RATIONALE: Androgens can cause the growth of prostate cancer cells. Antihormone therapy, such as leuprolide acetate, goserelin, flutamide, or bicalutamide may lessen the amount of androgens made by the body. Monoclonal antibodies, such as ipilimumab, can block cancer growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry cancer-killing substances to them. Giving antihormone therapy together with ipilimumab may kill more tumor cells.

PURPOSE: This randomized phase II trial is study how well giving hormone therapy and ipilimumab together works in treating patients with advanced prostate cancer.

OBJECTIVES:

I. To generally test whether the addition of CTLA-4 blockade can enhance clinical treatment response in advance prostate cancer patients compared with treatment with AA therapy alone.

II. To specifically examine whether concomitant AA therapy + MDX-010 can be used to prolong the progression-free interval in advanced prostate cancer patients compared with inductive short-term AA therapy alone.

III. To specifically examine whether concomitant AA therapy + MDX-010 can be used to enhance initial PSA responses in advanced prostate cancer patients compared with inductive short-term AA therapy alone.

IV. To specifically examine whether delayed MDX-010 can be used to induce PSA response in patients experiencing disease progression following cessation of short-term AA therapy.

V. To generally examine whether MDX-010 enhances host immune response that might be involved in conferring treatment advantages to patients receiving AA therapy.

VI. To specifically examine whether MDX-010 potentiates T-cell responses in advanced prostate cancer patients initiating inductive short-term AA therapy.

VII. To further examine whether treatment induced T-cell responses correlate with clinical response to treatment.

VIII. To examine whether short-term AA there (+/- MDX-010) induces the appearance of newly emigrated T or immature and/or B cells.

OUTLINE:

Patients are randomized to 1 of 2 treatment arms.

ARM I: Patients receive either leuprolide acetate intramuscularly (IM) or goserelin subcutaneously (SC) on days 0, 28, and 56. Patients also receive oral flutamide three times daily or oral bicalutamide once daily. Treatment with antiandrogen (AA) therapy continues for 3 months (3-4 months for patients who initiated AA therapy <= 21 days prior to enrollment) in the absence of disease progression or unacceptable toxicity. Patients receive ipilimumab IV over 90 minutes on day 7 (within 7-28 days post-initiation of AA therapy for patients who initiated AA therapy <= 21 days prior to enrollment) of AA therapy.

Arm II: Patients receive AA therapy as in arm I. Patients may crossover to arm II in the case of disease progression.

After completion of study treatment, patients are followed periodically.

Inclusion Criteria:

• NOTE: All values must be obtained =< 14 prior to study entry
• Histologically confirmed adenocarcinoma of the prostate staged within 180 days of study enrollment, >cT2cN0/M0 stage with or without metastatic disease, with the exclusion of central nervous system (CNS) metastases; includes post radical prostatectomy patients with a rising PSA
• An initial PSA >= 4.0 ng/mL (Hybritech Assay)
• For those patients who have received hormone therapy =< 21 days, a documented PSA of >= 4.0 prior to initiation of hormone therapy is acceptable.
• For patients who are post radical prostatectomy, a rising PSA is acceptable.
• Adequate organ function defined as: WBC >= 3,000/uL; platelets >= 75,000/uL; total bilirubin =< 1.5 mg/dL; transaminases =< 2.5 x upper limit of normal (ULN); serum creatine =< 2.0 mg/dL or calculated creatinine clearance >= 60 mL/min
• ECOG performance status of 0-2
• Able to understand and sign informed consent

Exclusion Criteria:

• Underlying other serious medical condition which, in the opinion of the investigator precludes study participation; this includes immune-suppressive disease such as AIDS or autoimmune disorders such as multiple sclerosis, lupus, or myasthenia gravis
• Patients not recovered from major infections and/or surgical procedures
• Prior hormonal therapy > 21 days prior to enrollment, including estrogens, LH/RH agonists, or antiandrogens
• Recent (=< 3 months of informed consent) usage of immune-suppressive medication including steroids, Immuran, Cyclosporin; topical or inhalational steroid use is permissible
• Prior systemic chemotherapy
• Prior radiation therapy to the prostate
• Prior malignancy, unless the patient has been cancer-free for five years or more
• Uncontrolled underlying medical or psychiatric illness, or serious active infections
• Patient unwilling to complete all required follow-up visits
• History of motor neuropathy considered of the autoimmune origin (e.g. Guillian-Barre Syndrome)
• Concurrent malignancy, except for adequately treated basal cell or squamous cell skin cancer
• For patients who elect to undergo the baseline transrectal needle biopsy of the prostate, current usage of systemic anticoagulation therapy, i.e. heparin or Coumadin or inability to discontinue aspirin, aspirin-containing products or ibuprofen for seven days prior to the prostate biopsies required for this study
• No other investigational drugs will be allowed during the study
• Other chemotherapy, radiation therapy, immunotherapy, hormonal therapy, or biologic therapy may not be used while the patient is on study