Modelling and computer simulation of patient flow

Abstract

The population of the United Kingdom is increasingly ageing and diseases, likecancer and stroke, are becoming more common in our society. This is having a detri-mental affect on the performance of the National Health Service. Various schemes and services have been introduced to increase efficiency, and key performance indi-cators help to identify areas of best practice. By realistically modelling healthcare facilities with analytic and simulation models, based on queueing theory, we can pro-vide detailed information to healthcare managers and clinicians. These models can help to identify issues and cost inefficiencies for early intervention. Analytic mod-els are less data and computationally intensive, and provide results in a quick time frame compared to simulation models. However, they tend to be mathematically complex which means healthcare managers can find them difficult to understand, and are more reluctant to implement the solutions. Simulations are more data and computationally intensive compared to analytic models, but they are much easier to explain to healthcare managers when they are built in a user friendly environment. This means that managers tend to be more willing to introduce the results of the model into their department. Therefore, we use both analytic and simulation models in this work to utilise the benefits of both techniques.

In this body of work a novel analytic cost model has been presented for a system which can be regarded as a network of M/M/∞ queues. The model considers the flow of patients through primary and secondary care, and is based on a mixture of Coxian phase-type models with multiple absorbing states. Costs are attached toeach state of the model allowing the average cost per patient in the system to becalculated. We also provide a model which assesses whether the implementation ofa new intervention is cost-effective. The model calculates the maximum cost the intervention can incur before the benefits no longer outweigh the cost of administer-ing it. These analytic models have been applied to stroke patients deemed eligible for thrombolysis in order to assess the cost-effectiveness of thrombolytic therapy. We also present a novel simulation model for stroke patients, who are eligible for thrombolysis, in order to validate our analytic models. ‘What-If’ scenarios and Probabilistic Sensitivity Analysis have also been carried out to provide healthcare managers with more confidence in our models. An analytic model has been pre-sented for a complex system of M/M/c queues in steady state. The model analyses the system to find bottlenecks and assesses whether the staff are being efficiently utilised. Two resource allocation models have then been defined: the first determines the minimum number of resources required within the department, and the second efficiently distributes the resources throughout the department. These resource allo-cation models have been applied to orthopaedic Integrated Clinical Assessment and Treatment Service (ICATS) data to reduce the current queues within the depart-ment. A novel simulation model has also been created for orthopaedic ICATS which includes extra variation and realistic features. This allows us to assess how robust and reliable our analytic models are, as the results are applied to our simulation model which has different assumptions.

The novel analytic models provide very similar results to the simulation mod-els built for each healthcare environment. This implies that our analytic models are robust and reliable even when applied to a department which includes differ-ent assumptions. Therefore, our analytic models will provide reliable results when healthcare managers need to make decisions in a short time frame. Simulation models have been found to be a good validation technique for analytic models, as healthcare managers understand them better. Extra components can also be easily included within a simulation model, such as complex distributions to represent theinter-arrival and service rate, and realistic features such as shift patterns.

Date of Award	Feb 2013
Original language	English
Sponsors	Department of Employment and Learning (DEL)
Supervisor	Sally McClean (Supervisor) & Bryan Scotney (Supervisor)