Carboplatin and Paclitaxel or Oxaliplatin and Capecitabine With or Without Bevacizumab as First-Line Therapy in Treating Patients With Newly Diagnosed Stage II-IV or Recurrent Stage I Epithelial Ovarian or Fallopian Tube Cancer

PRIMARY OBJECTIVES: I. To determine if capecitabine and oxaliplatin reduces the death rate compared to carboplatin and paclitaxel in women with mucinous adenocarcinoma of the ovary or fallopian tube. II. To determine if bevacizumab reduces the death rate compared to no bevacizumab in women with mucinous adenocarcinoma of the ovary or fallopian tube. SECONDARY OBJECTIVES: I. To determine if capecitabine and oxaliplatin increases the duration of progression-free survival (PFS) compared to carboplatin and paclitaxel in women with mucinous adenocarcinoma of the ovary or fallopian tube. II. To determine if bevacizumab increases the duration of PFS compared to no bevacizumab in women with mucinous adenocarcinoma of the ovary or fallopian tube. III. To compare the response rates for capecitabine and oxaliplatin versus carboplatin and paclitaxel in patients with mucinous adenocarcinoma of the ovary or fallopian tube with measurable disease after initial tumor reductive surgery. IV. To compare the response rates for bevacizumab versus no bevacizumab in patients with mucinous adenocarcinoma of the ovary or fallopian tube with measurable disease after initial tumor reductive surgery. V. To determine the nature and degree of toxicity of capecitabine and oxaliplatin compared with that of carboplatin and paclitaxel in this cohort of patients. VI. To determine the nature and degree of toxicity of bevacizumab in this cohort of patients. VII. To compare capecitabine and oxaliplatin versus carboplatin and paclitaxel with respect to changes in patient reported neurotoxicity. VIII. To determine the impact on quality of life (QOL, as measured by the Functional Assessment of Cancer Therapy-Ovarian \[FACT-O\] Trial Outcome Index \[TOI\]) following treatment with the above regimens. TERTIARY OBJECTIVES: I. To collect fixed and/or frozen tissue and whole blood for future research studies. OUTLINE: Patients are randomized to 1 of 4 treatment arms. ARM I: Patients receive carboplatin intravenously (IV) over 30-60 minutes on day 1 and paclitaxel IV over 3 hours on day 1. Treatment repeats every 3 weeks for 6 courses in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive oxaliplatin IV over 2-6 hours on day 1 and capecitabine orally (PO) twice daily (BID) on days 1-14. Treatment repeats every 3 weeks for 6 courses in the absence of disease progression or unacceptable toxicity. ARM III: Patients receive carboplatin and paclitaxel IV as in arm I and bevacizumab IV over 30-90 minutes on day 1. Treatment repeats every 3 weeks for 6 courses in the absence of disease progression or unacceptable toxicity. Patients then receive bevacizumab IV over 30-90 minutes alone on day 1. Treatment repeats every 3 weeks for 12 courses in the absence of disease progression or unacceptable toxicity. ARM IV: Patients receive oxaliplatin and capecitabine as in arm II, and bevacizumab as in arm III. After completion of study treatment, patients are followed up at 4-6 weeks, every 3 months for 2 years, and then every 6 months for 3 years.