Study to Compare Selective Internal Radiation Therapy (SIRT) Versus Sorafenib in Locally Advanced Hepatocellular Carcinoma (HCC)

Inclusion Criteria: * Disease must be locally advanced as defined by BCLC (B) intermediate stage or BCLC (C) advanced stage without extra-hepatic disease (only with branch portal vein thrombosis). * Willing, able and mentally competent to provide written informed consent prior to any testing undertaken for this study protocol, including screening tests and evaluations that are not considered to be part of the subject's routine care. * Aged 18 years/older (either gender). * Unequivocal diagnosis of HCC. * HCC not amenable to surgical resection or immediate liver transplantation, or cannot be optimally treated with local ablative techniques such as RFA, consistent with the practice of the clinical trial centre. * Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with spiral CT scan or MRI. * ECOG performance status 0-1. * Child-Pugh A-B (up to 7 points) * Adequate haematological, renal and hepatic function as follows: * Leukocytes ≥ 2,500/μL * Platelets ≥ 80,000/μL * Haemoglobin \> 9.5g/dL * Total bilirubin \< 2.0mg/dL * INR ≤ 2.0 * ALP ≤ 5 x institutional ULN * AST and ALT ≤ 5 x institutional ULN * Albumin ≥ 2.5g/dL * Creatinine ≤ 2.0mg/dL * Life expectancy of at least 3 months without any active treatment. * Suitable for protocol treatment as determined by clinical assessment undertaken by the Investigator. * Female patients must be either postmenopausal or, if premenopausal, must have a negative pregnancy test and agree to use 2 forms of contraception if sexually active during their study participation. * Male patients must be surgically sterile, or if sexually active and having a pre-menopausal female partner then must be using an acceptable form of contraception. Exclusion Criteria: * Have had more than 2 administrations of hepatic artery directed therapy. * Subjects who have had hepatic artery directed therapy done \< 4 weeks prior to study entry. * Have had systemic chemotherapy for HCC except for prior adjuvant or neoadjuvant therapy given more than 6 months from enrolment. * have had prior treatment with Sorafenib or VEGF inhibitors. * Prior hepatic radiation therapy for HCC or other malignancy. * Currently receiving any other investigational agents for the treatment of their cancer. * Has intractable clinical ascites (in spite of optimal diuretic treatment) or any other clinical signs of liver failure, on physical examination. * Complete main portal vein thrombosis. * Any metastatic disease (local-regional lymph nodes measuring less than 2 cm in greatest diameter or lung nodules measuring less than 1 cm are not contraindications as per Investigator discretion). * Any other concurrent malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer for which the patient has been disease-free for at least 5 years. * Presence of clinical signs of CNS metastases due to their poor prognosis and because progressive neurologic dysfunction would confound the evaluation of neurologic and other adverse events. * Uncontrolled inter-current illness including, but not limited to, ongoing or active infection (except viral hepatitis), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Any of the following contraindications to angiography and selective visceral catheterization: * Bleeding diathesis, not correctable by the standard forms of therapy. * Severe peripheral vascular disease that would preclude arterial catheterization. * Portal hypertension with hepato-fugal flow as documented on baseline spiral CT scan. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to SIR-Spheres or Sorafenib. * Inability or unwillingness to understand or sign a written informed consent document. * Female subjects who are pregnant or currently breastfeeding. * Female subjects, unless postmenopausal or surgically sterile, unwillingness to practice effective contraception, as per Investigator discretion during the study. The rhythm method is not to be used as the sole method of contraception. * Male subjects, unwillingness to practice effective contraception (per Investigator discretion) while taking part in this study, because the effect of the SIR-Spheres treatment on sperm or upon the development of an unborn child are unknown. * Current enrolment in any other investigational therapeutic drug or device study.