# The Uses of Mathematical Modelling Techniques in Health Service Planning

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A model is a (usually simplified) representation of a complex system, designed to represent the system in a way that allows analysis, e.g. of utilisation, efficiency and effectiveness, so as to support service planning and management decisions, both at the operational and strategic levels, in terms of the systems goals. Originally, modelling techniques used in health were adaptions from other fields such as telecommunications and traffic engineering, using technical skills such as operational research

https://en.wikipedia.org/wiki/Operations_research [accessed 22/08/2018]

Analytical models aid decision making.

https://www.on-course.eu/courses/analytical-models-for-decision-making-phm201g/ [accessed 24/08/2018]

In health service planning, modelling techniques derived from queuing theory can be used to forecast the effects of changes on access to services and to calculate the required capacity of services given assumptions about patterns of demand and levels of utilisation; techniques derived from the physics of gravitation may be used to estimate catchment  areas of  new facilities; models utilising network analysis may be used to study patients' travel requirements to services; models based on Markov chains https://en.wikipedia.org/wiki/Markov_chain can be used to assess patients' progress though through treatment and also in economic assessments. Other modelling techniques are used in epidemiology and in Health Impact Assessment, and in clinical audit. They can also help to identify where there may be problems or pressures, identify priorities and focus efforts. Where the mathematics results in equations that are too complex to solve directly modellers have recourse to simulation.  Modelling is important in a range of areas such as:

• Predicting health needs in the future such as the number of people with eye conditions see the National Eye Health Epidemiological Model. http://www.eyehealthmodel.org//#[accessed 22/08/2018]
• Depicting what could happen with important public health issues if no intervention are undertaken.  For example, projecting year on year increase in childhood obesity prevalence has helped to identify this issue as a national priority and allocate resources to tackle it.
• Understanding the impact of service redesign on different areas, such as general practice waiting times, and hospital bed occupancy.
• Estimating prevalence when detailed data are not available.
• Predicting demand on services from subgroups of the population, such as those at risk of emergency admissions or re-admissions

Examples

Predictive risk models

1. Diabetes prevalence model

2. This is a spreadsheet model that generates expected total numbers of persons with diabetes mellitus. The estimates are available by Local authority and CCG: https://www.gov.uk/government/publications/diabetes-prevalence-estimates-for-local-populations [accessed 22/08/2018] Patients at risk of re-hospitalisation (PARR model)

PARR was a risk prediction system produced a number of years ago for use by the then NHS local commissioning authorities called primary care trusts (PCTs) ( as of now Clinical Commissioning Groups (CCGs)) to identify patients who are at high risk of re-admission to hospital. The first set of algorithms, known as PARR+, utilised routine inpatient data in order to identify individuals at risk of re-admission to hospital. The existing models have been withdrawn

3. The combined predictive model
Developed by the same Consortium that worked on the PARR model, this model links inpatient data with other routine data on utilisation of care in order to predict future risk of emergency admission.

Also see https://www.networks.nhs.uk/ [accessed 22/08/2018]

4. The health inequalities intervention tool.
http://www.ukhealthforum.org.uk/prevention/pie/?entryid43=20558&cord=ASC&p=10 [accessed 24/08/2018]

Health Inequalities Intervention Toolkit | APHO and DoH, UK
This Health Inequalities Intervention Toolkit, developed jointly by the Association of Public Health Observatories and the Department of Health, focuses on improving life expectancy and infant mortality rates, especially in disadvantaged areas.

Based on local authority boundaries, it is designed to assist evidence-based local service planning and commissioning, including Joint Strategic Needs Assessments.

See ‘Health inequalities’ on the page

and

5. Stop before the Op
A briefing on the benefits of pre-operative smoking cessation (both health gain and cost savings) based on a model developed to estimate
• the numbers of adult smokers who were admitted electively for surgery (by both CCG of residence and by acute hospital)
• the number likely to quit if offered smoking cessation interventions preoperatively, and
• the effect in terms of complications and length of stay.

https://www.neessexccg.nhs.uk/stop-before-the-op [both accessed 22/08/2018]

1. Health Impact Assessment of environmental threats such as incinerators

http://www.who.int/quantifying_ehimpacts/methods/en/fehr.pdf [accessed 22/08/2018]

1. Capacity planning and access (including waiting list and times)
Based mostly on queuing theory, analysing times to service and required capacity.
https://iris.ucl.ac.uk/iris/publication/1425954/1 [accessed 22/08/2018]
http://discovery.ucl.ac.uk/10023370/
http://discovery.ucl.ac.uk/10023370/1/Palmer_A%20systematic%20literature%20review%20of%20operational...%20-%20Ryan%20Palmer%20et%20al.%20%282017%29.pdf [accessed 22/08/2018]
http://www.ucl.ac.uk/operational-research/publications [accessed 22/08/2018]
http://www.ucl.ac.uk/operational-research  [accessed 22/08/2018]

2. Clinical Audit
https://www.england.nhs.uk/clinaudit/ [accessed 22/08/2018] The following models use cumulative-sum (CUSUM) methods to assess clinical performance. See review article on the web page:

Sherlaw-Johnson C. ( 2005)
A method for detecting runs of good and bad clinical outcomes on Variable Life-Adjusted Display (VLAD) charts
Health Care Management Science 8, 61-65

Sherlaw-Johnson C, Morton A, Robinson MB, Hall A. (2005)
Real-time monitoring of coronary care mortality: A comparison and combination of two monitoring tools
International Journal of Cardiology 100, 301 – 307

Treasure T, Gallivan S, Sherlaw-Johnson C. (2004)
Monitoring cardiac surgical performance: a commentary on control chart methods for monitoring cardiac surgical performance and their interpretation by Rogers et al.
The Journal of Thoracic and Cardiovascular Surgery. 128: 823-825.

3. Economic evaluation of screening, using Markov chain modelling
Johnstone, K, Modelling the future costs of breast screening, European Journal of Cancer 37 (2001) 1752-1758

4. Use of gravity modelling for catchments and patient flows
P.Congdon (2001) The development of gravity models for hospital patient flows under system change: a Bayesian modelling approach, Health Care Management Science, 4, 289-304

© M Goodyear & N Malhotra 2007, D Lawrence 2018