Chemoembolization With or Without Sorafenib Tosylate in Treating Patients With Liver Cancer That Cannot Be Removed by Surgery

Inclusion Criteria:

   - Patients must have a diagnosis of hepatocellular carcinoma by at least one criterion
   listed below:

      - Histologically confirmed

      - Magnetic resonance imaging (MRI) or computerized tomography (CT) consistent with
      liver cirrhosis AND at least one solid liver lesion > 2 cm with early enhancement
      and delayed enhancement washout regardless of alpha-feto protein levels (AFP)

      - AFP > 400 ng/mL AND evidence of at least one solid liver lesion > 2 cm regardless
      of specific imaging characteristics on CT or MRI

   - Patients must have hepatocellular carcinoma (HCC) limited to the liver; there must be
   no clinical or radiographic evidence of extrahepatic HCC

   - Portal lymphadenopathy IS permitted for patients with hepatitis B virus (HBV) or
   hepatitis C virus (HCV) - as lymphadenopathy is commonly associated with hepatitis
   unrelated to malignancy

   - Staging CT of the chest and CT or MRI of the abdomen and pelvis must have been
   completed within 4 weeks of study registration

   - Patients must have measurable disease constituting < 50% of liver parenchyma within 4
   weeks of registration

   - Patients may not have ascites detectable on physical examination

   - Patients must not be candidates for curative resection, orthotopic liver
   transplantation, or radiofrequency ablation (RFA)

   - Patients may have been treated with RFA in the past, but no sooner than 4 weeks before
   study registration

   - Patients may have undergone previously attempted curative liver resection

   - Patients may NOT have been previously treated with brachytherapy such as yttrium-90
   microsphere

   - Patients may NOT have been previously treated with sorafenib, chemoembolization, or
   systemic chemotherapy including cytotoxic agents or molecularly targeted agents

   - Branch portal vein invasion by tumor is permitted but patients with main portal vein
   invasion by tumor are not eligible

   - Patients must have Child-Pugh score of A or B7 within 4 weeks prior to study
   registration

   - Serum total bilirubin =< 2.0 mg/dL

   - Alkaline phosphatase < 5 x upper limit of normal (ULN)

   - Aspartate aminotransferase (AST), alanine aminotransferase (ALT) < 5 x ULN

   - Serum creatinine =< 1.5 mg/dL

   - Platelet count >= 50,000/mm^3

   - Patients must not have any evidence of bleeding diathesis or active gastrointestinal
   bleeding

   - Patients must have no clinical signs of heart failure and meet New York Heart
   Association functional classification I or II defined as:

      - Class I - patients with no limitation of activities; they suffer no symptoms from
      ordinary activities

      - Class II - patients with slight, mild limitation of activity; they are
      comfortable with rest or with mild exertion

   - Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of
   0 or 1

   - Patients must have a life expectancy of at least 3 months

   - Patients must not be known to be human immunodeficiency virus (HIV) positive

   - Patients must not have other uncontrolled intercurrent illnesses excluding HBV or HCV,
   including, but not limited to: uncontrolled hypertension, symptomatic congestive heart
   failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/addictive
   disorders that would limit compliance with study requirements

      - Uncontrolled hypertension is defined as optimally treated baseline blood pressure
      that exceeds 150/90 mm Hg

   - Patients must not be taking cytochrome P450 enzyme inducing drugs

   - Age >= 18 years

   - Women must not be pregnant or breast-feeding; all females of childbearing potential
   must have a blood test or urine study within 2 weeks prior to registration to rule out
   pregnancy

   - Women of childbearing potential and sexually active males must be strongly advised to
   use an accepted and effective method of contraception

   - Patients must not have an allergy to iodine or gadolinium contrast that cannot be
   safely controlled with premedication

   - Patient must be able to swallow pills, as study medications cannot be crushed