Trial of Pembrolizumab for Advanced Penile Squamous Cell Carcinoma

Inclusion Criteria: 1. Locally advanced unresectable or metastatic stage 4 (i.e. T4 or N3 or M1) PSCC 2. Radiologic evidence for progressive disease after ≥1 prior chemotherapy regimen 3. Be at least 18 years of age on day of signing informed consent. 4. Have measurable disease based on RECIST 1.1. 5. Have a performance status of 0-2 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. 6. Demonstrate adequate organ function with all screening labs being performed within 14 days of treatment initiation. * Absolute neutrophil count (ANC) ≥1,500 /microLiters (mcL) * Platelets ≥100,000/mcL * Hemoglobin ≥9 g/dL or ≥5.6 mmol/L without transfusion or erythropoietin dependency (within 7 days of assessment) * Serum creatinine ≤1.5 X upper limit of normal (ULN); alternately measured or calculated creatinine clearance ≥30 mL/min with creatinine levels \>1.5 X institutional ULN (GFR can also be used in place of creatinine or CrCl) * Serum total bilirubin ≤1.5 X ULN or direct bilirubin ≤ ULN for subjects with total bilirubin levels \>1.5 ULN * Aspartate Transaminase (AST), also known as Serum Glutamic-Oxaloacetic Transaminase (SGOT) and Alanine Aminotransferase (ALT), also known as Serum Glutamic-Pyruvic Transaminase (SGPT) ≤ 2.5 X ULN or ≤ 5 X ULN for subjects with liver metastases * Albumin \>2.5 mg/dL * International Normalized Ratio (INR) or Prothrombin Time (PT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants 7. Subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy 8. Formalin-fixed paraffin embedded (FFPE) tumor tissue from previous biopsy is requested, but not mandatory. 9. Be willing and able to provide written informed consent/assent for the trial. Exclusion Criteria: 1. Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. 2. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. 3. Has a known history of active Bacillus Tuberculosis (TB) 4. Hypersensitivity to Pembrolizumab or any of its excipients. 5. Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. 6. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 7. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. 8. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. 9. Has 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. 10. Has known history of, or any evidence of active, non-infectious pneumonitis. 11. Has an active infection requiring systemic therapy. 12. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 14. Is pregnant expecting to father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. 15. Has received prior therapy with an anti-Programmed Cell Death-1 (PD-1), anti-PD-Ligand 1 (L1), or anti-PD-Ligand 2 (L2) agent. 16. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 17. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (HCV) (e.g., HCV RNA \[qualitative\] is detected). 18. Has known active Tuberculosis infection. 19. Has received a live vaccine within 30 days of planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.