Testing Docetaxel-Cetuximab or the Addition of an Immunotherapy Drug, Atezolizumab, to the Usual Chemotherapy and Radiation Therapy in High-Risk Head and Neck Cancer
* PHASE II INCLUSION CRITERIA (COMPLETE AS OF 20-MAR-2020)
* Pathologically (histologically or cytologically) proven diagnosis of head and neck squamous cell carcinoma (HNSCC) involving the oral cavity (excluding lips), oropharynx (p16 negative), larynx, or hypopharynx
* Patients must have undergone gross total surgical resection of high-risk oral cavity, oropharynx (p16 negative), larynx, or hypopharynx within 63 days prior to registration; Note: patients may have biopsy under general anesthesia in an operating room followed by definitive ablative cancer surgery representing gross total resection; the gross total resection has to be done within 63 days prior to registration; if, however, patients have ablative resection but shortly recur or are determined to have persisting disease requiring re-resection to achieve gross total resection, then the patient is not eligible
* Patients must have at least 1 of the following high-risk pathologic features: extracapsular nodal extension or invasive cancer at the primary tumor resection margin (tumor on ink)
* Pathologic stage III or IV HNSCC, including no distant metastases, based upon the following minimum diagnostic workup:
* General history and physical examination by a radiation oncologist and/or medical oncologist within 84 days prior to registration;
* Examination by an ear nose throat (ENT) or head \& neck surgeon prior to surgery; a laryngopharyngoscopy (mirror and/or fiber optic and/or direct procedure), if appropriate, is recommended but not required; intra-operative examination is acceptable documentation
* Pre-operative (op) Imaging of the head and neck: A neck computed tomography (CT) (with contrast) or CT/positron emission tomography (PET) (with contrast) and/or an magnetic resonance imaging (MRI) of the neck (T1 with gadolinium and T2) within 84 days prior to surgery; Note: this imaging data (diagnostic pre-operative scan showing gross disease) is to be submitted in Digital Imaging and Communications in Medicine (DICOM) format via TRIAD; the report is to be uploaded into Rave
* Chest CT scan (with or without contrast) or CT/PET that includes the chest (with or without contrast) either within 84 days prior to surgery or within 120 days prior to registration; Note: if the CT/PET with or without contrast is done within 84 days prior to surgery, it fulfills the chest imaging requirement
* Zubrod performance status of 0-1 within 14 days prior to registration
* Age \>= 18
* Absolute granulocyte count (AGC) \>= 1,500 cells/mm\^3 (obtained within 14 days prior to registration on study)
* Platelets \>= 100,000 cells/mm\^3 (obtained within 14 days prior to registration on study)
* Hemoglobin \>= 8.0 g/dl (Note: the use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 8.0 g/dl is acceptable)
* Total bilirubin \< 2 x institutional upper limit of normal (ULN) within 14 days prior to registration
* Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 3 x institutional ULN within 14 days prior to registration
* Serum creatinine institutional ULN within 14 days prior to registration or; creatinine clearance (CC) \>= 50 ml/min within 14 days prior to registration determined by 24-hour collection or estimated by Cockcroft-Gault formula
* Negative urine or serum pregnancy test within 14 days prior to registration for women of childbearing potential
* The following assessments are required within 14 days prior to registration: sodium (Na), potassium (K), chloride (Cl), glucose, calcium (Ca), magnesium (Mg), and albumin; Note: patients with an initial magnesium \< 0.5 mmol/L (1.2 mg/dl) may receive corrective magnesium supplementation but should continue to receive either prophylactic weekly infusion of magnesium and/or oral magnesium supplementation (e.g., magnesium oxide) at the investigator's discretion
* Patients with feeding tubes are eligible for the study
* Women of childbearing potential and male participants who are sexually active must agree to use a medically effective means of birth control
* Patient must provide study specific informed consent prior to study entry, including consent for mandatory tissue submission for epidermal growth factor receptor (EGFR) analysis and for oropharyngeal cancer patients, human papilloma virus (HPV) analysis
* PHASE III: Pathologically (histologically or cytologically) proven diagnosis of head and neck squamous cell carcinoma (HNSCC) involving the oral cavity (excluding lips), oropharynx (p16 negative), larynx, or hypopharynx
* PHASE III: Patients with oropharyngeal cancer must have p16-negative based on central review prior to Step 2 registration. All patients with oropharyngeal primary must consent for mandatory tissue submission for central p16 confirmation
* PHASE III: Patients must have undergone gross total surgical resection of high-risk oral cavity, oropharynx (p16 negative), larynx, or hypopharynx within 63 days prior to registration
* Note: Patients may have biopsy under general anesthesia in an operating room followed by definitive ablative cancer surgery representing gross total resection. The gross total resection has to be done within 63 days prior to registration. If, however, patients have ablative resection but shortly recur or are determined to have persisting disease requiring re-resection to achieve gross total resection, then the patient is not eligible
* PHASE III: Patients must have at least 1 of the following high-risk pathologic features: extracapsular nodal extension or invasive cancer at the primary tumor resection margin (tumor on ink or tumor in a final separately submitted margin)
* PHASE III: Pathologic stage III or IV HNSCC (American Joint Committee on Cancer \[AJCC\] 7th edition), including no distant metastases, based upon the following minimum diagnostic workup:
* General history and physical examination by a radiation oncologist or medical oncologist within 84 days prior to registration;
* Examination by an ENT or head \& neck surgeon prior to surgery; a laryngopharyngoscopy (mirror or fiberoptic or direct procedure), if appropriate, is recommended but not required. Intra-operative examination is acceptable documentation.
* Pre-op Imaging of the head and neck: A neck CT (with contrast and of diagnostic quality) or PET/CT (with contrast and of diagnostic quality) and/or an MRI of the neck of diagnostic quality (T1 with gadolinium and T2) within 84 days prior to surgery; Note: this imaging data (diagnostic pre-operative scan showing gross disease) is to be submitted in DICOM format via TRIAD. The report is to be uploaded into Rave.
* Chest CT scan (with or without contrast) or PET/CT that includes the chest (with or without contrast) either within 84 days prior to surgery or within 120 days prior to registration; Note: If the PET/CT with or without contrast is done within 84 days prior to surgery, it fulfills the chest imaging requirement
* PHASE III: Zubrod performance status of 0-1 within 14 days prior to registration
* PHASE III: Age \>= 18
* PHASE III: Leukocytes \>= 2,500 cells/mm\^3 (obtained within 14 days prior to registration on study)
* PHASE III: Absolute neutrophil count (ANC) \>= 1,500 cells/mm\^3 (obtained within 14 days prior to registration on study)
* PHASE III: Platelets \>= 100,000 cells/mm\^3 (obtained within 14 days prior to registration on study)
* PHASE III: Hemoglobin \>= 8.0 g/dL (Note: The use of transfusion or other intervention to achieve Hgb \>= 8.0 g/dL is acceptable) (obtained within 14 days prior to registration on study)
* PHASE III: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x institutional ULN may be enrolled) (within 14 days prior to registration)
* PHASE III: AST or ALT =\< 3 x institutional ULN (within 14 days prior to registration)
* PHASE III: Alkaline phosphatase =\< 2.5 x institutional ULN (within 14 days prior to registration)
* PHASE III: Creatinine clearance (CrCl) \>= 50 mL/min within 14 days prior to registration determined by 24-hour collection or estimated by Cockcroft-Gault formula
* PHASE III: Patients with feeding tubes are eligible for the study
* PHASE III: Negative urine or serum pregnancy test within 14 days prior to registration for women of childbearing potential
* PHASE III: All patients must provide study specific informed consent prior to study entry
* PHASE III: Patients positive for human immunodeficiency virus (HIV) are allowed on study, but HIV-positive patients must have:
* A stable regimen of highly active anti-retroviral therapy (HAART);
* No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections;
* A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based tests
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