Tivozanib in Treating Patients With Liver Cancer That Is Metastatic or Cannot Be Removed by Surgery

PRIMARY OBJECTIVES: I. Progression free survival (PFS) at 24 weeks in patients with advanced hepatocellular carcinoma (HCC). SECONDARY OBJECTIVES: I. To determine the safety of tivozanib in HCC. II. To determine the overall survival (OS) and clinical benefit rate (complete response \[CR\], partial response \[PR\] and stable disease \[SD\]) by Response Evaluation Criteria in Solid Tumors (RECIST). III. To determine the steady state pharmacokinetics (PK) and soluble vascular endothelial growth factor receptor 2 (VEGFR-2) baseline/change with tivozanib and use modeling to correlate exposure with biomarker change and the primary outcome measure of PFS. IV. To determine the change in viral load (hepatitis B virus \[HBV\] and hepatitis C virus \[HCV\]) during therapy in patients with HBV or HCV associated HCC. V. To determine the change in tumor marker (alfa fetoprotein) with tivozanib therapy is in the effect of tivozanib on several tumor-associated immune response markers. OUTLINE: This is a phase I, dose-escalation study followed by a phase II study. Patients receive tivozanib orally (PO) once daily (QD) on days 1-21. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 6 months.