Docetaxel and Prednisone With or Without Vaccine Therapy in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer

PRIMARY OBJECTIVES: I. To evaluate the overall survival in patients treated with PSA-TRICOM (fowlpox-PSA-TRICOM vaccine and rilimogene-galvacirepvec) and docetaxel chemotherapy versus docetaxel chemotherapy only. SECONDARY OBJECTIVES: I. To evaluate the time to radiographic progression after beginning docetaxel chemotherapy in patients previously treated with PSA-TRICOM vaccine versus those not treated with this vaccine. II. To compare objective responses (according to Response Evaluation Criteria in Solid Tumors \[RECIST\]) between the two treatment groups in those patients with measurable disease. III. To evaluate prostate-specific antigen (PSA) response rates (decline \>= 50%) in patients treated with PSA-TRICOM and docetaxel chemotherapy versus docetaxel chemotherapy only. IV. To evaluate immune responses elicited in patients treated before and after docetaxel chemotherapy. V. To evaluate the association between development of prostate antigen-specific immune responses and time to progression and overall survival. VI. To evaluate the association of predicted survival (by Halabi nomogram) with actual survival in patients treated with PSA-TRICOM vaccine versus those not treated with this vaccine. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM A (vaccine and chemotherapy): Patients receive rilimogene-galvacirepvec subcutaneously (SC) on day 1 of course 1 and fowlpox-PSA-TRICOM vaccine SC on days 15, 29, 43, and 57 of course 1. Beginning on day 85 (day 1 of course 2), patients receive docetaxel intravenously (IV) over 1 hour on day 1 and prednisone orally (PO) twice daily (BID) on days 1-21. Treatment with docetaxel and prednisone repeats every 21 days for up to 12 courses in the absence of disease progression or unacceptable toxicity. ARM B (chemotherapy): Patients receive docetaxel IV over 1 hour on day 1 and prednisone PO BID on days 1-21. Treatment repeats every 21 days for up to 12 courses in the absence of disease progression or unacceptable toxicity. After completion of study therapy, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.