Men ≥ 18 years of age

Histologically documented Gleason 8 or greater prostatic adenocarcinoma in at least 3 biopsy cores and at least 8 mm of disease on a single core of Gleason 8 or greater. Prostate biopsy within 3 months of screening is allowed for entry requirements. Prostate biopsy must be reviewed at MD Anderson Cancer Center. Patients with small cell, neuroendocrine, or transitional cell carcinomas or mixed histologies are not eligible

Eastern Cooperative Oncology Group (ECOG) performance status (PS) grade of 0 or 1

No evidence of metastatic disease as documented by technetium-99m (99mTc) bone scan and by computed tomography (CT) or magnetic resonance imaging (MRI) scans. Imaging may be obtained up to 60 days prior to enrollment

Localized or locally advanced disease deemed by the surgeon to be resectable. Patients must be appropriate candidates for radical prostatectomy plus pelvic lymph node dissection

No prior treatment for prostate cancer including prior surgery (excluding transurethral resection of the prostate \[TURP\]), cryoablation, pelvic lymph node dissection, radiation therapy, hormonal therapy or chemotherapy

Hemoglobin ≥ 11 g/dL

Absolute neutrophil count ≥ 1.5 x 10\^9/L

Platelet count ≥ 100 x 10\^9/L

Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or estimated glomerular filtration rate \> 50 mL/min/1.73 m\^2. A 24-hour urine creatinine collection may substitute for the calculated creatinine clearance to meet eligibility criteria

Total bilirubin ≤ 1.5 x ULN * NOTES: Patients with Gilbert's syndrome do not need to meet total bilirubin requirements provided their total bilirubin is not greater than their historical level. Gilbert's syndrome must be documented appropriately as past medical history

Aspartate aminotransferase (AST) ≤ 2.5 x ULN

Alanine aminotransferase (ALT) ≤ 2.5 x ULN

Alkaline phosphatase (ALP) ≤ 2.5 x ULN

Consent to MD Anderson laboratory protocol PA13-0291

Willing and able to comply with clinic visits and study-related procedures

Provide informed consent signed by study patient

To avoid risk of drug exposure through the ejaculate (even men with vasectomies), subjects must use a condom during sexual activity while on study drug and for 3 months following the last dose of study drug. If the subject is engaged in sexual activity with a woman of childbearing potential, a condom is required along with another effective contraceptive method consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies and their partners. Donation of sperm is not allowed while on study drug and for 3 months following the last dose of study drug

Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or luteinizing hormone-releasing hormone (LHRH) agonists/antagonists

Currently enrolled in another interventional study

Concurrent treatment with systemic corticosteroids (prednisone dose \> 10 mg per day or equivalent) or other immunosuppressive drugs \< 14 days prior to treatment initiation. Steroids that are topical, inhaled, nasal (spray), or ophthalmic solution are permitted

History of or known or suspected autoimmune disease (exception\[s\]: subjects with vitiligo, resolved childhood atopic dermatitis, hypothyroidism, or hyperthyroidism that is clinically euthyroid at screening are allowed)

Known evidence of an active infection requiring systemic therapy such as human immunodeficiency virus (HIV), active hepatitis, or fungal infection. Patients with known HIV infection which is well-controlled (undetectable viral load by HIV ribonuclecid acid \[RNA\] polymerase chain reaction \[PCR\]) and CD4 counts greater than 350 are permitted to participate

History of clinically significant cardiovascular disease including, but not limited to: * Myocardial infarction or unstable angina ≤ 6 months prior to treatment initiation * Clinically significant cardiac arrhythmia * Deep vein thrombosis, pulmonary embolism, stroke ≤ 6 months prior to treatment initiation * Congestive heart failure (New York Heart Association class III-IV) * Pericarditis/clinically significant pericardial effusion * Myocarditis * Endocarditi

History of major implant(s) or device(s), including but not limited to: * Prosthetic heart valve(s) * Artificial joints and prosthetics placed ≤ 12 months prior to treatment initiation * Current or prior history of infection or other clinically significant adverse event associated with an exogenous implant or device that cannot be remove

Other prior malignancy (exceptions: adequately treated basal cell or squamous cell skin cancer, superficial bladder cancer, or any other cancer in situ currently in complete remission) ≤ 2 years prior to enrollment

Has received major surgery within 14 days of first administration of study drug

Encephalitis, meningitis, neurodegenerative disease (with the exception of mild dementia that does not interfere with activities of daily living \[ADLs\]) or uncontrolled seizures in the year prior to first dose of study therapy

Known history of, or any evidence of interstitial lung disease, or active, non-infectious pneumonitis (past 5 years)

Receipt of a live vaccine within 4 weeks of planned start of study medication

Prior allogeneic stem cell transplantation or recipients of organ transplants at any time, or autologous stem cell transplantation within 12 weeks of the start of study treatment

Any medical, psychological or social condition that in the opinion of the investigator, would preclude participation in this study