Avastin Plus Chemotherapy vs. Avastin Plus Chemotherapy Guided by Cancer Stem Cell Test in Recurrent Ovarian Cancer

Inclusion Criteria: * 1\. Informed consent obtained and signed; * 2\. Willing and able to commit to study procedures including long-term follow-up visit(s); * 3\. At least 18 years old at the time of enrollment; * 4\. Negative pregnancy test for women of childbearing potential * 5\. Experiencing 1st, 2nd, or 3rd recurrent epithelial ovarian cancer of any stage regardless of platinum sensitivity, (platinum-sensitive, -resistant, or -refractory); * 6\. Histopathological or cytological confirmation of recurrent epithelial ovarian carcinoma, peritoneal cancer or fallopian tube cancer. * 7\. Evaluable disease - defined as RECIST 1.1 measurable disease OR not measurable disease (defined as solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions OR ascites and/or pleural effusion that has been pathologically demonstrated to be disease-related in the setting of a CA125 \> 2x ULN). * 8\. At least 30 days post-cytotoxic chemotherapy and/or monoclonal antibody therapy prior to enrollment; * 9\. Toxicities of prior therapy (excepting alopecia) should be resolved to less than or equal to Grade 1 as per CTCAE v4.0 (http://ctep.cancer.gov/protocol development/electronic\_applications/ctc.htm). Patients with long-standing stable grade 2 neuropathy may be considered after discussion with the Study Chair. * 10\. ECOG Performance Status Score of ≤ 2, KPS≥70, or 0-1 GOG status * 11\. Adequate laboratory values within 60 days of enrollment to study defined as follows: 1. WBC ≥ 3000/mm3 2. Hgb ≥ 10 mg/dl 3. Hct ≥ 28% 4. Platelet count ≥ 100,000/μL 5. Serum creatinine ≤ 2.0 mg/dl 6. Total bilirubin ≤ 2.5 mg/dl 7. AST/SGOT ≤ 3 times ULN. If intrahepatic liver metastases are present, AST and ALT must be ≤ 5 times institutional ULN. 8. Random urine protein/creatinine ratio ≤ 1 or 24 hour urine protein \< 0.1 gram. * 12\. Appropriate for tissue sampling either by tumor biopsy or peritoneal or pleural fluid collection. Exclusion Criteria: * 1\. Estimated life expectancy of \<6 months, as estimated by the investigator in consultation with participating oncologists; * 2\. Ovarian cancer of a low grade serous, mucinous, or clear cell histology; * 3\. Uncontrolled diabetes; * 4\. Patients with clinically significant proteinuria; urine protein should be screened by urine protein-creatinine ratio (UPCR); the UPCR has been found to correlate directly with the amount of protein excreted in a 24 hour urine collection; specifically, a UPCR of 1.0 is equivalent to 1.0 gram of protein in a 24-hour urine collection; obtain at least 4 ml of a random urine sample in a sterile container (does not have to be a 24-hour urine); send sample to lab with request for urine protein and creatinine levels (separate requests); the lab will measure protein concentration (mg/dL) and creatinine concentration (mg/dL); the UPCR is derived as follows: protein concentration (mg/dL)/creatinine (mg/dL); patients must have a UPCR ≤ 1.0 to allow participation in the study; * 5\. Symptomatic cardiac conditions; * 6\. Contraindications to bevacizumab including uncontrolled hypertension, known arterial or venous thromboembolism, known nephrotic syndrome, history of abdominal fistula, GIP, or intra-abdominal abscess; clinical signs or symptoms of GI obstruction and/or requirement for parenteral hydration or nutrition; nonhealing wound, ulcer, or bone fracture; bleeding diathesis or significant coagulopathy; known CNS disease, clinically significant cardiovascular disease; and a major surgical procedure within 28 days of enrollment or anticipated to occur while participating in study; * 7\. Enrollment in another clinical study that precludes allowing the oncologist to select chemotherapy regimens; * 8\. Previously participated in this study; * 9\. Any condition that would, in the opinion of the investigator, place the participant at an unacceptable risk, or render the participant unable to meet the requirements of the protocol (including long-term study follow-up). * 10\. Documented history of ovarian cancer of a low malignant potential phenotype or unclear cell histology. * 11\. CA-125 only disease without RECIST 1.1 measurable or otherwise evaluable disease * 12\. Patients may not use any complementary or alternative medicines including natural herbal products or folk remedies as they may interfere with the effectiveness of the study treatments.