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The Uses of Mathematical Modelling Techniques in Health Service Planning

Applications: The Uses of Mathematical Modelling Techniques in Health Service Planning

A model is a simplified representation of a complex system, designed to focus in on a specific question. In general, modelling techniques used in health are adaptions from other fields such as telecommunications and traffic engineering. 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 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:

  • Preparing for flu outbreak - modelling the impact of an epidemic
    http://www.hpa.org.uk/infections/topics_az [accessed 30/11/2007].
  • Predicting health needs in the future such as the long term health service  resource requirements
    http://www.hm-treasury.gov.uk/media [accessed 30/11/2007].
  • 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, 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

    This is a spreadsheet model that generates expected total numbers of persons with Type 1 and Type 2 diabetes mellitus (diagnosed plus undiagnosed combined) in 2001 for England, Government Office Regions, Strategic Health Authorities, Local Authority Districts, Primary Care Trusts, electoral wards and user-defined populations including GP practices. The model applies age/sex/ethnic group-specific estimates of diabetes prevalence rates, derived from epidemiological population studies, to 2001 Census resident populations. Forecasts of 2010 diabetes prevalence are also presented for sub-national areas based on projected population change and trends in obesity.

    N.B.  This model was developed before the Quality and Outcomes Framework of the GP contract.  Subsequently it has been possible to compare prevalence measures from both to identify where methods could be improved
    http://www.yhpho.org.uk/viewResource.aspx?id=7
    [accessed 30/11/2007].

  2. Patients at risk of re-hospitalisation (PARR model)

    PARR is a risk prediction system for use by primary care trusts (PCTs) to identify patients who are at high risk of re-admission to hospital. The first set of algorithms, known as PARR+, utilise routine inpatient data in order to identify individuals at risk of re-admission to hospital. http://www.kingsfund.org.uk/health_topics [accessed 30/11/2007].

  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.
    http://www.kingsfund.org.uk/current_projects [accessed 11/1/2008]

    Also see http://www.networks.nhs.uk/uploads

  4. The health inequalities intervention tool

    The Health Inequalities Intervention Tool has been commissioned by the Department of Health through the Association of Public Health Observatories (APHO). The tool is designed to assist commissioners in Spearhead Primary Care Trusts (PCTs) with their Local Delivery Planning (LDP) and to assist Spearhead Local Authorities (LAs) with the delivery of Local Area Agreements (LAAs). It highlights key issues for Spearhead PCTs and LAs to consider in order to achieve the life expectancy element of the Government's Public Service Agreement (PSA) on health inequalities by 2010 http://www.lho.org.uk/viewResource.aspx?id=11252 [accessed 11/1/2008]

  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 PCT 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. 

    Briefing http://www.lho.org.uk/viewResource.aspx?id=10495 [accessed 11/1/2008]
    Model http://www.lho.org.uk/viewResource.aspx?id=9776 [accessed 11/1/2008]
     

  6. Health Impact Assessment of environmental threats such as incinerators

    http://www.ucl.ac.uk/operational-research/publications [accessed 11/1/2008]

  7. Capacity planning and access (including waiting list and times)

    Based mostly on queuing theory, analysing times to service and required capacity.
    http://www.ucl.ac.uk/operational-research/publications [accessed 11/1/2008]

  8. Clinical Audit

    The following models use cumulative-sum (CUSUM) methods to assess sequential runs of  surgical outcomes.

    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.

  9. 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

  10. 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