A Salvage Trial of AR Inhibition With ADT and Apalutamide With Radiation Therapy Followed by Docetaxel in Men With PSA Recurrent Prostate Cancer After Radical Prostatectomy (STARTAR)

Inclusion Criteria: 1. Histologically-confirmed diagnosis of prostate adenocarcinoma. Variants of prostate cancer, including neuroendocrine features and small cell carcinoma of the prostate, are not permitted. 2. Gleason sum of 7 (with pT3 disease or positive margins or positive nodes \[4 or fewer\]), 8, 9, or 10 based on the radical prostatectomy specimen 3. PSA relapse within 4 years of prostatectomy defined by persistently detectable or rising PSA after surgery. 4. Evidence of disease recurrence or progression as evidenced by a PSA \> 0.20. This requires 2 consecutive rises in PSA, at least 1 week apart, over the post-prostatectomy nadir OR one PSA value above 0.20 ng/mL IF the patient failed to achieve a post-prostatectomy nadir of \< 0.2 ng/mL. 5. Age ≥ 18 years 6. Karnofsky performance status ≥ 80 7. Adequate laboratory parameters * Adequate bone marrow function: ANC ≥1.5 x 109/L, Platelets ≥100 x 109/L, Hb \>9g/dL * AST/SGOT and ALT/SGPT ≤ 2.5 x Institutional Upper Limit of Normal (ULN) * Serum bilirubin ≤ 1.5 x Institutional ULN (In subjects with Gilbert's syndrome, if total bilirubin is \> 1.5xULN, measure direct and indirect bilirubin and patient is eligible if direct bilirubin ≤ 1.5xULN). * Glomerular filtration rate (either estimated or calculated from 24-hour urine collection) ≥ 45 mL/min * Serum potassium ≥3.5 mmol/L 8. A minimum of 4 weeks from any major surgery prior to Cycle 1 Day 1. 9. Ability to swallow, retain, and absorb oral medication. 10. Ability to understand and the willingness to sign a written informed consent document. 11. Must use a condom if having sex with a pregnant woman. 12. Male patient and his female partner who is of childbearing potential must use 2 acceptable methods of birth control (one of which must include a condom as a barrier method of contraception) starting at screening and continuing throughout the study period and for 3 months after final study drug administration. Exclusion Criteria: 1. Radiographic evidence of metastatic disease. Patients with node-positive disease (≤4 positive nodes) at the time of radical prostatectomy are eligible. Patients with pelvic nodes less than 1.5 cm by short axis at the time of screening are eligible. Patients with any enlarged lymph nodes in the retroperitoneum or above the aortic bifurcation or with pelvic nodes ≥ 1.5 cm must be excluded. 2. PSA ≥ 4.0 ng/mL. 3. Testosterone level ≤ 100 ng/dL. 4. More than 1 month of prior hormone exposure or hormone exposure within 30 days of enrollment (up to 1 month of prior LHRH agonist and/or anti-androgen therapy as neoadjuvant therapy prior to prostatectomy is allowed). Prior enzalutamide, apalutamide, ketoconazole, abiraterone, or TAK700 for prostate cancer are prohibited. Prior antiandrogen therapy (including but not limited to bicalutamide, flutamide, nilutamide, enzalutamide, and apalutamide) and prior estrogen therapy (including estrogen patch) are not allowed. All investigational agents are prohibited within 30 days of enrollment. 5. The following medications are prohibited within 2 weeks of enrollment and while on study drug: * 5 α-reductase inhibitors (finasteride, dutasteride); * Biologic or other agents with anti-tumor activity against prostate cancer; * Systemic glucocorticoids greater than the equivalent of 10 mg per day of prednisone; oPremedication with systemic glucocorticoids greater than the equivalent of 10 mg per day of prednisone is permitted prior to docetaxel infusions. * Androgens (testosterone, dihydroepiandrosterone \[DHEA\], etc.) 6. Prior immunotherapy including sipuleucel-T. 7. Prior systemic chemotherapy (docetaxel, cabazitaxel, estramustine, other cytotoxic agents) 8. History of solid organ or stem cell transplantation. 9. History of seizure or any condition that may predispose to seizure (e.g., prior cortical stroke, prior head or traumatic brain injury with loss of consciousness, prior or current space-occupying lesion in the brain). Also, history of loss of consciousness or transient ischemic attack within 12 months of Day 1 visit. 10. Known or suspected brain metastasis or active leptomeningeal disease. 11. Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g., active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol. 12. Severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (eg, pulmonary embolism, cerebrovascular accident including transient ischemic attacks), or clinically significant ventricular arrhythmias within 6 months prior to enrollment 13. Sustained uncontrolled hypertension (\>150/90 average over 1 week) despite optimal medical management 14. Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of apalutamide or increase the risk of radiation (e.g., uncontrolled nausea, vomiting, diarrhea, malabsorption syndromes, prior small bowel resection, or inflammatory bowel disease). 15. Patients who have received prior prostate or pelvic radiotherapy, including external beam or brachytherapy. 16. Patients who have not recovered from side effects of prior systemic therapy prior to Cycle 1 Day 1. 17. Use of medications known to lower the seizure threshold within 4 weeks prior to study entry. 18. Patients unable or unwilling to abide by the study protocol or cooperate fully with the investigator.