Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

by  Alexander Browning, Thomas Lewin, Ruth Baker, Philip Maini, Eduardo Moros, Jimmy Caudell, Helen Byrne and Heiko Enderling

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Mathematical models have the potential to revolutionise clinical practise by providing real-time insights that guide decision-making and predict patient responses. Challenges associated with the application of mathematical models are perhaps, however, most acute for single-patient clinical data of cancer tumour progression. Data are often noisy, sparse, and simplistic; patient responses are often highly variable; and mathematical models may be necessarily complex.

In this work, we develop and present a novel, simple, mathematical model of tumour volume progression in response to radiotherapy that can capture a full gamut of patient responses observed in the clinic. To maximise the utility of data collected from a large clinical cohort whilst accounting for significant patient-to-patient variation, we present alongside the model a Bayesian statistical method that allows for real-time clinical predictions to be drawn throughout a patient's course of treatment.

All model parameters vary between patients, with prior parameter knowledge for new patients informed by a weighted mixture of posterior parameter knowledge from previously observed patients. We demonstrate the ability of our model and statistical framework by considering a subset of patients for which predictions are continuously updated throughout their course of treatment.

The research was led by Alexander Browning (from 2023), a research fellow, and Thomas Lewin (until 2022), a DPhil student.

Caption: Data from a cohort of training data are used to calibrate population-level posterior distributions that account for patient-to-patient variability. Individual-level predictions are then drawn and then updated throughout a patients’ course of treatment