Optimization of Prostate Biopsy Referral Decisions

Prostate cancer is the most common solid tumor in American men and is screened for using prostate‐specific antigen (PSA) tests. We report on a nonstationary partially observable Markov decision process (POMDP) for prostate biopsy referral decisions. The core states are the patients' prostate cancer related health states, and PSA test results are the observations. Transition probabilities and rewards are inferred from the Mayo Clinic Radical Prostatectomy Registry and the medical literature. The objective of our model is to maximize expected quality‐adjusted life years. We solve the POMDP model to obtain an age and belief (probability of having prostate cancer) dependent optimal biopsy referral policy. We also prove a number of structural properties including the existence of a control‐limit type policy for the biopsy referral decision. Our empirical results demonstrate a nondecreasing belief threshold in age, and we provide sufficient conditions under which PSA screening should be discontinued for older patients. Finally, the benefits of screening under the optimal biopsy referral policy are estimated, and sensitivity analysis is used to prioritize the model parameters that would benefit from additional data collection.