Nab-paclitaxel and Carboplatin Followed by Response-Based Local Therapy in Treating Patients With Stage III or IV HPV-Related Oropharyngeal Cancer

PRIMARY OBJECTIVES: I. To determine the 2-year progression-free survival (PFS). SECONDARY OBJECTIVES: I. Clinical complete response rate (nab-paclitaxel based induction, compared to European Prospective Investigation into Cancer and Nutrition \[EPIC\] induction \[paclitaxel based\]). II. Response rate (nab-paclitaxel based induction, compared to EPIC induction \[paclitaxel based\]). III. Proportion of patients with \>= 50% shrinkage by Response Evaluation Criteria In Solid Tumors (RECIST) (nab-paclitaxel based induction, compared to EPIC induction, paclitaxel based). IV. Toxicity (nab-paclitaxel based induction, compared to EPIC induction \[paclitaxel based\]). V. To assess swallowing function and speech at 6 months (mos) and 12 mos post therapy. VI. To determine the rates of late toxicity with chemoradiation following surgery as determined by xerostomia, dental decay, osteroradionecrosis, G-tube dependency, tracheostomy placement and dysphagia. VII. 2-year overall survival (OS) in patients treated on the Low-Risk, Intermediate-Risk Arm, and High-Risk Arms. VIII. 2-year PFS in patients treated on the Low-Risk, Intermediate-Risk Arm, and High-Risk Arms - early and late toxicities. IX. Evaluate need for post radiotherapy/chemoradiotherapy (RT/CRT) surgery on low- and intermediate-risk arms based on response from induction chemotherapy. X. Evaluate in a descriptive manner the role of transoral robotic surgery (TORS) resection/lymph node dissection (LND) when integrated into a de-escalation trial. TERTIARY OBJECTIVES: I. To evaluate pathologic/histologic appearance of tumor after induction chemotherapy and after CRT. II. Translational research on blood and tissue samples. III. To profile tumors genetically and immunologically in order to assess in a descriptive manner genetic or immunological features characteristic of clinical behavior. OUTLINE: INDUCTION CHEMOTHERAPY: All patients receive paclitaxel albumin-stabilized nanoparticle formulation intravenously (IV) over 60 minutes on days 1, 8, and 15 and carboplatin IV over 30-60 minutes on day 1. Treatment repeats every 21 days for 3 courses in the absence of disease progression or unacceptable toxicity. Patients are then assigned to 1 of 3 treatment groups based on response to induction chemotherapy. GROUP A (LOW-DOSE ARM): Patients undergo radiation therapy once daily for 5 weeks. GROUP B (INTERMEDIATE-DOSE ARM): Patients receive hydroxyurea orally (PO) twice daily (BID) on days 0-5, fluorouracil IV continuously on days 1-5, and paclitaxel IV over 60 minutes on day 1. Patients also receive low-dose radiation therapy BID on days 1-5. Treatment repeats every 14 days for 3 courses in the absence of disease progression or unacceptable toxicity. GROUP C (STANDARD-DOSE ARM): Patients receive hydroxyurea PO BID on days 0-5, fluorouracil IV continuously on days 1-5, and paclitaxel IV over 60 minutes on day 1. Patients also receive standard-dose radiation therapy BID on days 1-5. Treatment repeats every 14 days for up to 5 courses in the absence of disease progression or unacceptable toxicity.\* \*NOTE: At the discretion of the principal investigator (PI), patients may receive cisplatin IV over 1-3 hours every 3 weeks during radiation therapy instead of paclitaxel and undergo daily radiation therapy. After completion of study treatment, patients are followed up for 30 days, every 3 months for 1 year, every 6 months for 2 years, and then annually for 2 years.