Androgen Receptor Signaling and Prostate-Specific Membrane Antigen Expression

Inclusion Criteria: * Patients age 40 or higher with prostate cancer that has been previously treated with primary definitive local therapies (prostatectomy with or without salvage radiation, or primary prostate radiation) and subsequently experiencing rising PSA meeting criteria for biochemical failure (PSA \>0.2 ng/dL x2 following prostatectomy, or PSA \> 2 + nadir value following primary radiation). * PSMA PET/CT (Ga68, piflutolastat F-18, or other FDA-approved tracer) during time of biochemical recurrence, and within 6 weeks of registration, showing at least one lesion suspicious for recurrent prostate cancer based on size and/or SUV. * Testosterone \>100 ng/dL within 6 months prior to enrollment with no intervening hormonal therapies. * Assigned by treating physician to receive standard-of-care AR antagonist monotherapy, using FDA-approved apalutamide, darolutamide, or enzalutamide. Exclusion Criteria: * High disease burden, significant symptoms of disease, or other clinical situation requiring medical/surgical castration and/or docetaxel during the time of the study. * Not suitable for AR antagonist therapy (e.g. inability to swallow pills, poor adherence, advanced liver disease, prohibitive co-payment without available patient assistance funding, contraindicated drug-drug interaction). * Older-generation AR antagonists (e.g. bicalutamide) are not allowed on study.