A Study on Using Cell-Free Tumor DNA (ctDNA) Testing to Decide When to StartRoutine Treatment in People With Human Papilloma Virus (HPV)- Associated Oropharynx Cancer (OPC)

Inclusion Criteria: * Age ≥ 18 * ECOG 0-2 * HPV-16 squamous cell carcinoma of the oropharynx or HPV-16 head and neck squamous cell carcinoma of unknown primary . HPV status must be confirmed by in-situ hybridization. * HPV ctDNA detectable by HPV digital PCR (Naveris assay) with a minimum of 50 copies/mL pre-operatively. * Surgical resection of all gross disease with no gross disease visualized on post-operative imaging. o For patients with pT0 (unknown primary) evaluation for the primary should include PET/CT, direct laryngoscopy, ipsilateral tonsillectomy, and targeted biopsy. This should be followed by a neck dissection. * Two, undetectable (\<1 copy/mL) post-operative HPV ctDNA within 2-6 weeks following surgery (blood drawn at least one week apart preferred). * A minimum of one of the following pathologic criteria: (Arm A) * AJCC 7 Stage: pT0N1-N2b, pT1N1, pT2N1, or ≥pT3 * AJCC 7 ≥pN2 * Lymphovascular invasion * Perineural invasion * Close pathologic margin (≤ 3 mm) * Signed informed consent form by the participant or their legally authorized representative (LAR). * A minimum of one of the following pathologic criteria (Arm B): * Microscopic positive margin * Extracapsular extension * Signed informed consent form by the participant or their legally authorized representative (LAR). Additional criteria for Arm B only: * Adequate hematologic function within 30 days prior to registration, defined as follows: * White Blood Count (WBC) ≥ 2 K/mcL * Absolute neutrophil count (ANC) ≥ 1,000 cells/mm3 * Platelets ≥ 100,000 cells/mm3 * Hemoglobin ≥ 8.0 g/dl; Note: The use of transfusion or other intervention to achieve Hgb ≥ 8.0 g/dl is acceptable * Adequate renal function within 30 days prior to registration, defined as follows: * Serum creatinine \< 1.5 mg/dl or creatinine clearance (CC) ≥ 50 ml/min determined by 24-hour collection or estimated by Cockcroft-Gault formula: * CCr male = \[(140 - age) x (wt in kg)\] divided by \[(Serum Cr mg/dl) x (72)\] * CCr female = 0.85 x (CrCl male) * Adequate hepatic function within 30 days prior to registration, defined as follows: \- Bilirubin \< 2 mg/dl o AST or ALT \< 3 x the upper limit of normal * Negative serum pregnancy test within 14 days prior to registration for women of childbearing potential Exclusion Criteria: * Metastatic disease * Non-HPV16 genotype (i.e. HPV-18,-31, -33, -35) * Patients who receive surgery at outside institution. Exceptions can be made for high-volume surgical centers at the discretion of the PI/co-PI * Prior head and neck radiation * Patients without pre-operative HPV ctDNA or pre-operative HPV ctDNA ≤ 50 copies/mL * Subjects with simultaneous primary cancers outside of the oropharynx o Note: Exceptions can be made for patients with simultaneous primaries outside of the oropharynx if determined by the PI/Co-PI, then the patient can proceed with protocol activities * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for 3 years or if cure rate from treatment at 5 years is 90% or greater o Note: Exceptions can be made for patients with prior invasive malignancy if determined by the PI/Co-PI, then the patient can proceed with protocol activities * Prior systemic chemotherapy for the study cancer o Note: prior chemotherapy for a different cancer is allowable * Severe, active co-morbidity defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization within 30 days of registration * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects * Lack of ability to understand and willingness to sign a written informed consent and complete questionnaires.