Trial on Trabectedin (ET-743) vs Clinician's Choice Chemotherapy in Recurrent Ovarian, Primary Peritoneal or Fallopian Tube Cancers of BRCA Mutated or BRCAness Phenotype Patients

Inclusion Criteria: 1. Female of age 18 years or older 2. Histologically or cytologically documented invasive epithelial ovarian cancer, primary peritoneal carcinoma, or fallopian tube cancer 3. Platinum resistant or sensitive patients with either: 1. BRCA mutated patients 2. BRCAness phenotype patients: patients who have received and responded (subsequent PFI\>6 months) to at least 2 previous platinum based chemotherapy lines 3. Platinum sensitive patients who are not able to receive or not willing to receive other platinum treatments 4. Measurable and evaluable disease per RECIST 1.1(Subjects with isolated rising CA-125 without radiologically visible disease are excluded) 5. ECOG performance status 0 or 1 6. No limits in the number of previous chemotherapy lines, previous treatment with parp inhibitors is allowed 7. Left Ventricular Ejection Fraction (LVEF) ≥ institutional lower limit normal 8. Life expectancy of at least 3 months 9. Adequate organ functions: 1. Hematopoietic: Absolute neutrophil count ≥ 1,500/mm3; Platelet count ≥ 100,000/mm3; Hemoglobin ≥ 9 g/dl 2. Hepatic: AST and ALT ≤ 1.5 times upper limit of normal (ULN)\* ; Alkaline Phosphatase ≤ 2.5 times ULN\* ; Bilirubin ≤ 1.5 times ULN. NOTE: \* ≤ 3 times ULN if liver metastases are present 3. Renal: Creatinine Clearance ≥ 45 ml/min or Serum Creatinine ≤1.5 x ULN 4. Serum Albumin \>2.5 g/dl 10. No other invasive malignancy within the past 3 years except non-melanoma skin cancer or in situ cervical cancer (patients with previous cancers may be enrolled providing that no recurrences have be reported in the last 3 years) 11. Written Informed Consent 12. Adequately recovered from the acute toxicity of any prior treatment 13. For agents in the standard arm, also refer to the local prescribing information with regards to warnings, precautions, and contraindications Exclusion Criteria: 1. Prior exposure to trabectedin 2. Known hypersensitivity to any of the components of the trabectedin i.v. formulation or dexamethasone 3. Subjects with borderline ovarian cancer, ie. Subject with low malignant potential tumors are excluded 4. Less than 2 reported responses to platinum (i.e. subsequent recurrences at least 6 months after the first and the second platinum based treatment), unless BRCA mutation is documented. 5. Less than 4 weeks from last dose of therapy with any investigational agent, or chemotherapy 6. History of another neoplastic disease (except basal cell carcinoma or cervical carcinoma in situ adequately treated) unless in remission for 3 years or longer 7. Known clinically relevant CNS metastases, unless treated and asymptomatic 8. Other serious illnesses, such as: 1. Congestive heart failure or angina pectoris; myocardial infarction within 1 year before enrolment; uncontrolled arterial hypertension or arrhythmias. 2. Psychiatric disorder that prevents compliance with protocol. 3. Active viral hepatitis; or chronic liver disease. 4. Active infection. 5. Any other unstable medical conditions.