Using Discrete Event Simulation to explore "what-if" waiting list scenarios in NHS Scotland

Cataract case study results

Improving our understanding of the system: direct TTG additions

One of the benefits of the DES modelling approach is that it is straightforward to update and re-validate the model as learning about the system, or process, develops. In relation to the cataract case study we initially set the model up in the simple mode where all TTG additions arrive following an NOP consultation. Some health boards allow individuals requiring cataract surgery in both eyes to re-join the TTG waiting list after surgery on one eye – the “direct TTG additions” previously described in the Modelling definitions section. To capture this the model was then expanded to also include the second mode with the direct TTG dynamics.

The model was updated to be able to capture this new flow of patients going from day case surgery directly to the TTG list for their second eye. The corresponding theoretical conversion rate and direct TTG rate were estimated using a multiple linear regression model (see Annex). The model can now be run in two different modes: a mode with no direct TTG additions, and a mode with direct TTG additions.

The mode with no direct TTG additions could be more reflective of an ophthalmology patient journey if immediate sequential bilateral cataract surgeries were the standard approach. That is, if individuals that require cataract surgery in both eyes, had the surgery in both eyes at the same time and so these individuals would not need to re-join the TTG list and wait for a second time. The mode with direct TTG additions is assumed to be more reflective of the ophthalmology patient journey if all health boards used the direct TTG process. It is likely that the reality in Scotland sits somewhere in between these two modes.

The mode with direct TTG additions had new distributions estimated for the conversion rate, and the direct TTG rate. It was therefore necessary to validate and verify this model version as well. Figure 3 shows that this new model version with direct TTG additions aligns very well with the no direct TTG version. The averages for the two model versions are nearly equal. The main difference is that the model with direct TTG has much wider standard deviation, as shown with the ribbons. This increased uncertainty in the TTG list projection is due to the addition of another distribution with its own uncertainty to the model i.e. the distribution for the direct TTG rate.

Figure 3 : Including direct TTG additions does not significantly change the baseline output.

Verifying and validating the model mode with direct TTG additions compared to the actuals. The model mode with no direct TTG is included for direct comparison. Both model mode projections for the TTG list size are the average of 30 runs and are overlapping. The shaded areas bounded by lines represent the standard deviation.

Process change scenario: impact of direct TTG additions

The two simulation modes, with and without direct TTG additions, output very similar average projections for the TTG list size when the rest of the process continues with no changes. A scenario was therefore devised to explore the impact of the system design when there are activity changes. The simulated scenario increased cataract surgical activity while holding everything else constant. This assumes that changing surgical activity has no impact on the conversion rate or the direct TTG rate.

A very high level of surgical activity was chosen to stress test the process change. The same activity level was explored using both simulation modes, to gauge the impact that the new flow could have on the TTG waiting list size reduction .

The simulation was set up to begin on the 1st April 2024 and run until the end of March 2026. The increase in surgical activity was applied on the 1st January 2025 (in “simulation time”) as an instantaneous step change. The different projections from the two simulation modes can be seen in Figure 4. Both simulation modes follow the same average projection up to January 2025 at which point the uplift to surgical activity is applied, and the average projections diverge. The simulation with no direct TTG additions suggests that increasing surgical throughput while everything else in the system remains the same would result in significantly smaller TTG list size by March 2026 (an average of roughly 1,500), with some model runs completely clearing the waiting list.

In contrast the simulation with direct TTG additions has a very wide spread of possible outcomes following the uplift in surgical activity, depending on the initial simulation trajectory before the change is applied. There is still an overall decrease in the projected TTG list size by March 2026, but the average TTG list size is above the baseline target of 7,500 with roughly 18,500 individuals on the list by March 2026. The very wide uncertainty range that develops in this simulation mode could indicate that this method is more suited to shorter term projections, but could also reflect the underlying uncertainty in the system, especially when the number of direct TTG additions is not fully understood.

Figure 4 : Direct TTG additions dampen the impact of increased surgical activity.

Increasing TTG surgical activity in January 2025 leads to a significant drop in the projected TTG list size in the mode without direct TTG, with a more moderate average decrease in the mode with direct TTG. Shaded areas represent the standard deviation from 30 model runs.

This type of process change could be relevant when considering immediate bilateral sequential cataract operations. The expectation from the modelling would be that if more bilateral sequential operations were performed, this would reduce the number of direct TTG additions. This would in turn amplify the impact of any increased surgical throughput leading to a more rapid and pronounced reduction in the TTG waiting list size.

Productivity scenario: increasing cataract surgical throughput

Simul8 models are ideal for testing what-if scenarios such as changes in productivity. Similarly to the process change scenario, there is a change in surgical activity in the productivity scenario. However, in this case, the change in activity is more precisely derived from potential productivity improvements. Additionally, this scenario uses the direct TTG simulation mode only (on the assumption that this is a better reflection of how the system is currently structured) and compares the baseline (no change to activity) with the proposed productivity scenario.

Hypothetical productivity scenario details:

• The National Treatment Centres at Highland and Golden Jubilee deliver a higher volume of surgeries per session - 10 cataract surgeries per list, in line with a high volume list (7).
• All other sites (operating on adults) achieve 1 more cataract per list in line with guidelines from the Royal College of Ophthalmologists (7).
• The activity uplift for the scenario is applied on the 1st January 2025 (in model time), as a step change i.e. activity immediately increases to the target level .

The simulation was set up to begin on the 1st April 2024 and run until the end of March 2026.

The productivity scenario whilest being theoretically feasible, does not look like it would have a significant impact on the TTG list size. The final average TTG list size in the productivity scenario is around 22,000 compared to 24,500 in the baseline model. There would likely be a small reduction in the list size but there is such a wide degree of variation that it would not be clear if there was a positive impact of the initiative for at least a year after implementation. There is an assumption in this scenario that the direct TTG rate remains static over time, and when the cataract surgery throughput increases.

Figure 5 : Productivity scenario – higher cataract throughput.

The "higher cataract throughput" scenario is applied to the direct TTG simulation model. There is a moderate decrease in projected TTG list size by March 2026. Shaded areas represent the standard deviation across 30 runs.