Durvalumab in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer

PRIMARY OBJECTIVES: I. Determine the response rate to durvalumab in metastatic castration-resistant prostate cancer (mCRPC) patients with microsatellite instability (MSI), where response rate is defined either according to modified Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria or a reduction in prostate specific antigen (PSA) level of \>= 50%. SECONDARY OBJECTIVES: I. Determine the percent of mCRPC patients with MSI achieving a radiographic response per modified RECIST 1.1 criteria following treatment with durvalumab. II. Determine the percent of mCRPC patients with MSI achieving a reduction in PSA level of \>= 50% following treatment with durvalumab. III. Determine the radiographic progression free survival (PFS) in hypermutated mCRPC patients with MSI treated with durvalumab using modified RECIST 1.1 criteria for soft tissue metastases and Prostate Cancer Working Group 3 (PCWG3) criteria for bone metastases. IV. Determine the PSA PFS rate according to PCWG3 criteria in hypermutated mCRPC patients with MSI treated with durvalumab. V. Determine the time to response in hypermutated mCRPC patients with MSI treated with durvalumab using modified RECIST 1.1 criteria. VI. Determine the overall survival in hypermutated mCRPC patients with MSI treated with durvalumab. VII. Determine the change in PSA doubling time 12-weeks after the initiation of durvalumab. VIII. Track pain as assessed by the Brief Pain Inventory during the course of treatment with durvalumab. IX. Assess the incidence and severity of adverse events according to the National Cancer Institute - Common Terminology Criteria for Adverse Events (CTCAE) version 4.0. TERTIARY OBJECTIVES: I. Determine mismatch repair gene mutational status and mutational load (by UWOncoPlex). II. Determine mismatch repair gene mutational status, mutational load and microsatellite stability from circulating tumor cells (CTCs) and/or cell-free tumor DNA (ctDNA). III. PD-L1 expression by immunohistochemistry (IHC) and transcript profiling (e.g. quantitative real-time polymerase chain reaction \[qRT-PCR\]). IV. Determine the relative location of T-cells within the tumor microenvironment (i.e. stroma vs. tumor edge) using CD3/CD8 IHC. V. Evaluate for tumor specific T-cell responses in blood and within the tumor microenvironment using next generation sequencing assays. OUTLINE: Patients receive durvalumab intravenously (IV) over 60 minutes on day 1. Courses repeat every 4 weeks for up to 12 months in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 30 days, at 2, 3, 4, 6, 8, and 10 months, and then every 6 months.