A Study Comparing Personalized Radiation Therapy With Standard Radiation Therapy in People With HPV-Positive Throat Cancer

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of HPV associated squamous cell carcinoma of the oropharynx (tonsil, base of tongue, or oropharyngeal walls) or squamous cell carcinoma with an unknown primary. Surgical removal of primary site is allowed. * Patients must test positive for both p16 expression (70% nuclear and cytoplasm expression; Ventana Medical Systems) and mRNA HPV in situ hybridization (RNAscope® 2.5 HD Reagent kit (Advanced Cell Diagnostics, Inc, Hayward, CA). Any CLIA certified testing method can be used. * Clinical stage Tx-2, N1-2c (AJCC, 7th ed.) without evidence of distant metastasis based on FDG PET/CT. * ECOG Performance Status of 0-1 or KPS \>/=70 * Age ≥ 18 * Adequate hematologic function within 30 days prior to registration, defined as follows: * White Blood Count (WBC) ≥ 2 K/mcL * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm\^3 * Platelets ≥ 100,000 cells/mm\^3 * Hemoglobin ≥ 10.0 g/dl * Adequate renal function within 30 days prior to registration, defined as follows: o 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 = \[(140 - age) x (wt in kg)\] \[(Serum Cr mg/dl) x (72)\] CCr female = 0.85 x (CrCl male) * Negative serum pregnancy test within 14 days prior to registration for women of childbearing potential * The patient must provide study-specific informed consent prior to study entr…