This randomized pilot trial studies vaccine therapy and pembrolizumab in treating patients with prostate cancer that does not respond to treatment with hormones (hormone-resistant) and has spread to other places in the body (metastatic). Vaccines made from deoxyribonucleic acid (DNA), such as pTVG-HP plasmid DNA vaccine, may help the body build an effective immune response to kill tumor cells. Monoclonal antibodies, such as pembrolizumab, may find tumor cells and help kill them. Giving pTVG-HP plasmid DNA vaccine and pembrolizumab may kill more tumor cells.

PRIMARY OBJECTIVES:

I. To evaluate the safety of pembrolizumab in combination with pTVG-HP (pTVG-HP plasmid DNA vaccine) in patients with castration-resistant, metastatic prostate cancer.

II. To determine the 6-month progression-free survival and median time to radiographic progression in patients with castration-resistant metastatic prostate cancer treated with pembrolizumab in combination with pTVG-HP.

III. To evaluate the anti-tumor response rates (objective response rate and prostate specific antigen [PSA] response rate, using Prostate Cancer Clinical Trials Working Group 2 [PCWG2] criteria) in patients with castration-resistant metastatic prostate cancer treated with pembrolizumab in combination with pTVG-HP.

SECONDARY OBJECTIVES:

I. To determine whether either treatment sequence, or prostatic acid phosphatase (PAP)-specific immune response, is associated with prolonged (6-month) radiographic progression-free survival.

II. To evaluate effects of schedule (concurrent versus delayed administration of pembrolizumab) on the magnitude of PAP-specific T-cell responses, programmed death receptor-1 (PD-1) expression on circulating T cells, and ligands for PD-1 (PD-L1) expression on circulating epithelial cells (CEC) and on tumor biopsies.

III. To determine the median time to radiographic progression using a concurrent administration schedule

TERTIARY OBJECTIVES:

I. To evaluate effects of treatment on number of circulating tumor cells. II. To evaluate PAP-specific antibody responses following treatment with pembrolizumab and pTVG-HP DNA vaccine (pTVG-HP plasmid DNA vaccine).

III. To determine whether either treatment sequence elicits immunologic antigen spread to other prostate-associated antigens.

IV. To determine whether pre-existing or vaccine-induced PD-L1 expression on CEC or tumor biopsies is predictive of objective clinical response.

V. To determine whether treatment elicits expression of other regulatory molecules on tumor-specific T cells (e.g. hepatitis A virus cellular receptor 2 [TIM3], B and T lymphocyte associated [BTLA], and lymphocyte-activation gene 3 [LAG3]) or tumor cells (e.g. tumor necrosis factor receptor superfamily, member 14 [HVEM], phosphatidyl serine, ligands for programmed death receptor-2 [PD-2] [PD-L2]).

VI. To determine whether PD-1-regulated antigen-specific T cells identified by trans vivo delayed-type hypersensitivity (DTH) testing can identify patients who develop objective clinical responses with PD-1 blockade therapy in combination with pTVG-HP.

VII. To determine whether changes in lymph nodes and soft tissue tumor lesions are observed by fluorothymidine F-18 (FLT) positron emission tomography (PET)/computed tomography (CT) after treatment with vaccine with or without pembrolizumab.

VIII. To determine if PD-1 inhibitor therapy in combination with pTVG-HP will change number and activity (SUV) in osteoblastic metastases as measured by NaF PET/CT.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM I: Patients receive pTVG-HP plasmid DNA vaccine intradermally (ID) every other week on days 1, 15, 29, 43, 57, and 71 and pembrolizumab intravenously (IV) over 30 minutes every 3 weeks on days 1, 22, 43, and 64.

ARM II: Patients receive pTVG-HP plasmid DNA vaccine ID as in Arm I and pembrolizumab IV over 30 minutes every 3 weeks on days 85, 106, 127, and 148.

After completion of study treatment, patients are followed up 3, 6, 9, and 12 months and then annually for 2 years.

ARM III: Extended Treatment. Patients received pTVG-HP + Pembrolizumab Extended Treatment

ARM IV: Extended Treatment. Patients receive pTVG-HP every two weeks, and Pembrolizumab every 4 weeks

Inclusion Criteria:

• Histologically confirmed diagnosis of prostate cancer (adenocarcinoma of the prostate)

• Metastatic disease as evidenced by the presence of soft tissue and/or bone metastases on imaging studies (CT of abdomen/pelvis, bone scintigraphy)

• Castrate-resistant disease, defined as follows:

  • All patients must have received (and be receiving) standard of care androgen deprivation treatment (surgical castration versus gonadotropin-releasing hormone [GnRH] analogue or antagonist treatment); subjects receiving GnRH analogue or antagonist must continue this treatment throughout the time on this study
  • Patients may or may not have been treated previously with a nonsteroidal antiandrogen; for patients previously treated with an antiandrogen, they must be off use of anti-androgen for at least 4 weeks (for flutamide) or 6 weeks (for bicalutamide or nilutamide) prior to registration; moreover, subjects who demonstrate an anti-androgen withdrawal response, defined as a >= 25% decline in PSA within 4-6 week of stopping a nonsteroidal antiandrogen, are not eligible until the PSA rises above the nadir observed after antiandrogen withdrawal
  • Patients must have a castrate serum level of testosterone (< 50 ng/dL) within 6 weeks of day 1

• Progressive disease while receiving androgen deprivation therapy defined by any one of the following as per the Prostate Cancer Clinical Trials Working Group 2 (PCWG2) bone scan criteria or Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 during or after completing last therapy:

  • PSA: at least two consecutive rises in serum PSA, obtained at a minimum of 1-week intervals, with the final value >= 2.0 ng/mL
  • Measurable disease: >= 50% increase in the sum of the cross products of all measurable lesions or the development of new measurable lesions; the short axis of a target lymph node must be at least 15 mm by spiral CT to be considered a target lesion
  • Non-measurable (bone) disease: the appearance of two or more new areas of uptake on bone scan (or fluorine F 18 sodium fluoride [NaF] PET/CT) consistent with metastatic disease compared to previous imaging during castration therapy; the increased uptake of pre-existing lesions on bone scan will not be taken to constitute progression, and ambiguous results must be confirmed by other imaging modalities (e.g. X-ray, CT or magnetic resonance imaging [MRI])

• Prior treatment with abiraterone or enzalutamide is permitted, but patients must have been off prior corticosteroid treatment for at least 3 months

• Life expectancy of at least 6 months

• Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2

• White blood cells (WBC) >= 2000/mm^3

• Absolute neutrophil count (ANC) >= 1000/mm^3

• Hemoglobin (HgB) >= 9.0 gm/dL

• Platelets >= 100,000/mm^3

• Creatinine =< 2.0 mg/dL

• Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =< 2.5 x institutional upper limit of normal

• No known history of human immunodeficiency virus (HIV) 1 and 2, human T-lymphotropic virus (HTLV)-1, or active hepatitis B or hepatitis C

• Patients must be at least 4 weeks from any prior treatments and have recovered (to < grade 2) from acute toxicity attributed to this prior treatment, unless considered chronic

• Patients must be willing and able (in the opinion of the treating physician) to undergo two research biopsies for the investigational component of this trial

• Patients must be willing to undergo two leukapheresis procedures for the investigational component of this trial

• Patients must be willing to undergo FLT PET/CT or NaF PET/CT scans for the investigational component of this trial and have no known allergies to FLT or NaF

• For those patients who are sexually active, they must be willing to use barrier contraceptive methods during the period of treatment on this trial (and for four weeks after the last DNA immunization treatment for patients in Arm 1)

• Patients must be informed of the experimental nature of the study and its potential risks, and must sign an Institutional Review Board (IRB)-approved written informed consent form indicating such an understanding

Exclusion Criteria:

• Small cell or other variant (non-adenocarcinoma) prostate cancer histology, unless there is evidence that the tumor expresses PAP

• Patients may not be receiving other investigational agents or be receiving concurrent anticancer therapy other than standard androgen deprivation therapy

• Concurrent bisphosphonate therapy is not excluded, however patients should not start bisphosphonate therapy while on this study; those patients already receiving bisphosphonate therapy should continue at the same dosing and schedule as prior to study entry

• Rapidly progressive symptomatic metastatic disease, as defined by the need for increased opioid analgesics within one month of registration for the treatment of pain attributed to a prostate cancer metastatic lesion; patients receiving opioids must receive approval from the principal investigator (PI) for eligibility

• Treatment with any of the following medications within 28 days of registration, or while on study, is prohibited:

  • Systemic corticosteroids (at doses over the equivalent of 5 mg prednisone daily) - not permitted within 3 months of registration; inhaled, intranasal or topical corticosteroids are acceptable
  • Prostate cancer (PC)-SPES
  • Saw palmetto
  • Megestrol
  • Ketoconazole
  • 5-alpha-reductase inhibitors - patients already taking 5-alpha-reductase inhibitors prior to 28 days prior to registration may stay on these agents throughout the course of therapy, but these should not be started while patients are on study
  • Diethyl stilbestrol
  • Abiraterone
  • Enzalutamide
  • Radium 223 (Xofigo)
  • Any other hormonal agent or supplement being used with the intent of cancer treatment

• External beam radiation therapy within 4 weeks of registration is prohibited, or anticipated need for radiation therapy (e.g. imminent pathological fracture or spinal cord compression) within 3 months of registration

• Major surgery within 4 weeks of registration is prohibited

• Prior cytotoxic chemotherapy (for example, but not limited to, docetaxel, mitoxantrone, cabazitaxel) within 6 months of registration is prohibited

• Patients with a history of life-threatening autoimmune disease

• Patients with a history of allergic reactions to filgrastim (GM-CSF) or the tetanus vaccine

• Patients who have undergone splenectomy

• Patients must not have other active malignancies other than non-melanoma skin cancers or superficial bladder cancer; subjects with a history of other cancers who have been adequately treated and have been recurrence-free for >= 3 years are eligible

• Patients with known brain metastases

• Any antibiotic therapy or evidence of infection within 1 week of registration

• Any other medical intervention or condition, which, in the opinion of the PI or treating physician, could compromise patient safety or adherence with the study requirements (including biopsies or leukapheresis procedures) over the primary 3-6 month treatment period

• Patients cannot have concurrent enrollment on other phase I, II, or III investigational treatment studies

NOTE: There is no exclusion for prior immune-based therapy. This includes patients previously treated on Arms 1 or 2 who are otherwise eligible for treatment on Arm 3 or 4.