Study of Tremelimumab and Durvalumab (MEDI4736) (T300+D) in Advanced Hepatocellular Carcinomas With Child-Pugh-B Cirrhosis

Inclusion Criteria: 1. Patients diagnosed with HCC based on pathologic diagnosis from biopsy or radiographic diagnosis on CT liver or MRI liver (i.e., Barcelona Clinic Liver Cancer (BCLC) stage B and not candidate for locoregional therapies or BCLC stage C)10 2. Patients with Child-Pugh-B7 or -B8 liver cirrhosis11 3. ECOG performance status score 0-1 4. Patients with Hepatitis B Virus (HBV) infection are required to receive effective antiviral therapy and have a viral load less than 500 IU/mL at screening; antiviral therapy is not required for patients with Hepatitis C Virus (HCV) infection. 5. Adequate organ and bone marrow function: 1. Absolute neutrophil counts ≥1000/uL 2. Platelets ≥60 × 100/uL 3. Hemoglobin ≥8.0 g/dL 4. ALT and AST ≤5× upper limit of normal each 5. Bilirubin ≤3 mg/dL, 6. International normalized ratio (INR) ≤2.3 or prothrombin time ≤6 seconds above control) 7. Measured creatinine clearance (CL) \>40 mL/min or Calculated creatinine clearance CL\>40 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance: Males: Creatinine CL (mL/min)=Weight (kg) x (140 - Age) /72 x serum creatinine (mg/dL) Females: Creatinine CL (mL/min)=Weight (kg) x (140 - Age) x 0.85 /72 x serum creatinine (mg/dL) 6. Body weight \>30 kilogram (kg) 7. Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization (e.g., Health Insurance Portability and Accountability Act in the US) obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations. 8. Age \>18 years at time of study entry or adult male or female (according to age of majority as defined as ≥18 years) 9. Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. 10. Must have a life expectancy of at least 12 weeks. 11. At least 1 lesion, not previously irradiated, that qualifies as a RECIST 1.1 target lesion (TL) at baseline. Exclusion Criteria: 1. Patients who are candidates for curative treatments 2. History of uncontrolled hepatic encephalopathy in the past 6 months; patients who are stable on medical therapy are eligible. 3. Active substance abuse or alcohol abuse at the time of consent or enrollment, which in the opinion of the treating physician would interfere with the safety of the patient and/or adherence to the study protocol. 4. Participants must not have a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) has the potential to interfere with the safety or efficacy assessment of the investigational regimen. 5. Prior systemic therapy for locally advanced or metastatic HCC 6. Participation in another clinical study with an investigational product during the last 1 month. 7. Concurrent enrolment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study. 8. Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable. \<\<amend as required based on any combination studies with other anticancer agents\>\> 9. Radiotherapy treatment to more than 30% of the bone marrow or with a wide field of radiation within 4 weeks of the first dose of study drug 10. Major surgical procedure (as defined by the Investigator) within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent is acceptable. 11. History of allogenic organ transplantation 12. Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.\]). The following are exceptions to this criterion: 1. Patients with vitiligo or alopecia 2. Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement. 3. Any chronic skin condition that does not require systemic therapy 4. Patients without active disease in the last 5 years may be included but only after consultation with the study physician. 5. Patients with celiac disease controlled by diet alone. 13. Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent 14. History of leptomeningeal carcinomatosis 15. History of active primary immunodeficiency 16. Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab or tremelimumab. The following are exceptions to this criterion: 1. Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) 2. Systemic corticosteroids at physiologic doses not to exceed \<\<10 mg/day\>\> of prednisone or its equivalent. 3. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) 17. Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 90 days after the last dose of IP. 18. Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab monotherapy or180 days after the last dose of durvalumab and tremelimumab combination therapy. 19. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. 20. Prior randomisation or treatment in a previous durvalumab and/or tremelimumab clinical study regardless of treatment arm assignment. 21. Known allergy or hypersensitivity to IP or any excipient. 22. History of another primary malignancy except for: 1. Malignancy treated with curative intent with no known active disease ≥2 years before the first dose of study intervention and of low potential risk for recurrence. 2. Basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or lentigo maligna that has undergone potentially curative therapy.