Randomized Phase III Study of Sorafenib Versus Stereotactic Body Radiation Therapy Followed by Sorafenib in Hepatocellular Carcinoma

• Patients must have a diagnosis of HCC by at least one criterion listed below within 360 days prior to study entry:

‣ Pathologically (histologically or cytologically) proven diagnosis of HCC,(biopsies are recommended, and are to be submitted for research evaluation if patients consent)

⁃ At least one solid liver lesion or vascular tumor thrombosis (involving portal vein, inferior vena cava (IVC) and/or hepatic vein) \> 1 cm with arterial enhancement and delayed washout on multi-phasic computerized tomography (CT) or magnetic resonance imaging (MRI) in the setting of cirrhosis or chronic hepatitis B or C without cirrhosis.

⁃ For patients whose CURRENT disease is vascular only: enhancing vascular thrombosis (involving portal vein, IVC and/or hepatic vein) demonstrating early arterial enhancement and delayed washout on multi-phasic CT or MRI in a patient with known HCC (diagnosed previously \<720 days) using the above criteria.

• Measureable hepatic disease and/or presence of vascular tumor thrombosis (involving portal vein, IVC and/or hepatic vein) which may not be measureable as per Response Evaluation Criteria in Solid Tumors (RECIST) on liver CT or MRI, within 28 days of registration

• Appropriate for protocol entry based upon the following minimum diagnostic workup:

‣ History/physical examination including examination for encephalopathy, ascites, weight, height, and blood pressure within 14 days prior to study entry

⁃ Assessment by radiation oncologist and medical oncologist or hepatologist who specializes in treatment of HCC within 28 days prior to study entry

⁃ Pre-randomization Scan (REQUIRED for All Patients): Within 28 days prior to study entry, multiphasic liver CT or multiphasic liver MR scan.

⁃ Within 28 days prior to study entry CT chest with CT or MR abdomen and CT or MR pelvis, or positron emission tomography (PET) CT chest/abdomen/pelvis.

• Zubrod performance status 0-2 within 28 days prior to study entry

• All blood work obtained within 14 days prior to study entry with adequate organ marrow function defined as follows:

‣ Absolute neutrophil count (ANC) \>= 1,500 cells/mm\^3

⁃ Platelets \>= 60,000 cells/mm\^3

⁃ Hemoglobin \>= 8.0 g/dl (note: the use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 8.0 g/dl is acceptable)

⁃ Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 6 times upper limit of normal (ULN)

⁃ Serum creatinine =\< 2 x ULN or creatinine clearance \>= 60 mL/min

• Barcelona Clinic Liver Cancer (BCLC) stage: intermediate (B) or advanced (C) within 28 days prior to study entry

• Child-Pugh score A within 14 days prior to study entry

• Women of childbearing potential and male participants must agree to practice adequate contraception while on study and for at least 6 months following the last dose of radiation therapy (RT) and for at least 28 days following the last dose of sorafenib (whichever is later)

• Unsuitable for resection or transplant or radiofrequency ablation (RFA)

• Unsuitable for or refractory to transarterial hepatic chemo-embolization (TACE) or drug eluting beads (DEB) for any of the following reasons, as described by Raoul et al (2011):

‣ Technical contraindications: arteriovenous fistula, including, surgical portosystemic shunt or spontaneous portosystemic shunt

⁃ Severe reduction in portal vein flow: due to tumor portal vein, IVC or atrial invasion or bland portal vein occlusion

⁃ Medical contraindications including congestive heart failure, angina, severe peripheral vascular disease

⁃ Presence of extrahepatic disease

⁃ No response post TACE (or DEB) or progressive HCC despite TACE; prior TACE or DEB is allowed but must be \> 28 days from study entry

⁃ Serious toxicity following prior TACE (or DEB); prior TACE or DEB must be \> 28 days from study entry

⁃ Other medical comorbidities making TACE (or DEB) unsafe and/or risky (e.g. combination of relative contraindications including age \> 80 years, tumor \> 10 cm, \> 50% replacement of the liver by HCC, extensive multinodular bilobar HCC, biliary drainage)

• Patients treated with prior surgery are eligible for this study if they otherwise meet eligibility criteria

• Patient must be able to provide study-specific informed consent prior to study entry