Ipilimumab, Nivolumab, and Radiation Therapy in Treating Patients With HPV Positive Advanced Oropharyngeal Squamous Cell Carcinoma

Inclusion Criteria: * Histologically or cytologically newly confirmed diagnosis of squamous cell carcinoma (including the histological variants of papillary or basaloid) of the oropharynx (tonsil, base of tongue, soft palate, or oropharyngeal walls) * Clinical American Joint Committee on Cancer (AJCC) 7th edition stage T1N2a-N2CM0, T2N1-N2CM0, T3N0-N2CM0, equivalent to AJCC 8th edition stage 1 and 2 (T1 N2, T2 N1-N2, T3 N0-N2) excluding T1N0-N1 and T2N0 (Brian O'Sullivan et al. 2016) * Tumor positive for p16 immunohistochemistry (IHC) (defined as greater than 70% strong nuclear or nuclear and cytoplasmic staining of tumor cells) and HPV DNA in situ hybridization or HPV messenger ribonucleic acid (mRNA) RNAScope. Repeat samples may be required if adequate diagnostic tissue is unavailable for testing * Zubrod Performance Status of 0-1 * Patients must have radiographically evident measurable disease at the primary site or at nodal stations per response evaluation criteria in solid tumors (Response Evaluation Criteria in Solid Tumors \[RECIST\]) 1.1 documented by diagnostic quality CT or magnetic resonance imaging (MRI) of the neck with contrast within 28 days prior to registration; a FDG-PET/CT of the neck performed for the purposes of radiation planning is acceptable as a substitute if the CT is of diagnostic quality * Diagnostic quality cross sectional imaging of the thorax within 28 days prior to registration. A 18-FDG-PET/CT or conventional CT are acceptable * FDG-PET/CT of…