A Study of Tremelimumab Combined With the Anti-PD-L1 MEDI4736 Antibody in Malignant Mesothelioma (NIBIT-MESO-1)

Inclusion Criteria: * Willing and able to give written informed consent. * Histologic diagnosis of malignant mesothelioma. * Subjects who have refused a first line platinum-based chemotherapy, or subjects in progression of disease after a maximum of one line of platinum-based therapy for advanced disease. * Disease not amenable to curative surgery. * Measurable disease, per modified Response Evaluation Criteria in Solid Tumor \[RECIST\] for pleural mesothelioma or RECIST version 1.1 for peritoneal mesothelioma). * Life expectancy ≥ 12 weeks. * ECOG performance status of 0 or 1 * Normal laboratory tests * Negative screening tests for HIV, Hepatitis B, and Hepatitis C. * Availability of archival tumor tissue or feasibility to perform a new tumor biopsy at screening phase. * Men and women, of and over 18 years old. Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy for 180 days after the last dose of investigational drug. Exclusion Criteria: * Involvement in the planning and/or conduct of the study. * Participation in another clinical study with an investigational product during the last 6 weeks. * Any previous treatment with a CTLA4, PD-1 or PD-L1 inhibitor, including tremelimumab or MEDI4736. * History of another primary malignancy except for: malignancy treated with curative intent and with no known active disease ≥3 years before the first dose of study drug and of low potential risk for recurrence. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. Adequately treated carcinoma in situ without evidence of disease eg, cervical cancer in situ. * Receipt of the last dose of anti-cancer therapy ≤ 6 weeks prior to the first dose of study drug. * Mean QT interval corrected for heart rate (QTc) ≥470 ms using Bazett's Correction. * Current or prior use of immunosuppressive medication within 28 days before the first dose of tremelimumab and MEDI4736, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid. * Any unresolved toxicity (CTCAE grade \>2) from previous anti-cancer therapy. * Any prior Grade \>3 immune-related adverse event (irAE) while receiving any previous immunotherapy agent, or any unresolved irAE \>Grade 1. Active or prior documented autoimmune or inflammatory disorders * History of primary immunodeficiency or allogeneic organ transplant. * History of hypersensitivity to tremelimumab or MEDI4736 or any excipient. * Uncontrolled intercurrent illness including, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diatheses * Known history of previous clinical diagnosis of tuberculosis. * History of leptomeningeal carcinomatosis. * Receipt of live attenuated vaccination within 30 days prior to study entry or within 30 days of receiving tremelimumab and MEDI4736. * Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive of but not limited to surgery, radiation and/or corticosteroids. * Subjects with uncontrolled seizures.