Standard Systemic Therapy With or Without Definitive Treatment in Treating Participants With Metastatic Prostate Cancer

PRIMARY OBJECTIVES: I. To compare overall survival in metastatic prostate cancer patients who are randomized to standard systemic therapy (SST) plus definitive treatment of the primary tumor versus standard systemic therapy alone. SECONDARY OBJECTIVES: I. To compare overall survival in metastatic prostate cancer patients who received SST plus surgical excision of the primary tumor versus SST alone in the subset who specify the surgical intent stratification factor. II. To compare the rate of symptomatic local progression between the treatment arms. III. To compare progression-free survival (PFS) between the two treatment arms. IV. To compare rates of progression-free survival between arms for the subsets of patients with and without metastasis directed therapy (MDT) to oligometastatic sites. QUALITY OF LIFE OBJECTIVES: I. To compare between arms patient-reported urinary function and urinary bother over time (after initiation of SST at 6 months, 1, 2, and 3 years) using the Expanded Prostate Cancer Index Composite (EPIC) and patient-reported pain and physical functioning using the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire (EORTC QLQ-C30) between patients receiving standard systemic therapy and those receiving systemic therapy and definitive management of the primary prostate cancer. OTHER OBJECTIVES: I. To bank tissue and whole blood specimens for future use. OUTLINE: INDUCTION: Participants receive 1 of 6 acceptable forms of SST for 22-28 weeks. I. Participants undergo a bilateral orchiectomy. II. Participants receive goserelin acetate subcutaneously (SC) every 28 days or 12 weeks, histrelin acetate SC every 12 months, leuprolide acetate SC or intramuscularly (IM) every 1, 3, 4, or 6 months, and triptorelin every 1, 3, or 6 months. III. Participants receive goserelin acetate SC every 28 days or 12 weeks, histrelin acetate SC every 12 months, leuprolide acetate SC or IM every 1, 3, 4, or 6 months, and triptorelin every 1, 3, or 6 months. Participants also receive nilutamide orally (PO) daily, flutamide PO every 8 hours, and bicalutamide PO daily. IV. Participants receive degarelix via injection for 2 doses and then every 28 days. V. Participants receive nilutamide PO daily, flutamide PO every 8 hours, and bicalutamide PO daily. Participants also receive docetaxel over 1 hour every 3 weeks with or without prednisone PO every 12 hours. VI. Participants receive nilutamide PO daily, flutamide PO every 8 hours, and bicalutamide PO daily. Participants also receive abiraterone PO daily or prednisone PO every 12 hours. After completion of 22-28 weeks of SST, participants are then randomized to 1 of 2 arms. ARM I: Participants receive 1 acceptable form of SST as in Induction except for treatment with docetaxel and prednisone. ARM II: Participants receive 1 acceptable form of SST as in Induction except for treatment with docetaxel and prednisone. Participants undergo prostatectomy within 8 weeks after randomization or radiation therapy within 4 weeks of randomization. After completion of study treatment, participants are followed up for 8 years.