A Phase 2 Study of Durvalumab in Combination With Tremelimumab in Malignant Pleural Mesothelioma

Inclusion Criteria: * Written informed consent obtained prior to any study-specific procedures not considered part of routine medical care * Histologically or cytologically confirmed unresectable or medically inoperable malignant pleural mesothelioma * Disease progression after treatment with at least one line of chemotherapy that included a first-line platinum agent in combination with an anti-folate * Participants must have measurable disease according to modified RECIST for pleural malignant mesothelioma. (Bone metastases are not considered measurable.) Prior radiation to the only site of measurable disease will make the participant ineligible unless the lesion has been demonstrated to grow after completion of radiation therapy. * Participants must be willing and able to undergo a biopsy at the start of this study and an on-treatment biopsy if safe and feasible. * Participants must have be at least 28 days from any major surgery. * ECOG performance status of 0 or 1. * Subjects must have adequate hematologic, renal, and organ and marrow function * Age 18 years or older * Female subjects of childbearing potential who are sexually active with a non sterilized male partner must agree to use at least one highly effective method of contraception from the time of screening and must agree to continue using such precautions for 180 days after the last dose of investigational product. Male partners of a female subject must also agree to use male condom plus spermicide throughout this period. Cessation of birth control after this point should be discussed with a responsible physician. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however, occasional abstinence, the rhythm method, and the withdrawal method are not acceptable methods of contraception. Female patients should refrain from breastfeeding throughout this period. * Females of childbearing potential are defined as those who are not surgically sterile (i.e., bilateral tubal ligation, bilateral oophorectomy, or complete hysterectomy) or post-menopausal (defined as greater than or equal to 12 months with no menses without an alternative medical cause) * Non-sterilized male subjects who are sexually active with a female partner of childbearing potential must use male condom plus spermicide from screening through 180 days after the last dose of investigational product. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however, occasional abstinence, the rhythm method, and the withdrawal method are not acceptable methods of contraception. Male patients should refrain from sperm donation throughout this period. Female partners of a male subject must use a highly effective method of contraception throughout this period. * Ability to understand and the willingness to sign a written informed consent document * Subject 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 Exclusion Criteria: * Previous treatment with an immune check-point inhibitors, CTLA-4, PD-1, or PD-L1, including prior treatment with either durvalumab or tremelimumab * Known central nervous system metastasis. Patients with known brain metastases, spinal cord compression, carcinomatous meningitis, or leptomeningeal disease may be enrolled if they have been treated, are no longer taking corticosteroids, and have been stable on imaging for at least 3 weeks * Subjects currently receiving systemic corticosteroids above 10 mg per day for more than 14 days; subjects receiving other systemic immunosuppressive drugs for more than 14 days. Exceptions include: inhaled, intranasal, ophthalmic, and topical corticosteroids, local corticosteroid injections (e.g., intra-articular injections), and subjects requiring corticosteroid pre-medication for hypersensitivity reactions (e.g. CT scan premedication) * Subjects with medical conditions that require the chronic use of systemic corticosteroids. Exceptions include: inhaled, intranasal, ophthalmic, and topical corticosteroids, local corticosteroid injections (e.g., intra-articular injections), and subjects requiring corticosteroid pre-medication for hypersensitivity reactions (e.g. CT scan premedication) * Active or prior documented autoimmune disease within the past 2 years, including but not limited to systemic lupus erythematosus, sarcoidosis syndrome, or Wegener's granulomatosis. NOTE: Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment within the past 2 years are not excluded. * Active or prior documented inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis, celiac disease, diverticulitis), or any other chronic, serious gastrointestinal condition associated with diarrhea. NOTE: Subjects with known diverticulosis are permitted to enroll. * History of interstitial lung disease or pneumonitis that has required steroid administration. * History of primary immunodeficiency * History of allogeneic organ transplant * History of hypersensitivity to tremelimumab, durvalumab, or any excipient * Known history of active tuberculosis * Receipt of live attenuated vaccination within 30 days prior to study entry or within 30 days of receiving durvalumab or tremelimumab * Participants with a history of a second primary malignancy. Exceptions include: patients with a history of malignancies that were treated curatively and have not recurred within 5 years prior to study entry; resected basal and squamous cell carcinomas of the skin, and completely resected carcinoma in situ of any type. * Participants who have had chemotherapy, biologic therapy, or investigational therapy within 21 days (including bevacizumab) or radiotherapy within 7 days prior to entering the study or those who have not recovered from adverse events due to agents administered * Any history of a prior immune-related adverse event (irAE) at least or greater than grade 3 while receiving any previous immunotherapy agent. * Participants who are receiving any other investigational agents. * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Gastritis * Symptomatic congestive heart failure * Severe hypertension (defined as BP at least or greater than160/100 during the screening period despite optimal medical management) * Unstable angina pectoris * Cardiac arrhythmia * Active bleeding diatheses * Active peptic ulcer disease * Psychiatric illness/social situations that would limit compliance with study requirements * Mean QT interval corrected for heart rate (QTc) ≥470 ms calculated from 3 electrocardiograms (ECGs) using Fredericia's Correction * Known past or present medical history HIV-positive * Subjects with known acute or chronic hepatitis B or hepatitis C. * Pregnant women are excluded from this study because tremelimumab and durvalumab have unknown effects on the developing fetus. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with tremelimumab or durvalumab, breastfeeding women are also excluded. Female subjects of child bearing potential must have a negative serum pregnancy test obtained prior to trial registration. * Subjects who are involved in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site). * Subjects who have undergone a pneumonectomy due to known potential for pulmonary toxicities and heightened risk for complications.