Atezolizumab With or Without Cobimetinib in Treating Patients With Metastatic Bile Duct Cancer That Cannot Be Removed by Surgery or Gallbladder Cancer

Inclusion Criteria

• Pathologically confirmed metastatic or unresectable cholangiocarcinoma or gallbladder carcinoma (GBC), having received at least 1 prior line of systemic therapy, and received no more than 2 prior lines of therapy in the metastatic setting (disease recurrence = = 20 mm (>= 2 cm) with conventional techniques or as >= 10 mm (>= 1 cm) with spiral CT scan, MRI, or calipers by clinical exam; assessment must be completed within 4 weeks of randomization
• Age >= 18 years. Because no dosing or adverse event data are currently available on the use of cobimetinib in combination with atezolizumab in patients = 80%)
• Life expectancy of greater than 2 months
• Leukocytes >= 2, 500/mcL (within 2 weeks of randomization)
• Absolute neutrophil count >= 1, 500/mcL (within 2 weeks of randomization)
• Platelets >= 75, 000/mcL (within 2 weeks of randomization)
• Hemoglobin >= 8 g/dL (within 2 weeks of randomization)
• Total bilirubin = = 30 mL/min/1.73 m^2 by Cockcroft-Gault OR creatinine = 92% on room air

Exclusion Criteria

• Received chemotherapy or radiotherapy within 3 weeks prior to randomization or those who have not recovered to = = 2 weeks prior to randomization
• Prior treatment with a MEK inhibitor or ERK inhibitor
• Prior treatment with any anti-PD-1 or anti-PD-L1 antibody, prior allogeneic bone marrow transplantation, or prior solid organ transplantation
• Treatment with any investigational agent within 4 weeks prior to cycle 1, day 1, or five drug half-lives (whichever is longer)
• Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor [anti-TNF] agents) within 6 weeks prior to cycle 1 day 1;
• Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled
• The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed
• Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases, with the following exceptions:
• Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following:
• Radiographic demonstration of clinical stability upon the completion of CNS directed therapy and no evidence of interim progression between the completion of CNS directed therapy and the screening radiographic study
• No stereotactic radiation or whole-brain radiation within 28 days prior to randomization
• Screening CNS radiographic study >= 4 weeks from completion of radiotherapy and >= 2 weeks from discontinuation of corticosteroids
• Has a known concurrent malignancy that is expected to require active treatment within two years, or may interfere with the interpretation of the efficacy and safety outcomes of this study in the opinion of the treating investigator; superficial bladder cancer, non-melanoma skin cancers, or low grade prostate cancer not requiring therapy should not exclude participation in this trial
• Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies
• Allergy or hypersensitivity to components of the cobimetinib formulations
• History of congenital long QT syndrome or corrected QT interval (QTc) > 450 msec within 2 weeks of randomization
• Left ventricular ejection fraction (LVEF) below institutional lower limit of normal (LLN) or below 50%, whichever is lower, as determined by echocardiogram or multi-gated acquisition (MUGA) scan within 4 weeks of randomization
• Patients who meet any of the following exclusion criteria related to ocular disease will be excluded from study entry:
• Known risk factors for ocular toxicity, consisting of any of the following:
• History of serous retinopathy
• History of retinal vein occlusion (RVO)
• Evid