Intensity-Modulated Proton Beam Therapy or Intensity-Modulated Photon Therapy in Treating Patients With Stage III-IVB Oropharyngeal Cancer

PRIMARY OBJECTIVES: To compare the progression-free survival (PFS) between concurrent chemo-radiation strategies with IMRT and IMPT following the treatment of oropharyngeal tumors. SECONDARY OBJECTIVES: 1. To assess and compare overall survival between IMRT and IMPT along with estimating disease-related outcomes such as: \[2-year progression-free survival, patterns of failure, 2-year overall survival, 2-year distant metastasis free survival, and second primary cancers\] 2. To assess acute and chronic/late side effects, and to compare the rates of Grade 3-5 toxicity between IMRT and IMPT following the treatment of oropharyngeal tumors. 3. To assess Patient Reported Outcome (PRO) measures of symptoms using MD Anderson Symptom Inventory (MDASI), MD Anderson Dysphagia Inventory (MDADI), FACT-HN, Xerostomia and Health Questionnaire (EQ-5D-3L), Work status (WPAI: SHP) 4. To assess Physician Reported Toxicity using Common Terminology Criteria for Adverse Events (CTCAE)-4.0 5. To evaluate and compare Quality-Adjusted-Life-Years (QALY) between IMPT and IMRT; 6. To perform Cost-benefit economic analysis of treatment; 7. To determine whether specific molecular profiles are associated with overall or progression-free survival; 8. To investigate associations between changes in blood biomarkers, or HPV-specific cellular immune responses, or HPV ctDNA (measured at baseline and three months and at each follow-up visit for up to 10 years) with overall or progression-free survival; 9. To bank peripheral blood at time of enrollment, weeks 2, 4, and 6 during treatment and at each follow up visits for up to 10 years to explore the ability of circulating markers to predict outcome; 10. To bank head and neck tissues to explore the ability of tissue-based markers to predict outcome; 11. To bank peripheral blood and tissues for future interrogations; Finally, all additional secondary endpoints EXPLORATORY OBJECTIVE: I. To assess potential differences between patients on study and patients who were considered eligible for randomized, were randomized to a treatment arm, but were denied insurance coverage for the treatment arm she/he was randomized to; or may have dropped out of the study for other reasons after being randomized. These patients will compromise Group 3: consisting of patients randomized to Protons but not treated and Group 4: consisting of patients randomized to IMRT but not treated at the designated institution. Furthermore, these patients will only be followed for recurrence and survival.(Phase III) OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients undergo IMRT once daily (QD) five days a week for approximately 6.5 weeks. ARM II: Patients undergo IMPT QD five days a week for approximately 6.5 weeks. After completion of study treatment, patients are followed up every 3 months for 1 year, every 4 months for 1 year, and then every 6 months for 5 years.