Technological advancements in radiation therapy (RT) allow the collection of biomarker data on individual patient response during treatment. Although biomarker data remains subject to substantial uncertainties, information extracted from this data may allow the RT plan to be adapted in an informative way. We present a mathematical framework that optimally adapts the treatment-length of an RT plan based on the acquired mid-treatment biomarker information, and also consider the inexact nature of this information. We formulate the adaptive treatment-length optimization problem as a 2-stage problem, where after the first stage we acquire information about model parameters and decisions in stage 2 may depend on this information. Using Adjustable Robust Optimization (ARO) techniques we derive explicit optimal decision rules for the stage-2 decisions and solve the optimization problem. The problem allows for multiple worst-case optimal solutions. To discriminate between these, we introduce the concept of Pareto Adjustable Robust Optimal (PARO) solutions. In extensive numerical experiments based on liver cancer patient data, ARO is benchmarked against several other static and adaptive methods, including robust optimization with a folding horizon. Results show good performance of ARO both if acquired mid-treatment biomarker data is exact and inexact. We also investigate the effect of biomarker acquisition time on the performance of the ARO solution and the benefit of adaptation. Results indicate that a higher level of uncertainty in biomarker information pushes the optimal moment of biomarker acquisition backwards.
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