Designing patient-specific follow-up strategy is a crucial step towards personalized medicine in cancer. Tools to help doctors deciding on treatment allocation together with next visit date, based on patient preferences and medical observations, would be particularly beneficial. Such tools should be based on realistic models of disease progress under the impact of medical treatments, involve the design of (multi-)objective functions that a treatment strategy should optimize along the patient's medical journey, and include efficient resolution algorithms to optimize personalized follow-up by taking the patient's history and preferences into account. We propose to model cancer evolution with a Piecewise Deterministic Markov Process where patients alternate between remission and relapse phases with disease-specific tumor evolution. This model is controlled via the online optimization of a long-term cost function accounting for treatment side-effects, hospital visits burden and disease impact on the quality of life. Optimization is based on noisy measurements of blood markers at visit dates. We leverage the Partially-Observed Monte-Carlo Planning algorithm to solve this continuous-time, continuous-state problem, taking advantage of the nearly-deterministic nature of cancer evolution. We show that this approximate solution approach of the exact model performs better than the counterpart exact resolution of the discrete model, while allowing for more versatility in the cost function model.