PROSTVAC in Combination With Nivolumab in Men With Prostate Cancer

* INCLUSION CRITERIA:

For the neoadjuvant cohort, patients must have histopathological documentation of adenocarcinoma of the prostate prior to starting this study and evaluable biopsy tissue (e.g., unstained slides or blocks) available for analysis. If evaluable tissue is not available, the patient must agree to undergo a pre-vaccination prostate biopsy on study. For the castration-resistant prostate cancer (CRPC) lead in cohort, if histopathological documentation is unavailable, a rising prostate specific antigen (PSA) and a clinical course consistent with prostate cancer would be acceptable.

* Age greater than or equal to 18 years. Because no dosing or adverse event data are currently available on the use of PROSTVAC in combination with nivolumab, ipilimumab or both in participants \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
* Participants must not have other active invasive malignancies within the past 2 years (with the exception, of non-melanoma skin cancers) (for CRPC cohort only).
* Participants must be willing to travel to the study site for follow-up visits
* All participants who have received prior vaccination with vaccinia virus (for smallpox immunization) must not have a history of serious adverse reaction to the vaccine.
* The effects of PROSTVAC in combination nivolumab, ipilimumab or both on the developing human fetus are unknown. For this reason, men must agree to use adequate contraception (abstinence, vasectomy) or female partner must use (intrauterine device (IUD), hormonal \[birth control, pills, injections, or implants\], tubal ligation\] prior to study entry and for up to 7 months after the last dose.
* Participants must understand and sign informed consent that explains the neoplastic nature of their disease, the procedures to be followed, the experimental nature of the treatment, alternative treatments, potential risks and toxicities, and the voluntary nature of participation.
* Participants must have normal organ and marrow function as defined below:

  * hemoglobin greater than or equal to 8 g/dL
  * granulocytes greater than or equal to 1,500/mcL
  * platelets greater than or equal to 100,000/mcL
  * total bilirubin \< 1.5 mg/dL (or less than or equal to 3.0 mg/dL in patients with Gilbert syndrome)
  * Aspartate aminotransferase (AST)serum glutamic oxaloacetic transaminase (SGOT)(SGOT)/alanine transaminase (ALT)serum glutamic-pyruvic transaminase (SGPT) less than or equal to 2.5 X institutional upper limit of normal
  * creatinine less than or equal to 1.5 X ULN
* For the lead in cohort:

  * Castrate testosterone level (\<50ng/dl or 1.7nmol /L)
  * Progressive disease at study entry defined as one or more of the following criteria occurring in the setting of castrate levels of testosterone:

    * Radiographic progression defined as any new or enlarging bone lesions or growing lymph node disease, consistent with prostate cancer OR
    * PSA progression defined by sequence of rising values separated by \>1 week (2 separate increasing values over a minimum of 2ng/ml (Prostate Cancer Clinical Trials Working Group (PCWG2) PSA eligibility criteria). If participants had been on flutamide, PSA progression is documented 4 weeks or more after withdrawal. For patients on bicalutamide or nilutamide disease progression is documented 6 or more weeks after withdrawal.
  * Participants must agree to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone agonist/antagonist or bilateral orchiectomy
* For all neoadjuvant cohorts:

  * Participants must be a surgical candidate for radical prostatectomy based on standard workup of PSA, biopsy results, and if necessary supplemental imaging.
  * Participants must have chosen radical prostatectomy as their definitive treatment of choice for management of their prostate cancer.
  * No systemic steroid or steroid eye drop use within 2 weeks prior to initiation of experimental therapy. Limited doses of systemic steroids to prevent intravenous (IV) contrast, allergic reaction or anaphylaxis (in patients who have known contrast allergies) are allowed.

EXCLUSION CRITERIA:

* Prior splenectomy.
* The recombinant vaccinia vaccine should not be administered if the following apply to either recipients or, for at least 3 weeks after vaccination, their close household contacts (Close household contacts are those who share housing or have close physical contact):

  * persons with active or a history of eczema or other eczematoid skin disorders
  * those with other acute, chronic or exfoliative skin conditions (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne or other open rashes or wounds) until condition resolves
  * pregnant or nursing women; children under 3 years of age
* Participants should have no evidence, as listed below, of being immunocompromised:

  * Human immunodeficiency virus (HIV) positivity due to the potential for decreased tolerance and risk for severe side effects.
  * Hepatitis B or C positivity.
* Concurrent use of systemic steroids or steroid eye drops. This is to avoid immunosuppression which may lead to potential complications with vaccinia (priming vaccination). Nasal, topical, or inhaled steroid use is permitted.
* Participants with known allergy to eggs or to compounds with a similar chemical or biologic composition to PROSTVAC, ipilimumab or nivolumab.
* No prior immune checkpoint inhibitors (e.g., anti-cytotoxic T-lymphocyte associated protein 4 (CTLA4), anti-programmed cell death protein 1 (PD-1) or anti-programmed death-ligand 1 (PDL1) are allowed.
* Other serious intercurrent illness.
* Participants with a history of unstable or newly diagnosed angina pectoris, recent myocardial infarction (within 6 months of enrollment) or New York Heart Association class II-IV congestive heart failure.
* Participants with significant autoimmune disease that is active or potentially life threatening if activated.
* Participants with clinically significant cardiomyopathy requiring treatment.
* Participants with ongoing toxicities related to prior therapies targeting T cell coregulatory proteins (immune checkpoints) such as anti-PD-1, anti-PD-L1, or anti-CTLA-4 antibody are excluded
* No transfusion of blood or blood products within 2 weeks and no granulocyte colony stimulating factor (G-CSF) or granulocyte-macrophage colony-stimulating factor (GM-CSF) within 2 weeks prior to initiations of experimental therapy.
* Contraindication to biopsy or prostatectomy (for sequential neoadjuvant cohorts only):

  * Bleeding disorders
  * Artificial heart valve
  * Prothrombin time (PT)/partial thromboplastin time (PTT) greater than or equal to 1.5 in participants not taking anticoagulation. Participants on anticoagulation (e.g., enoxaparin, oral anticoagulants) are eligible regardless of PT/PTT. Prior to biopsy, anticoagulation will be held per standard practice.
* For participants with localized prostate cancer contraindication to magnetic resonance imaging (MRI):

  * Participants weighing \>136 kilograms (weight limit for the scanner tables)
  * Allergy to magnetic resonance (MR) contrast agent
  * Participants with pacemakers, cerebral aneurysm clips, shrapnel injury or implantable electronic devices
* History of radiation proctitis (for lead-in CRPC cohort only)