Patient centred care that follows a person’s entire treatment pathway needs new models to effectively accommodate its different phases. Sally McClean and colleagues show how stroke care can be improved using mathematics


In recent years it has become increasingly important that healthcare provision be patient centred and deal with the entire episode of care. This is a difficult task as patients can take numerous diverse pathways through a healthcare facility or system, depending on their needs. Also, with increasing budget cuts, a cost-effective service is necessary.

We advocate a multiphase modelling approach to pathway management that facilitates the study of both the specific elements of a patient pathway and its overall impact on cost, patient quality of life and clinical outcome.

‘Statistical models provide a useful framework for abstracting essential features of patient behaviour’

This is important as previous healthcare solutions typically dealt with specific elements of the pathway – such as emergency care – and often with specific patient groups or pathologies. Silo planning and budgeting is also resulting in a tendency to focus on a specific part of the pathway.


Urgent requirements

There is an urgent requirement to provide cost-effective solutions to the delivery of care, particularly for older people who follow complex pathways and are heavy users of health and social care services.

As such, a robust methodology is needed to provide a framework that enables decision makers and resource providers to better understand their services and pre-test the impact of their decisions before costly mistakes are made.

In addition, the complexity and interdisciplinary nature of human activity systems, such as health and social care pathways, mean it is difficult for decision makers to fully understand the complete system. Statistical models provide a useful framework for abstracting essential features of patient behaviour and the wider environment.

‘We can use models to predict future care requirements and costs for cohorts of patients’

Peter Millard, emeritus professor of geriatric medicine at St George’s Hospital, London, observes that older patients’ length of stay can be modelled by a simple statistical model: the mixed exponential distribution. This two-phase model of patient behaviour was previously developed and shown to give a good fit to a range of hospital inpatient data.

Similarly, multiphase models have also been employed to describe the behaviour of patients in social care. Such models of patient dynamics can be used in various ways to enhance understanding of patient behaviour and assess the impact of changes. In particular this article describes the use of modelling to evaluate and help to improve stroke patient pathways.

Model behaviour

Stroke costs the UK about £10bn per annum and is the leading cause of disability. Such costs are partly due to a prolonged length of stay in hospital, which is considered to be an inefficient use of resources. 

Additional costs are incurred through ongoing care in the community. Furthermore, patients with stroke go through many phases of care, ranging from initial diagnosis and treatment in accident and emergency to long term support and care in the community.

Stroke disease is therefore particularly amenable to cost modelling as patients that do not receive appropriate therapy or rehabilitation may subsequently build up huge costs over time. Thus, we can use models to predict future care requirements and costs for cohorts of patients. Such predictions are, of course, highly variable so we use statistical models to quantify the variability.

A useful feature of the multiphase approach is that it enables us to attach differential costs to the different phases. Acute and assessment phases require urgent medical testing, diagnosis and treatment with associated costs and intensive nursing; longer stay phases may require more hotel-type costs, combined with physiotherapist and occupational therapist expenses.

We focus on the use of such an approach for modelling care of patients with stroke to enhance our understanding of patient behaviour and assess the impact of change.

In particular we consider the use of multiphase models to assess the consequence of investing in thrombolysis across pathways, mainly in terms of increased computerised tomography scanning and administration of appropriate drugs. This is important because, although thrombolysis has been licensed in the UK since 2003, until recently it was still only administered to a small percentage of eligible patients.

Testing, testing

In our stroke model we have used statistical survival analysis applied to data about length of stay with discharge destinations as outcome measures, based on data from Belfast City Hospital.

From patients who were eligible for thrombolysis, we created two initial (logical) groups: one received thrombolysis, the other did not. On the basis of the survival analysis we then created several subgroups corresponding to patient pathways.

Coxian phase-type distributions were used to model length of stay and cost for each pathway. Northern Ireland provides a particularly useful test bed for such models because health and social services are unified at government, board and trust levels.

‘The model predicted thrombolysis drugs would reduce time in hospital, community rehabilitation and nursing homes’

Various scenarios were explored focusing on potential savings in the service, particularly in community rehabilitation, alongside improvements in quality of life, should the proportion of patients who are administered thrombolysis be increased.

In particular, the model was used to investigate the effect of more widely prescribing thrombolysis drugs and predicted they would reduce time in hospital, community rehabilitation and nursing homes; so although they cost money up front, there are benefits such as long term savings and improved quality of life.

Key concepts of patient pathway modelling

  • Sophisticated tools are needed to describe patient pathways for patient-centred care
  • A multiphase approach allows us to quantify durations and costs of stages on the patient pathway
  • This approach can be based on readily available hospital and social service data
  • Better decisions can then be made, for patient-centred care and optimal use of health service resources

Our use of mathematical modelling and simulation techniques, based on real world data, to consider the effects of proposed changes before they are put in place has allowed the service to confidently and rapidly expand its thrombolysis rates, with consequent impact on healthcare budgets and patients’ quality of life.

In respect of stroke thrombolysis, the model has also demonstrated that significantly increasing the proportion of patients with stroke who are treated with thrombolysis has value in terms of better outcomes and reduced costs.

These reduced costs are associated with less disability, less need for rehabilitation and less likelihood of institutional care. As such, for appropriate patients with stroke, health outcomes have been improved while, for others, quality of life has been enhanced because larger centres mean better coverage and more expertise.

Results and recommendations

Our results suggest that provision of thrombolysis should produce moderate overall improvement if current levels of funding are maintained. As such, the overall multiphase modelling framework represents initial work towards developing integrated models of pathways including both hospital and community care, with the aim of supporting integrated planning.

‘This research evidence has, among other things, led to a reorganisation of acute stroke services’

Thrombolysis with alteplase is now included in the National Institute for Health and Care Excellence’s stroke care pathway and recommended, within the marketing authorisation, for treating acute ischaemic stroke in suitable adults. The guidelines also suggest that alteplase should be administered only within a well organised stroke service with:

  • staff trained in delivering thrombolysis and monitoring for any associated complications;
  • level 1 and level 2 nursing care staff trained in acute stroke and thrombolysis; and
  • immediate access to imaging and re-imaging, and staff trained to interpret the images.

The benefits of thrombolysis have been previously demonstrated by randomised controlled trials for the UK in general, but also shown by our mathematical modelling approach for Belfast, in particular. This research evidence has, among other things, led to a reorganisation of acute stroke services in Belfast (indeed, Northern Ireland) to provide larger centres. Such centres are needed to comply with the guidelines.

Benefits include it being easier deliver thrombolysis 24/7 to more people and it being possible to develop expertise in terms of systems of care (to allow more rapid treatment), as well as individual clinician expertise, leading to better selection of patients who might benefit.

Better public awareness, better healthcare professional awareness and more robust systems of delivery have, in turn, led to increased provision across the UK.

Strong approach

The US mathematician Richard Bellman said “every equation we employ to describe the physical world is approximate”. This is particularly true of healthcare models, which are highly complex with huge variability between patients and diversity in the care systems they occupy.

‘Mathematical models allow us to predict how groups of patients move through the health and social care pathways’

Nonetheless, mathematical models allow us to predict how groups of patients move through the health and social care pathways, what resources they will consume and how outcomes might improve if we adopt the right strategy and focus on solutions that take all aspects of patient care into account.

A particular strength of the approach is that we can assess how the care system might perform in different operational settings and so provide recommendations for performance improvement with regard to criteria such as reducing queue lengths or decreasing length of stay in hospital.   

We believe stroke is an excellent paradigm example enabling modelling of a whole health and social care system. The experience gained and techniques learned are likely to be relevant to health and care of older persons in general. Current interest in both health and social care of older people demonstrates the importance for future planning this work could have.

Sally McClean is professor of mathematics at Ulster Univeristy; Jennifer Gillespie is a mathematician at Randox; Dorian Dixon is a lecturer in engineering at Ulster Univeristy; Peter Millard is emeritus professor of geriatrics at St George’s Hopspital, University of London; Ivan Wiggam is consultant physician at Belfast Health and Social Care Trust; and Ken Fullerton is associate medical director for unscheduled care at Belfast Health and Social Care Trust