Apalutamide With or Without Stereotactic Body Radiation in Treating Castration-Resistant Prostate Cancer

Inclusion Criteria:

* Histologically or cytologically confirmed adenocarcinoma of the prostate
* Progressive, castration-resistant prostate cancer demonstrated during continuous antiandrogen therapy (ADT), defined as 3 PSA rises at least 1 week apart, with a minimum PSA \> .05 ng/mL obtained during screening.
* At least one but no more than 5 discrete PSMA-avid radiation fields on baseline PSMA-PET scan; all PSMA-avid lesions in radiation fields must be amenable to SBRT in judgment of treating radiation oncologist; there are no restrictions on site of lesion/radiation fields (e.g. bone, lymph node, prostate, visceral). Equivocal lesions/radiation fields on PSMA PET scan that are not definitive for metastasis will not count towards the limit of 5 radiation fields and will not undergo SBRT
* Surgically or medically castrated, with testosterone levels of \< 50 ng/dL during screening; if the patient is medically castrated, continuous dosing with luteinizing hormone-releasing hormone (LHRH) analogue must have been initiated at least 4 weeks prior to randomization and must be continued throughout the study to maintain castrate levels of testosterone including post-treatment follow up period
* No prior systemic treatment initiated for the treatment of castration resistant prostate cancer, including abiraterone acetate, enzalutamide, apalutamide, darolutamide, other novel AR or CYP17 antagonist, or docetaxel.
* Patients receiving bone loss prevention treatment with bone-modifying agents (e.g. denosumab, zoledronic acid) must be on stable doses for at least 4 weeks prior to randomization
* Patients who received a first generation anti-androgen (e.g., bicalutamide, flutamide, nilutamide) as most recent treatment must have at least a 6-week washout prior to randomization and must show continuing disease (PSA) progression (an increase in PSA) after washout
* At least 4 weeks or 5 half-lives, whichever is shorter, must have elapsed from the use of any anti-cancer therapy, other than Luteinizing hormone-releasing hormone (LHRH) analog or first generation antiandrogen, prior to randomization
* At least 4 weeks must have elapsed from major surgery or radiation therapy prior to randomization
* Age \> 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status grade 0 or 1
* Resolution of all acute toxic effects of prior therapy or surgical procedure to grade 1 or baseline prior to randomization
* 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 known or suspected Gilbert's syndrome, if total bilirubin is \> 1.5 x ULN, direct bilirubin is ≤ 1.5 x ULN
* Glomerular filtration rate ≥ 45 ml/min based on Cockcroft-Gault equation
* Absolute neutrophil count (ANC) ≥ 1500/microliter
* Platelets ≥ 75,000/microliter without transfusion and/or growth factors in the 3 months prior to randomization
* Hemoglobin ≥ 9.0 g/dL without transfusion and/or growth factors in the 3 months prior to randomization
* Serum albumin ≥ 3.0 g/dL
* Signed and dated informed consent document indicating that the patient has been informed of all pertinent aspects of the trial prior to randomization
* Willingness and ability to comply with scheduled visits, treatment plans, laboratory and radiographic assessments, and other study procedures, including ability to swallow study drug tablets and long-term follow-up
* 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

Exclusion Criteria:

* Presence of visceral lesions (e.g. lung, liver) detectable on baseline imaging or bone lesions requiring focal radiation treatment at the time of study entry
* History of seizure or condition that may pre-dispose to seizure (e.g., prior stroke within 1 year prior to randomization, brain arteriovenous malformation, Schwannoma, meningioma, or other benign central nervous system (CNS) or meningeal disease which may require treatment with surgery or radiation therapy
* Concurrent therapy with any of the following (all must have been discontinued or substituted for at least 1 week prior to randomization, except for medications known to lower seizure threshold which must be discontinued or substituted at least 4 weeks prior to randomization)
* Medications known to lower the seizure threshold
* Herbal (e.g., saw palmetto) and non-herbal (e.g., pomegranate) products that may decrease PSA levels
* Systemic (oral/intravenous (IV)/intramuscular (IM)) corticosteroids; patients on chronic stable dose of steroids at an equivalent dose of prednisone ≤ 10 mg daily may be permitted to enroll at the discretion of principal investigator
* Any other experimental treatment on another clinical trial
* Any of the following within 6 months prior to randomization: Severe/unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (e.g., pulmonary embolism, cerebrovascular accident including transient ischemic attacks), or clinically significant ventricular arrhythmias
* Uncontrolled hypertension at study entry; patients with a history of uncontrolled hypertension are allowed provided blood pressure is controlled by antihypertensive treatment
* Gastrointestinal disorder affecting absorption
* Secondary malignancy requiring active treatment except for non-melanoma skin cancer and superficial bladder cancer
* Any medical condition that would be a contra-indication to radiation therapy, such as inflammatory bowel disease
* Spinal cord compression or impending spinal cord compression
* Any other condition that, in the opinion of the Investigator, would impair the patient's ability to comply with study procedures