# 4-year PhD Studentship: Mathematical modelling to provide optimal solutions to cardiovascular waiting lists.

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Dr Ben Gibbison, Prof A Champneys  No more applications being accepted  Self-Funded PhD Students Only

Cardiovascular disease (CVD) affects over 7 million people and accounts for 27% of all deaths in the UK. CVD has been the largest non-COVID-19 cause of excess mortality in England since March 2020[1]. Most CVDs are progressive and therefore timely treatment prevents both death and serious morbidity (and impact on healthcare costs). Care of CVD comprises a multidisciplinary pathway through primary, secondary, and tertiary care. General Practitioners, physicians and surgeons take inputs from diagnostics (e.g. echocardiography, MRI) and allied services (e.g. specialist nurses) and deliver non-pharmaceutical (e.g. cardiac rehab), pharmaceutical (e.g. drugs) and structural (e.g. valve replacement) interventions to treat patients. Flow of patients through the system is complex, non-linear and exists as a series of branched feed-forward and feed-back loops. However, previous approaches to modelling the referral-diagnostic-treatment (RDT) pathway have always been linear.

This project builds on work convened by the Newton Gateway to Mathematics. Clinicians and mathematicians co-designed a simple mathematical model using routinely collected open access data to provide insights and solutions to the challenge of prolonged waiting lists in UK CVD Care[2]. This nascent systems-dynamics model needs further development, optimisation, and validation.

### Aims and objectives

The over-arching aim of the project is to further develop, optimise and validate a systems-level, operations research model of the care pathway for patients waiting for referral, diagnosis and treatment of CV disease. Specific objectives are to:

1. Optimise the nascent systems dynamic model

a. Incorporate/ remove additional data streams and parameters

2. Validate the model using routinely collected, open access NHS data (e.g. NHS Digital)

a. Validate the effects of both COVID-19 and non-COVID-19 impacts on the model

3. Develop the model into a bespoke piece of software to be used by healthcare providers / commissioners.

### Methodology

The candidate will use a combination of mathematical modelling, expert elicitation, and software engineering. Specific methods which link to the objectives above are as follows:

WS1: Model Optimisation

A simple Python SD model has been created[2] and fitted using time-series data collected from NHS England. The model currently treats all CVD as a single patient flow, but separate pathways for different medical and surgical interventions need to be captured. More rigorous fitting is required, using mathematical optimisation theory that considers epistemic and aleatoric uncertainty, as well as utility functions that capture overall patient benefit.

WS2: Model Validation and User Engagement

A key requirement of the model is that it can be used by NHS trusts, care commissioning groups (CCGs) and national policy makers to run what-if scenarios. Working with UHBW NHS Trust, BNSSG CCG and the British Heart Foundation, the candidate will develop suitable metrics and adjustable parameters to enable real-time decision support.

WS3: Software Development

A suitable prototype app / web-based tool will be developed by the candidate (dependent on the experience and the outcome of WS2). This robust software tool will have commercialisation potential and could be extended to other patient pathways beyond CVD.

### How to apply for this project

This project will be based in Bristol Medical School - Translational Health Sciences in the Faculty of Health Sciences at the University of Bristol.

Please visit the Faculty of Health Sciences website for details of how to apply

## Funding Notes

This project is open for University of Bristol PGR scholarship applications (closing date 25th February 2022)
The University of Bristol PGR scholarship pays tuition fees and a maintenance stipend (at the minimum UKRI rate) for the duration of a PhD (typically three years but can be up to four years).

## References

1. NHS England. Excess mortality in England, 2022.
2. VKems and Newton Gateway. Modelling solutions to the impact of COVID-19 on cardiovascular waiting litsts: Newton Gateway to Mathematics, 2021.
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