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

Subjects will be randomized in a 1:1 ratio to receive one of the following treatments: Arm A: Trabectedin 1.3 mg/m2 d1 q 21 in 3 hours (central line) Arm B: Pegylated Liposomal Doxorubicin 40 mg/mq q 28 or Topotecan 4 mg/ m2 dd 1,8,15 q 28 or Gemcitabine 1000 mg/mq dd 1, 8, 15 q 28 Weekly Paclitaxel 80 mg/ m2 dd 1, 8, 15 q 28 Carboplatin AUC 5-6 q 21 or 28 Randomization will be stratified based on platinum-free interval (PFI) (PFI ≥ 0 and ≤ 6 months vs. PFI \> 6 months), presence / absence of measurable disease/number of previous chemotherapy lines, germline BRCA mutational status vs BRCAness phenotype. Platinum-free interval (PFI) is defined as the time from the last dose of the platinum containing regimen until the first date progression. Subjects will continue to receive chemotherapy treatment until disease progression (clinical progression meant as global deterioration in health status attributable to the disease requiring a change in therapy without objective evidence of progression is considered progression of disease), intolerability, patient refusal, investigator decision or death from any cause. Subjects will be evaluated every 12 weeks ± 1 week by Response Evaluation Criteria in Solid Tumors (RECIST 1.1) for objective radiographic response and radiographic disease progression.