = 0.001178, and a direct TTG rate of 65.0 15.1% p < 0.001.
Interestingly the result from the multiple linear regression of 65-75% of TTG attendances flowing back i.e. requiring an operation on the second eye, aligns with stakeholder estimates of 70%.
These coefficients and standard deviations using the timeseries data from March 2022 were used in Simul8. They were used to parametrise normal distributions from which to sample the conversion rate and direct TTG rate in different model runs.
Contact
Email: Emily.Henderson@gov.scot