Deriving evolutionary-informed biomarkers and treatment schedules for drug-resistant cancer

Thesis

Standard-of-care cancer treatment regimens fail when applied to metastaticcancers due to the inevitable emergence of drug resistance, leading to treatmentfailure and disease progression. This thesis presents a comprehensive mathematicalframework for optimising adaptive therapy (AT) protocols – an evolution-basedtreatment paradigm that dynamically adjusts treatment to control, rather thanminimise, tumour burden by exploiting inter-cellular competition.

Using mathematical models calibrated to prostate cancer dynamics, I considerboth analytic and machine learning (ML) approaches to deriving optimal ATstrategies. Extracting interpretable treatment strategies from the ‘black-box’ MLframework, I demonstrate that these match the analytically optimal solution, andpropose a translational pathway to bridge the gap between ML models and clinicalimplementation. This work extends prior AT protocols by accounting for clinicalconstraints such as the discrete time intervals between appointments. Consideringthese clinical realities reveals a fundamental trade-off between tumour monitoringfrequency and possible time to progression.

Prior clinical trials have identified significant heterogeneity in patients’ responsesto AT. Through a comparison of different mathematical tumour models, Iidentify distinct patient subpopulations requiring qualitatively different treatmentapproaches, including a subset that benefits from novel protocols with time-varyingthresholds. I further develop a set of predictive mathematical biomarkers to predictpatients’ time to progression and mean daily dose across various AT protocols,and integrate these into a stratified-treatment framework to personalise the ATprotocol prescribed for each patient.

Collectively, this work establishes a comprehensive mathematical foundationfor personalised adaptive cancer therapy, providing both theoretical insights intotumour-treatment dynamics and practical tools for clinical implementation. Theproposed frameworks address critical gaps in current adaptive treatment approacheswhilst maintaining clinical feasibility, offering a promising pathway towards moreeffective, evolution-informed cancer care.

Authors: Gallagher, C

• DOI: 10.5287/ora-zvxqogvew
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: adaptive therapy; treatment scheduling; prostate cancer; mathematical oncology
• Subjects: Mathematics; Oncology