  Longitudinal tumour volume data from head-and-neck cancer patients show that
tumours of comparable pre-treatment size and stage may respond very differently
to the same radiotherapy fractionation protocol. Mathematical models are often
proposed to predict treatment outcome in this context, and have the potential
to guide clinical decision-making and inform personalised fractionation
protocols. Hindering effective use of models in this context is the sparsity of
clinical measurements juxtaposed with the model complexity required to produce
the full range of possible patient responses. In this work, we present a
compartment model of tumour volume and tumour composition, which, despite
relative simplicity, is capable of producing a wide range of patient responses.
We then develop novel statistical methodology and leverage a cohort of existing
clinical data to produce a predictive model of both tumour volume progression
and the associated level of uncertainty that evolves throughout a patient's
course of treatment. To capture inter-patient variability, all model parameters
are patient specific, with a bootstrap particle filter-like Bayesian approach
developed to model a set of training data as prior knowledge. We validate our
approach against a subset of unseen data, and demonstrate both the predictive
ability of our trained model and its limitations.
