Nivolumab With or Without Ipilimumab in Treating Patients With Persistent or Recurrent Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

PRIMARY OBJECTIVE: I. To estimate the proportion of patients who have objective tumor response (complete or partial) by modified Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 in patients with persistent or recurrent epithelial ovarian, fallopian tube, primary peritoneal cancers, treated with nivolumab or the combination of nivolumab and ipilimumab and to assess the difference in objective response rate (ORR) between patients treated with nivolumab versus those treated with the combination of nivolumab and ipilimumab. SECONDARY OBJECTIVES: I. To estimate the progression-free survival (PFS) hazard ratio for patients treated with nivolumab versus those treated with the combination of nivolumab and ipilimumab. II. To estimate and compare the duration of overall survival (OS) for patients treated with nivolumab or the combination of nivolumab and ipilimumab. III. To determine the frequency and severity of adverse events associated with treatment with nivolumab or the combination of nivolumab and ipilimumab as assessed by Common Terminology Criteria for Adverse Events (CTCAE). IV. To determine whether cellular and molecular laboratory parameters in pre-treatment tissue and peripheral blood specimens predict overall survival (OS), tumor response by modified RECIST 1.1, and progression-free survival (PFS): IVa. PD-L1 expression in tumor cells and tumor-infiltrating lymphocytes (TILs) measured by quantitative immunohistochemistry (IHC). IVb. Natural anti-tumor immunity in tumor cells and TILs measured using IHC and T cell repertoire analyses. IVc. Tumor "immunogenicity" as determined by the neo-epitope landscape using next-generation whole exome sequencing (NGS). IVd. Anti-tumor immune response in peripheral blood, including serologic responses and analysis of T cell receptor (TCR) repertoires by deep sequencing. IVe. Shift in quantitative laboratory peripheral blood parameters after the first 6 and 12 weeks of therapy. OUTLINE: Patients are randomized to 1 of 2 treatment groups. GROUP I: INDUCTION: Patients receive nivolumab intravenously (IV) over 30 minutes every 2 weeks. Treatment repeats every 4 weeks for 2 cycles in the absence of disease progression or unacceptable toxicity. MAINTENANCE: Patients receive nivolumab IV over 30 minutes every 2 weeks. Treatment repeats every 4 weeks for up to 21 cycles in the absence of disease progression or unacceptable toxicity. GROUP II: INDUCTION: Patients receive nivolumab IV over 30 minutes and ipilimumab IV over 90 minutes. Treatment repeats every 3 weeks for 4 cycles in the absence of disease progression or unacceptable toxicity. MAINTENANCE: Patients receive nivolumab IV over 30 minutes every 2 weeks. Treatment repeats every 4 weeks for up to 21 cycles in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 100 days, every 3 months for 2 years, and then every 6 months for 3 years.