title: Bayesian Calibration, Validation and Uncertainty Quantification for Predictive Modelling of Tumour Growth: A Tutorial.
abstract: In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, UK. Joe.Collis@nottingham.ac.uk.
authors.forename: Joe
authors.identifier: http://orcid.org/0000-0001-8715-2813
authors.initials: J
authors.lastname: Collis
authors.affiliation: Mathematical Institute, University of Oxford, Oxford, UK.
authors.forename: Anthony J
authors.initials: AJ
authors.lastname: Connor
authors.affiliation: Mathematical Institute, University of Oxford, Oxford, UK.
authors.forename: Marcin
authors.initials: M
authors.lastname: Paczkowski
authors.affiliation: Gray Institute for Radiation Oncology and Biology, University of Oxford, Oxford, UK.
authors.forename: Pavitra
authors.initials: P
authors.lastname: Kannan
authors.affiliation: Department of Computer Science, University of Oxford, Oxford, UK.
authors.forename: Joe
authors.initials: J
authors.lastname: Pitt-Francis
authors.affiliation: Mathematical Institute, University of Oxford, Oxford, UK.
authors.forename: Helen M
authors.initials: HM
authors.lastname: Byrne
authors.affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, UK.
authors.forename: Matthew E
authors.initials: ME
authors.lastname: Hubbard
mesh_terms: D001499:Bayes Theorem; D002138:Calibration; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms; D011379:Prognosis; D035501:Uncertainty
keywords: Bayesian calibration; Model validation; Tumour growth