A compartmental modelling methodology to support strategic decision making for managing the elective hospital waiting list; application in England’s NHS

Waiting list models can support improved strategic management of elective hospital care through estimating possible performance impacts resulting from different demand and capacity related interventions. Single-compartment models have previously been used to model the referral ‘inflow’ and treatment ‘outflow’ onto a waiting list, with some also considering the outflow of patients reneging from the waiting list before treatment. The conceptual simplicity of these models promotes scalability through aligning to various waiting list problems and routine data sources. However, these single-compartment models are only able to model waiting list size, and not waiting times. To address this, we extend the single-compartment model with reneging to consider a multi-compartment model, where each compartment represents the number of individuals awaiting treatment for progressively longer periods of time. This problem is formulated in discrete time and solved through a series of difference equations. Open-source code for implementing the model is made freely available. To illustrate the versatility of the methodology, the model is calibrated using routine data for the total England NHS waiting list as of year-end 2023 and used to project various scenarios over the following two years to year-end 2025. Model validation is performed through backtesting (running the model on past unseen data), with 0.4% and 4.7% MAPE attained on six and twelve month windows respectively.