Flow Φ of the controlled continuous time PDMP.

Designing patient-specific follow-up strategies is key to personalized cancer care. Tools to assist doctors in treatment decisions and scheduling follow-ups based on patient preferences and medical data would be highly beneficial. These tools should incorporate realistic models of disease progression under treatment, multi-objective optimization of treatment strategies, and efficient algorithms to personalize follow-ups by considering patient history. We propose modeling cancer evolution using a Piecewise Deterministic Markov Process, where patients alternate between remission and relapse phases, and control the model via long-term cost function optimization. This considers treatment side effects, visit burden, and quality of life, using noisy blood marker measurements for feedback. Instead of discretizing the problem with a discrete Markov Decision Process, we apply the Partially-Observed Monte-Carlo Planning algorithm to solve the continuous-time, continuous-state problem, leveraging the near-deterministic nature of cancer progression. Our approach, tested on multiple myeloma patient data, outperforms exact solutions of the discrete model and allows greater flexibility in cost function modeling, enabling patient-specific follow-ups. This method can also be adapted to other diseases.