Cediranib Maleate and Combination Chemotherapy in Treating Patients With Advanced Biliary Cancers

Inclusion Criteria: * Patients with histopathological or cytopathological diagnosis of advanced biliary carcinoma (gallbladder cancer, cholangiocarcinoma, ampullary cancer) not amenable to conventional surgical approach are eligible * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral CT scan * No patients with untreated brain metastases * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Life expectancy of greater than 12 weeks * White blood cell (WBC)/leukocytes ≥ 3,000/μL * Absolute neutrophil count ≥ 1,500/μL * Platelets ≥ 100,000/μL * Hemoglobin ≥ 9 g/dL * Total bilirubin ≤ 3 mg/dL * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) ≤ 2.5 times institutional upper limit of normal * Creatinine within normal institutional limits OR calculated creatinine clearance ≥ 60 mL/min * No patients with proteinuria not meeting the criteria below; urine sample must be tested by urine protein:creatinine (UPC) ratio or by urinalysis method within 1 week of starting study treatment; depending upon the testing method used, the following criteria must be met: * UPC ratio must be \< 1.0; if UPC ratio is ≥ 1.0, a 24-hour urine specimen must be collected and must demonstrate \< 1 g of protein * Urinalysis must indicate 0-1+ protein; if urinalysis reading is ≥ 2+, a 24-hour urine specimen must be collected and must demonstrate \< 1 g of protein * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use adequate contraception (hormonal or barrier method of birth control; abstinence) before and during study treatment * Acceptable contraception includes abstinence, oral contraceptives, intra-uterine device (IUD), diaphragm, Norplant, approved hormone injections, condoms, or documentation of medical sterilization * Patients with evidence of heart disease must be New York Heart Association (NYHA) Class I or II * NYHA Class II patients controlled with treatment are considered at increased risk for compromised left ventricular ejection fraction (LVEF) and will undergo increased cardiac monitoring * No patients with other active invasive cancers except nonmelanoma skin cancer or carcinoma in-situ of the cervix * History of prior cancer is allowed as long as there has been no evidence of disease within the past 5 years * No patients with mean corrected QT interval (QTc) \> 480 msec (with Bazett's correction) in screening electrocardiogram or history of familial long QT syndrome * No patients with uncontrolled hypertension defined as systolic blood pressure (BP) ≥ 140 mm Hg or diastolic BP ≥ 90 mm Hg, with or without anti-hypertensive medication or history of hypertensive crisis or hypertensive encephalopathy * Patients with initial BP elevations are eligible once their BP is controlled to above parameters * No patients with uncontrolled intercurrent illness including, but not limited to: * Hypertension (\> 140/90 mm Hg) * Chronic or active infection requiring chronic suppressive antibiotics * History of or symptomatic congestive heart failure requiring chronic medical therapy * NYHA class III or IV heart disease * Unstable angina pectoris within 180 days prior to starting study treatment * Myocardial infarction within 180 days prior to study treatment * Gastroduodenal ulcer(s) determined by endoscopy to be active within 180 days prior to study treatment * Serious or non-healing wound, skin ulcers, or bone fracture * Any significant bleeding that is not related to the primary tumor within 180 days prior to study treatment * Known bleeding diathesis or coagulopathy * Paresthesias, peripheral sensory neuropathy \> gr. 1 per Common Terminology Criteria for Adverse Events (CTCAE) v.4, or peripheral motor neuropathy ≥ gr. 2 per CTCAE v.4 * Psychiatric illness/social situations that would limit compliance with study requirements * No patients with history of transient ischemic attack (TIA) or cerebrovascular accident (CVA) within 180 days prior to study treatment, symptomatic peripheral ischemia; history of arterial thrombotic event within 180 days prior to study treatment; gastrointestinal (GI) perforation within 180 days prior to study treatment * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients who are chemotherapy naive unless chemotherapy was given as adjuvant post-surgical treatment and at least 6 months have elapsed since adjuvant chemotherapy * No patients who have had major surgical procedures, open biopsies, or significant traumatic injury within 28 days prior to study treatment * Chemotherapy for prior cancer is permitted * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or PK of AZD2171 will be determined following review of their case by the Principal Investigator * Efforts should be made to switch patients with brain metastases who are taking enzyme-inducing anticonvulsant agents to other medications * Patients may not be receiving any other investigational agents nor have participated in an investigational trial within the past 30 days * Patients may not be receiving any medication that may markedly affect renal function (e.g., vancomycin, amphotericin, pentamidine) * Patients may not be receiving therapeutic doses of Coumadin or equivalent * No patients requiring drugs with proarrhythmic potential