Abstract
Prostate cancer screening, surveillance, and treatment are collectively modeled as a finite-horizon partially observable Markov decision process (POMDP) with three stages in each decision epoch. This integrated formulation could potentially help patients optimally decide when to have a PSA test, whether to follow up by a biopsy, and whether to subsequently initiate a definitive treatment like surgery or radiation therapy. A new approximation method is presented for solving the finite-horizon POMDP. The method uses fixed computing budgets to compute lower and upper bounds on the optimal value function of the POMDP at each decision epoch. The lower and upper bounds are obtained using inner and outer linearizations like surgery or radiation therapy, respectively. The performance is reported in terms of optimality gap and computation time. The method can obtain near optimal solutions with shorter computation time compared to a commonly used exact method.
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