Modelling survival functions and their critical points

Survival analysis has applications ranging across medicine, engineering and social sciences
where the main quantity of interest is time until an event. The methods in this project are applied to medical data where an 'event' will be defined as the death of a patient. There are a couple of models that are traditionally used by clinicians. The Kaplan Meier estimate can be used to determine whether a certain treatment has a significant effect on the survival time of a patient and the Cox proportional hazards model is used to identify individual factors that may contribute either positively or negatively to the prognosis of the patient.
This project uses a new method proposed by Bart et al. (2005) in which a survival function is determined by considering the underlying dynamics of the disease. This novel approach uses the opposing disease inhibiting and disease progressing factors. By estimating this disease progression function, the speed of disease progression and the period of the disease can be determined which allows the estimation of `critical points'. These critical points correspond to the best times that medical intervention should be applied to increase the length of survival of the patient. The aim of the project is to estimate these time points. The method is currently being applied to a small data set on acute pancreatitis (AP) , a serious inflammatory disease affecting around 37,000 people in the UK every year, with future plans to extend to a larger AP data set and other medical data sets that become available.

MAC-MIGS develops computational modelling and its application to a range of economic sectors, including high-value manufacturing, energy, finance and healthcare. These fields contribute over £500 billion to the UK economy. The CDT involves collaborations with more than a dozen companies and organisations, including large corporations (AkzoNobel, IBM, Dassault, P&G, Aberdeen Standard Investments, Intel), mid-size firms, particularly in the engineering and power sectors (NM Group, which provides monitoring services to power grid operators in 30 countries, Artemis Intelligent Power, the world leader in digital displacement hydraulics, Leonardo, a provider of defense, security and aerospace services, and Oliver Wymans, a management consultancy firm) and startups such as Brainnwave, which develops data-modelling solutions, and Opengosim which designs state-of-the-art and massively parallel software for subsurface reservoir simulation. Government and other agencies involved will include the British Geological Survey, Forestry Commission, James Hutton Institute, and Scottish National Heritage. Engagement will be via internships, short projects and PhD projects. BIS has stated that "Organisations using computer generated modelling and simulations and Big Data analytics create better products, get greater insights, and gain competitive advantage over traditional development processes". Our partners share this vision and are keen to develop deeper collaborations with us over the duration of the CDT.

Our CDT will achieve the following:

- Produce 76 highly skilled mathematical scientists and professionals, ready to take up positions in academia or in companies such as our partners. The students will have exposure to projects, modelling camps and high-level international collaborations.

- Deliver economic and societal benefits through student research projects developed in close collaboration with our partners in industry, business and government and other agencies.

- Create pathways for impact on computer science, chemistry, physics and engineering by involving interdisciplinary partners from Heriot-Watt and Edinburgh Universities in the supervision and training of our students.

- Organise a large number of lectures and seminars which will be open to staff and students of the two universities. Such lectures will inform the wide university communities about the state-of-the-art in computational and mathematical modelling.

- Work with other CDTs both in Edinburgh and beyond to organise a series of workshops for undergraduates, intended to foster an increased uptake of PhD studentship places in technical areas by female students and those from ethnic minorities, with potential impact on the broader UK CDT landscape.

- Organise industrial sandpits and modelling camps which offer the possibility for our partners to present a challenge arising in their work, and to explore innovative ways to tackle that challenge, fully involving the CDT students. This will kick-start a change in the corporate mindset by exposing the relevant staff to new approaches.

- Develop a new course, "Entrepreneurship for Doctoral Students in the Mathematical Sciences" in conjunction with Converge Challenge (Scotland's largest entrepreneurial training programme) and UoE's School of Business. This and other support measures will develop an innovation culture and facilitate the translation of our students' ideas into commercial activities.