Prostate-specific antigen (PSA) is the most common serum marker for prostate cancer. It is used to detect prostate cancer, to assess responses to treatment and recently even to determine when to switch treatment on and off in adaptive therapy protocols. However, the correlation between PSA and tumor volume is poorly understood. Moreover, even though there is empirical evidence that some cancer cell types produce more PSA than others, recent mathematical cancer models assume that all cell types contribute equally to the PSA level. Here, we compare time to competitive release of the PSA-based adaptive therapy protocol to that of the standard of care with continuous maximum tolerable dose under different assumptions on PSA production. In particular, we assume that androgen dependent, androgen producing, and androgen independent may contribute to the PSA production to different extents. Our results show that, regardless the assumption on how much each type contributes to PSA, adaptive therapy is always at least as good as standard of care in the sense that it prolongs the time of competitive release when resistant androgen independent cells outcompete the other types. The time to competitive release under adaptive therapy and standard of care coincides if the PSA dynamics are influenced only by the resistant cells. Furthermore, we observe that in the adaptive therapy protocol, the number of treatment cycles and their length strongly depend on the assumptions about the PSA contribution of the three types. Thus, our results suggest that investigating the patient-specific PSA dynamics is crucial to designing adaptive therapy protocols.

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