# Modelling techniques and health services

## Introduction

Learning objectives: You will learn about:

• the uses of mathematical modelling techniques in health service planning
• use of information technology in the processing and analysis of health services information and in support of the provision of health care

This section covers some advanced applications of health information, including the uses of mathematical modelling techniques in health service planning, use of information technology in the processing and analysis of health services information, and in support of the provision of health care.

## Resource text

### Health Information: The uses of mathematical modelling techniques in health service and health intervention planning

A model is a simplified representation of a complex system, designed to focus on a specific question. In general, modelling techniques used in health are adaptations 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 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 by modelling the impact of an epidemic.
• Predicting health needs in the future, such as the long-term health service resource requirements.
• Depicting what could happen with important public health issues if no interventions 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

Diabetes prevalence model

This is a spreadsheet model that generates expected total numbers of people 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.

The combined predictive model

This model links inpatient data with other routine data on utilisation of care in order to predict future risk of emergency admission.

### 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.

### Stop before the Op

The Stop before the Op project models the financial savings possible across London if a programme of preoperative smoking cessation is followed. The numbers of smokers admitted for elective surgery is required for the model plus the numbers of smokers likely to quit pre-operatively. Then the numbers of wound infections (and other post-operative complications) between smokers and ex-smokers who quit just before the operation are compared. The cost of one bed day is required for calculating the financial savings from reducing post-operative complications.

Briefing

Model

### Capacity planning and access (including waiting list and times)

Based mostly on queuing theory, analysing times to service and required capacity. See UCL: Capacity Planning.

### 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.

### 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.

### 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.

### Patients At Risk of Re-hospitalisation

PARR, short for 'Patients At Risk of Re-hospitalisation', is a software tool that can be run daily. When an individual is admitted to hospital, the tool uses the patient's recent admissions data (up to four years) to calculate the likelihood of re-admission over the next 12 months. This takes into account factors such as prior utilisation, diagnoses and socio-demographic information, and gives a high rate of predictive accuracy.

From the PARR getting started guide:

It is commonly recognised that significant morbidity and cost result from long-term conditions. Previous work by the King's Fund and others has shown that a large proportion of emergency admissions are for patients with conditions such as asthma, diabetes, chronic obstructive pulmonary disease (COPD) and sickle cell disease, for which effective primary care can reduce the risk of admission 1. Subsequently, the Department of Health commissioned the King's Fund, New York University and Health Dialog to produce a system to help Primary Care Trusts (PCTs) proactively identify high risk patients, many of which have these types of long-term conditions. In February 2006, the PARR+ tool was launched to identify very high intensity users of healthcare using routine Inpatient data.

### The mathematical study of queuing theory in healthcare

This model is used to manage variable demand in a fixed capacity environment, such as patients attending A&E. It could be used to model the queue for the hospital canteen. It assumes a Poisson distribution of arrivers into the queue. It has been shown to reduce waiting times and reduce hospital costs. There are many examples for this. See case history at St. John's Regional Health Center.