A Study of Androgen Annihilation in High-Risk Biochemically Relapsed Prostate Cancer

Inclusion Criteria: * Histologically confirmed prostate adenocarcinoma * Prior radical prostatectomy * Biochemically recurrent prostate cancer with PSA doubling time ≤ 9 months at the time of study entry. Calculation of PSA doubling time should include the use of all available PSA values obtained within past 6-12 months prior to randomization, with a minimum of 3 values separated by at least 2 weeks apart. PSA values obtained prior to therapeutic interventions (e.g. salvage radiation) will be excluded. PSA doubling time to be estimated using Memorial Sloan Kettering Cancer Center online calculator (https://www.mskcc.org/nomograms/prostate/psa-doubling-time) * Prior adjuvant or salvage radiation or not a candidate for radiation based upon clinical assessment of disease characteristics and patient co-morbidities. * Screening PSA \> 0.5 ng/mL * No definitive evidence of metastases on screening CT or MRI of abdomen/pelvis and radionuclide whole body bone scan per the judgment of the investigator. Abdominal and/or pelvic lymph nodes measuring 2 cm or less in short axis diameter are allowed. Lesions identified on other imaging modalities (e.g. PSMA or choline PET) that are not visualized on CT and/or MRI or radionuclide bone scan are allowed. Equivocal lesions on bone scan should be followed up with additional imaging as clinically indicated. * Screening serum testosterone \> 150 ng/dL * Eastern Cooperative Oncology Group (ECOG) Performance Status grade 0 or 1 * Age ≥ 18 years * Medications known to lower the seizure threshold must be discontinued or substituted at least 4 weeks prior to cycle 1 day 1 * Agrees to use a condom (even men with vasectomies) and another effective method of birth control if he is having sex with a woman of childbearing potential or agrees to use a condom if he is having sex with a woman who is pregnant while on study drug and for 3 months following the last dose of study drug. Must also agree not to donate sperm during the study and for 3 months after receiving the last dose of study drug. * Adequate organ function as defined by the following laboratory values at screening: * Serum aspartate transaminase (AST; serum glutamic oxaloacetic transaminase \[SGOT\]) and serum alanine transaminase (ALT; serum glutamic pyruvic transaminase \[SGPT\]) \< 2.5 x upper limit of normal (ULN) * Total serum bilirubin ≤1.5 x ULN. In subjects with Gilbert's syndrome, if total bilirubin is \>1.5 × ULN, measure direct and indirect bilirubin and if direct bilirubin is ≤1.5 × ULN, subject may be eligible) * Serum potassium ≥ 3.5 mmol/L. Supplementation and re-screening is allowed. * Estimated creatinine clearance \> 45 ml/min using Cockroft-Gault equation * Platelets ≥ 100,000/microliter independent of transfusion and/or growth factors within 3 months prior to randomization * Hemoglobin ≥ 9.0 g/dL independent of transfusion and/or growth factors within 3 months prior to randomization * Serum albumin ≥ 3.0 g/dL Exclusion Criteria: * Prior androgen deprivation therapy and/or first generation anti-androgen (e.g. bicalutamide, nilutamide, flutamide) for biochemically recurrent prostate cancer. Prior ADT and/or first generation anti-androgen in the (neo)adjuvant and/or salvage setting before, during, and/or following radiation or surgery is allowed provided last effective dose of ADT and/or first-generation anti-androgen is \> 9 months prior to date of randomization and total duration of prior therapy is ≤ 36 months. * Prior treatment with CYP17 inhibitor (e.g. ketoconazole, abiraterone acetate, galeterone) or second generation androgen receptor antagonist including apalutamide or enzalutamide * Prior chemotherapy for prostate cancer except if administered in neoadjuvant or adjuvant setting * Use of 5-alpha reductase inhibitor within 42 days prior to cycle 1 day 1 * Use of investigational agent within 28 days prior to randomization * Use of other prohibited medications within 7 days prior to cycle 1 day 1 on study (Arms B and C only) * Prior bilateral orchiectomy * Seizure or known condition that may pre-dispose to seizure (e.g. prior stroke within 1year to randomization, brain arteriovenous malformation, Schwannoma, meningioma, or other benign CNS or meningeal disease which may require treatment with surgery or radiation therapy) * Uncontrolled hypertension * Gastrointestinal disorder affecting absorption or the ability to swallow tablets * Baseline severe hepatic impairment (Child-Pugh Class B \& C) * Intercurrent illness that is not controlled such as active infection, psychiatric illness/social situations that would limit compliance with study requirements * Any chronic medical condition requiring a higher dose of corticosteroid than equivalent of 5 mg prednisone/prednisolone once daily