Testing the Addition of Immunotherapy Before Surgery for Patients With Sarcomatoid Mesothelioma

PRIMARY OBJECTIVES: I. To determine the percentage of patients with potentially resectable non-epithelioid mesothelioma who are able to proceed with surgery after neoadjuvant ipilimumab and nivolumab. II. To determine the progression-free survival rate at 12 months after the initiation of neoadjuvant ipilimumab and nivolumab. SECONDARY OBJECTIVES: I. To determine the rate of intra-operative or post-operative complications following neoadjuvant immunotherapy. II. Best response per modified pleural Response Evaluation Criteria in Solid Tumors (RECIST). III. Major pathologic response rate. IV. Time to recurrence after surgery. EXPLORATORY OBJECTIVES: I. To evaluate the association between the change in peripheral T cell clonality relative to baseline and treatment response. II. To evaluate the association between PD-L1 expression at baseline and treatment response. III. To evaluate whether a novel mesothelioma immune signature identified by Dr. Mansfield's laboratory is predictive of response. OUTLINE: Patients receive nivolumab intravenously (IV), ipilimumab IV, and may undergo surgery on study. Patients also undergo computed tomography (CT) or magnetic resonance imaging (MRI) and positron emission tomography (PET) throughout the trial.