Vaccine Therapy (pTVG-HP DNA Vaccine with or without pTVG-AR DNA Vaccine) and Pembrolizumab for the Treatment of Metastatic Castration-Resistant Prostate Cancer

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, apalutamide, or enzalutamide) 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 weeks 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 3 (PCWG3) 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 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 weaned to a daily corticosteroid dose equivalent of no more than 5 mg prednisone daily for at least 28 days prior to day 1
• 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 (within 6 weeks of day 1)
• Absolute neutrophil count (ANC) >= 1500/mm^3 (within 6 weeks of day 1)
• Hemoglobin (HgB) >= 9.0 gm/dL (within 6 weeks of day 1)
• Platelets >= 100,000/mm^3 (within 6 weeks of day 1)
• Creatinine =< 1.5 x institutional upper limit of normal (ULN) (within 6 weeks of day 1)
• Total bilirubin = < 1.5 x institutional ULN OR direct bilirubin =< ULN for participants with total bilirubin levels > 1.5 x ULN
• Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =< 2.5 x institutional upper limit of normal (within 6 weeks of day 1)
• Prothrombin time (PT) or international normalized ratio (INR) =< 1.5 x ULN unless participant is receiving anticoagulant therapy and PT is within therapeutic range of intended use of anticoagulant (only required for patients receiving biopsy) (within 6 weeks of day 1)
• Partial thromboplastin time =< 1.5 x ULN unless participant is receiving anticoagulant therapy and activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulant (only required for patients receiving biopsy) (within 6 weeks of day 1)
• 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
• A subset of patients (6 patients per treatment arm) treated at the lead University of Wisconsin (UW) site must be willing and able (in the opinion of the treating physician) to undergo two research biopsies for the investigational component of this trial
• A subset of patients (6 patients per treatment arm) treated at the lead UW site must be willing to undergo NaF PET/CT scans for the investigational component of this trial
• For those patients who are sexually active, they must be willing to use barrier contraceptive methods, and refrain from donating sperm, during the period of treatment on this trial and for four weeks after the last DNA immunization treatment
• 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 day 1, or while on study, is prohibited: • Systemic corticosteroids (at doses over the equivalent of 5 mg prednisone daily); inhaled, intranasal or topical corticosteroids are acceptable • PC-SPES • 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 • Apalutamide • Radium 223 (Xofigo) • Any other hormonal agent or supplement being used with the intent of cancer treatment must be reviewed by the PI for eligibility
• 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. Patients must have recovered from all radiation-related toxicities and not have had radiation pneumonitis
• Major surgery within 4 weeks of registration is prohibited
• Prior cytotoxic chemotherapy (for example, but not limited to, docetaxel, mitoxantrone, cabazitaxel) within 3 months of registration is prohibited
• Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, or with any agent directed to another T-cell stimulatory or inhibitory receptor (e.g. CTLA-4, OX-40, CD137)
• Patients with a history of life-threatening autoimmune disease
• Patients with a history of non-infectious pneumonitis that required corticosteroid treatment, or has current pneumonitis
• Patients with a history of allergic reactions to the tetanus vaccine
• Patients who have undergone splenectomy or who have a diagnosis of immunodeficiency
• Patients must not have other active malignancies other than non-melanoma skin cancers or superficial (non-muscle-invasive) carcinoma of the bladder. 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 and/or carcinomatous meningitis
• Patients who have received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed
• Any antibiotic therapy within 1 month of day 1, or anticipated need for antibiotic therapy within 1 month of beginning treatment
• Patients with active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment
• 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 confound results of the study, over the treatment period
• Any known psychiatric or substance abuse disorders that would interfere with cooperation with the requirement of the trial
• Patients cannot have concurrent enrollment on other phase I, II, or III investigational treatment studies