PhD Studentship: Uncertainty quantification for healthcare models: a route to precision medicine

Mathematical models are important tools for gaining insight into complex processes across biological systems and healthcare. To support high-stakes decisions in a clinical setting using these models, we need to ensure that their predictions are credible. Uncertainty Quantification (UQ) is one of the key principles of model credibility. Throughout this PhD project, the student will have an opportunity to work with a diverse suite of cardiovascular mathematical models to develop an efficient UQ pipeline. Cardiovascular disease remains the leading cause of death worldwide, and patient-specific models are increasingly proposed to guide diagnosis, device selection and treatment planning.

The barrier to clinical adoption is not modelling capability but credibility: regulators and clinicians need to know how far a prediction can be trusted for an individual patient. This project addresses that gap directly, developing UQ methods that make model predictions and their uncertainties defensible. The project sits at the intersection of statistics, cardiovascular physiology, mathematical modelling and scientific computing. Its methodological core emulation, calibration and the treatment of model discrepancy - comes from the UQ field, but the driving questions come from mathematical modelling: which parameters are identifiable from clinical measurements, and what confidence is defensible in a clinical setting. The student will have an opportunity to closely engage with these communities to explore these questions.

 Within the project, there are two main UQ focusses:

1. Emulation and surrogate modelling: to perform forward and inverse UQ, many runs of mathematical models are required. If we are dealing with a computationally expensive model, it is common to adopt a surrogate model to speed up the process. Cardiovascular models have a large number of unknown model parameters and generate multiple outputs at the same time. Training emulators in large input spaces and across multiple related outputs is non-trivial. The student will explore different existing methods, and develop novel, efficient emulation methodologies.
2. Inverse UQ. To make mathematical models actionable and relevant in practice, it is crucial to calibrate them using real-world observations while accounting for their limitations. The student will explore various calibration methods to find ‘good’ settings of model inputs, whilst explicitly accounting for structural uncertainty (model discrepancy) in the model, which Engineering and Physical Sciences Research Council Doctoral Landscape Award comes from the notion that the model is not a perfect representation of the physical process of interest. The goal is to provide insight of where different models outperform others, identifying limitations of existing models and where further development is needed to provide accurate and timely decisions. Whilst the overall goal of the PhD is to apply and develop emulation and calibration methodologies for cardiovascular modelling specifically, these will likely be applicable across a wider range of problems, and the project may seek additional partners to apply and test developed methods across further important application areas.

Funded by: EPSRC Engineering and Physical Sciences Research Council