Supervisor: Prof Tristan Pryer
Partners: National Physical Laboratory
About the Project
This project is co-funded and co-supervised by the National Physical Laboratory (NPL), offering a unique opportunity to engage in applied mathematics research with direct clinical and industrial relevance.
Modern radiotherapy aims to deliver a precise dose of radiation to a tumour while minimising harm to surrounding healthy tissue. As delivery technologies become increasingly accurate, treatment success becomes more sensitive to uncertainty, both physical (e.g. anatomical variation, setup and delivery errors) and biological (e.g. individual differences in tissue response). These sources of uncertainty are typically treated independently or handled heuristically. There is currently no unified mathematical framework for quantifying and incorporating them into treatment planning.
This project addresses that gap. We aim to develop a rigorous, data-informed mathematical formalism to represent, propagate and mitigate uncertainty in radiotherapy. The focus is on building tractable models that support robust optimisation and personalised treatment decisions.
The project will draw on tools from probability, statistics, optimisation and PDE-constrained inverse problems. Candidates will investigate how to model uncertainties using stochastic processes and Bayesian approaches, how to propagate these uncertainties through transport or diffusion-based models of radiation dose and how to incorporate them into treatment plan optimisation via multi-objective or risk-aware formulations.
Project keywords: uncertainty quantification, robust optimisation, radiotherapy
Candidate Requirements
In addition to the SAMBa entrance requirements, the ideal candidate will have a good understanding of probability, statistics and differential equations, together with experience in numerical or computational modelling.
Contact the SAMBa team at samba@bath.ac.uk if you are unsure about your eligibility and would like to discuss your potential application.
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Prof Tristan Pryer tmp38@bath.ac.uk.
Applications are open for entry in September 2026. Apply via the University of Bath’s online application form for an Integrated PhD in Statistical Applied Mathematics. Early applications are encouraged.
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Supervisor: Dr Thomas Burnett
Partners: Novartis
This project is offered by the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), for study commencing in September 2026.
Adaptive designs for clinical trials add flexibility to the clinical development process, using pre-planned interim analyses to allow alterations to the trial in progress. Such flexibility gives trials the potential to be more efficient and ethical, and these goals may be prioritised differently in different forms of adaptation.
Adaptive designs introduce further complication to the proper estimation of treatment effects compared to traditional fixed sampling designs. Decisions about trial modifications are typically based on the observations available at the time of the interim analysis and, since the final set of data is itself data-dependent, standard methods for deriving estimates and confidence intervals are not applicable. The recent publication of the ICH E20 draft Guideline on Adaptive Clinical Trials highlights the need to use appropriate estimation methods to inform cost-benefit decision making.
In this project the student will explore the problem of inference after a trial with an adaptive design. Research will be conducted to investigate trade-offs of different estimation methods and the impact of different choices for conditional estimation based on the decision that may be made. The work will be conducted in close collaboration with project partners at Novartis. This close collaboration with industry will allow the student to grow their professional network within the pharmaceutical industry. Working with an industrial supervisor will ensure the research keeps the practical implications of the problem as a core priority, leading to real world impact.
Keywords: clinical trials, adaptive designs, statistical inference, simulation studies
Approximate timeline
In the first 9 months – As a SAMBA student, you will complete the SAMBa training programme.
Year 1/2 – Review relevant literature; construct a general framework for the research; identify limitations with the current approaches, both theoretically and empirically (via simulations).
Year 3 – Develop guidelines for the implementation of different point and interval estimation methods for specific forms of adaptation, determining key questions through collaboration between the student and industrial partner. Begin dissemination of the research to the relevant communities. Prepare a paper for publication in a high quality Statistics Journal.
Year 4 – Explore generalisations of the proposed methods to trial designs with different forms of adaptation; identify theoretical advantages of the proposed methods over existing methods; consider possible extensions to the research findings so far; disseminate research results through presentations and further publications; prepare the PhD thesis.
Training and Development Opportunities
In addition to all the benefits of the SAMBa training course, you will have the opportunity for summer internships at Novartis in Basel, Switzerland. You will be given networking opportunities within the academic community and the pharmaceutical industry. This will involve attending and presenting at workshops, conferences and seminars. There will be additional career development opportunities through attending events such as the UK Young Statisticians’ Meeting, the UK Research Students Conference, and the annual conference held by PSI (Statisticians in the Pharmaceutical Industry).
In addition to the SAMBa entrance requirements, the ideal candidate will have a strong understanding of the fundamentals of statistics (through either undergraduate studies or postgraduate taught studies). Experience in programming in statistical software such as R and experience in clinical trials or medical statistics is desirable.
Informal enquiries are encouraged and should be directed to supervisor Dr Thomas Burnett tb292@bath.ac.uk
Supervisor: Dr Matthias Ehrhardt
The medical imaging technique Positron Emission Tomography (PET) is an important cornerstone in modern medicine allowing non-invasive, sensitive, and specific detection of disease. For example, PET is routinely used in the diagnosis of various cancers. Small metastases at the edge of the PET resolution limit are difficult to be correctly diagnosed with the current technology, leaving clinicians in a very difficult situation.
In this PhD project, we are investigating Bayesian inference backed by sound mathematical and statistical theory to tackle this problem. In particular, we use approaches based on convex optimisation to make it computationally efficient and thus translatable to current clinical applications. The project is supported by a highly interdisciplinary team consisting of mathematicians (Bath, Heriot-Watt), engineers, physicists (National Physical Laboratory) and medical professionals.
Project keywords: Mathematics, inverse problems, uncertainty quantification, medical imaging, Positron Emission Tomography
In addition to the SAMBa entrance requirements, the ideal candidate would have undergraduate experience in one or more of the following areas: inverse problems, mathematical imaging, optimisation, or numerical methods, but training can be provided for a suitably motivated candidate. Experience in programming is desirable (e.g., MATLAB / Python).
Informal enquiries are encouraged and should be directed to supervisor Dr Matthias Ehrhardt m.ehrhardt@bath.ac.uk
1. In the Finance section, enter ‘SAMBa’ when asked to name the scholarship or PhD studentship you wish to be considered for.
2. In the Your research interests section, quote the project title of this project at the top of your statement and the name of the lead supervisor in the appropriate box.
