Cancer Stem Cell Assay Directed Chemotherapy in Recurrent Platinum Resistant Ovarian Cancer

Inclusion Criteria: 1. Informed consent obtained and signed. 2. Participant is willing and able to commit to study procedures including long-term follow-up visit(s); 3. Participant must be a female and at least 18 years of age at the time of enrollment. 4. Negative pregnancy test for women of childbearing potential. 5. Participant has been diagnosed with recurrent platinum resistant epithelial ovarian, peritoneal, or fallopian tube carcinoma. 6. Participants must have an evaluable disease - defined as one of the following: 1\) RECIST 1.1 measurable disease (defined as one or more solid and/or cystic tumors on cross-sectional imaging that measures 1 cm or greater in long axis and/or lymph nodes measuring 1.5 cm or greater in short axis) 2) Evaluable disease (defined as solid and/or cystic tumors on radiographic imaging or physical exam that do not meet RECIST 1.1 definitions for target lesions) with elevated CA125 (GCIG recurrence and response criteria) by more than 2 times the upper limits of normal, confirmed in two successive samples, drawn at least one week apart). 7\. Participant has agreed to provide a core biopsy of the primary site, a secondary metastatic site, or to undergo a paracentesis or thoracentesis for fluid collection. 8\. An adequate fresh sample can be provided and submitted for ChemoID testing. 9\. Participant has disease of one of the following histologic epithelial cell types: high-grade serous adenocarcinoma, endometrioid adenocarcinoma, undifferentiated carcinoma, transitional cell carcinoma, clear cell carcinoma, or adenocarcinoma, not otherwise specified (N.O.S.). Cytologic confirmation of diagnosis is acceptable for participants treated with neoadjuvant therapy who have not had a surgical procedure for a histologic confirmation. Patients with low-grade serous or mucinous adenocarcinoma are not eligible, nor are patients with pure ovarian sarcomas. 10\. Participant has received ≤ 5 prior regimens including at least one platinum-based regimen for their ovarian, peritoneal, or fallopian tube carcinoma. 11\. Participant must have an estimated life expectancy of greater than six months, as determined by the investigator. 12\. Participant requires chemotherapy and the investigator plans to administer one of the regimens of interest as deemed by her physician. 13\. Participant must have an ECOG Performance Status Score of ≤ 2, KPS≥70, or 0-2 GOG status. 14\. Adequate laboratory values within 60 days of enrollment to study defined as follows: 1. ANC ≥ 1500/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. Exclusion Criteria: 1. Use of Avastin planned to treat participant. 2. Participant has ovarian stromal, germ cell tumors or pure sarcomas. 3. Participant has borderline carcinoma (uncertain malignant potential), mutinous or low-grade serous carcinoma. 4. Participant is pregnant or lactating. 5. Participants of childbearing potential not employing adequate contraception. 6. Participants who are at risk of failure of compliance to the visit schedules and procedures including those with psychiatric disease that would substantially impact compliance or consent. 7. Estimated life expectancy of \<6 months, as estimated by the investigator in consultation with participating oncologists. 8. Participants with symptomatic cardiac conditions (i.e. NYHA class III/IV or uncompensated angina). 9. Enrollment in another clinical study that precludes allowing the oncologist to select chemotherapy regimens. 10. Previously participated in this study. 11. 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). 12. CA-125 only disease without RECIST 1.1 measurable or otherwise evaluable disease. 13. Patients with third space fluid (for example pleural effusions) as only site of disease. 14. Participant 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.