Cabozantinib or Paclitaxel in Treating Patients With Persistent or Recurrent Epithelial Ovarian, Fallopian Tube, or Primary Peritoneal Cavity Cancer

PRIMARY OBJECTIVES: I. To assess the activity of cabozantinib (cabozantinib-s-malate) relative to weekly paclitaxel in patients with persistent or recurrent ovarian, fallopian tube, or primary peritoneal cancer with a log-rank test assessing progression-free survival (PFS) at 3.68 months (approximately pre-cycle 5) and 7.36 months (approximately pre-cycle 9). SECONDARY OBJECTIVES: I. To determine the frequency and severity of adverse events as assessed by Common Terminology Criteria for Adverse Events (CTCAE). II. To estimate and compare the proportion of patients responding to therapy by Response Evaluation Criteria for Solid Tumors (RECIST), cancer antigen 125 (CA125) response, the overall survival (OS), and the duration of response in each arm. TERTIARY OBJECTIVES: I. To retrospectively correlate c-met proto-oncogene (MET) expression with overall outcome. II. To retrospectively correlate c-MET copy number with overall outcome. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive cabozantinib-s-malate orally (PO) once daily (QD) on days 1-28. ARM II: Patients receive paclitaxel intravenously (IV) over 1 hour on days 1, 8, and 15. In both arms, courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.