A Randomized, Double-Blind Phase II Study of Adjuvant Pembrolizumab Versus Placebo in Head and Neck Cancers at High Risk for Recurrence- the PATHWay Study

Inclusion Criteria: * Patients must have histologically confirmed head and neck cancer (Squamous cell histology as well as HPV+ and/or EBV+ head and neck tumors), Stages IVA, IVB, and select cases of Stage III. * HPV status required prior to randomization for oropharyngeal primary tumors * EBV status is required prior to randomization for nasopharyngeal primary tumors * Completed curative intent therapy, without additional standard of care curative intent therapy feasible within 20 weeks prior to study enrollment * After prior curative intent treatment for HNC have estimated risk of recurrence ≥ 40-50% and fall into one of the below categories (A, OR B, OR C, OR D, OR E). While exact estimation of the risk of recurrence can be difficult the following categories will be included reflecting patients at substantial risk for tumor recurrence or already with early evidence of recurrence: * A: Any of the below HNC patients are eligible for adjuvant treatment on this protocol AFTER completion of curative intent therapy: * HPV(-) HNC: N2C, N3, bulky N2B disease (≥ 5cm LN/tumor conglomerate). * HPV(+) HNC: N2C, N3, AND ≥ 10 pack years of tobacco use * HPV(+) HNC with multilevel nodal involvement, AND bulky N2B disease (≥ 5cm LN/tumor conglomerate), AND ≥ 10 pack years of tobacco use * EBV(+) NPC may be eligible if other criteria under A, or alternative criteria B, or C, or D, or E are met. * HNC with supraclavicular or mediastinal nodal involvement (any HPV or EPV status ) at time of curative intent treatment and were treated as part of curative intent therapy * Residual mass in area of prior tumor that on biopsy does not show residual tumor, is equivocal/not highly-suspicious on imaging but remains of concern, requires close follow-up AND is not resected/amenable to resection OR immediate palliative treatment. * Non-responders to induction chemotherapy (PD on induction, or lack of tumor shrinkage (\< 15% per RECIST) * Interrupted treatment course or lower than intended radiation dose - i.e. interruption of radiation by ≥ 3 weeks (cumulative), or delivery of ≤ 50 Gy as part of a radiation based treatment (that was NOT a de-escalation approach). * B: Patient treated with salvage treatment (i.e. salvage surgery or re-irradiation) for residual or recurrent tumor after prior radiation based therapy (either HPV+ or HPV- or EBV+) AND not a candidate for additional curative intent therapy (for various reasons including poor performance status, comorbidities, refusal of patient, prior radiation or re-irradiation, etc). Positive margins or residual tumor may still be acceptable (see D)). Patients should also not be appropriate for systemic palliative therapy (e.g. in the case of overt disease). * C: Metastases or indeterminate distant lesions that are not appropriate for either local radiation/SBRT treatment and also not appropriate for initiation of palliative system therapy (e.g. in the setting of overt metastatic disease). Such lesions should be negative/equivocal by PET imaging and if amenable negative by biopsy, but remain of concern and require close follow-up * D: Oligometastatic disease treated with SBRT or other curative-intent therapy (e.g. surgery or RFA, etc) for oligometastatic disease. * E: Microscopic or very low volume residual tumor after surgery or radiation based treatment (including salvage treatment or SBRT for oligometastatic disease), AND not a candidate for either additional curative intent therapy (for various reasons including feasibility, poor performance status, comorbidities, refusal of patient, prior radiation or re-irradiation, etc) AND also not a candidate for systemic palliative therapy (for various reasons including microscopic/non-(RECIST) measurable low volume disease). Very low volume disease is defined as non-RECIST measurable). * F: Patients with multiple recurrences or multiple primaries: specifically patients who had malignant or pre-malignant tumors/changes (with severe dysplasia present), who have undergone surgery ≥ 2 times, and currently do not have an indication for additional (adjuvant) treatment such as radiation, or surgery, or other treatment. This may include multiple recurrences/incidences of early stage tumors or premalignant lesions, however at least one lesion needs to show squamous cell carcinoma on pathology. NOTE: There may be additional scenarios for patients that are considered very high risk for disease recurrence and not appropriate for either curative or standard of care palliative therapy. Such patients can be considered for enrollment after discussion and approval by the PI and/or co-PI. * Availability of tumor tissue (≥ 10 slides) for PD-L1, gene expression profiling (GEP), and additional testing. * Be willing and able to provide written informed consent/assent for the trial. * Be 18 years of age on day of signing informed consent. * Have a performance status of 0 or 1 on the ECOG Performance Scale. An ECOG performance status of 2 is acceptable if the patient was ECOG 0/1 prior to curative intent therapy and is in the midst of recovery from curative intent therapy * Demonstrate reasonable organ function, all screening labs should be performed within 10 days of treatment initiation. 9\. Female subject of childbearing potential should have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 10\. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. 11\. Male 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. 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 2 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 TB (Bacillus Tuberculosis) 4. Has 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 or typical side effects from radiotherapy 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 or any tumors that are not likely to influence live expectancy in the subsequent 3 years without active treatment (e.g. low grade prostate cancer in absence of therapy). 8. Has known active (=growing) central nervous system (CNS) metastases and/or carcinomatous meningitis. Radiation or resected brain metastasis are acceptable if clinically stable. 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 (eg., 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 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. 12. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 13. Is pregnant or breastfeeding, or expecting to conceive or 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. 14. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. 15. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 16. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). 17. 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 within 30 days prior to initiation of treatment