Doxorubicin Hydrochloride or Trabectedin in Treating Patients With Previously Untreated Advanced or Metastatic Soft Tissue Sarcoma

DISEASE CHARACTERISTICS: * Histologically confirmed intermediate- or high-grade malignant soft tissue sarcoma * Advanced and/or metastatic disease * Previously untreated disease * The following tumor types are not allowed: * Well-differentiated liposarcoma * Embryonal rhabdomyosarcoma * Chondrosarcoma (excluding extraskeletal myxoid chondrosarcoma) * Osteosarcoma (excluding extraskeletal osteosarcoma) * Ewing tumors/primitive neuroectodermal tumor (PNET) * Gastrointestinal stromal tumors (GIST) * Dermatofibrosarcoma protuberans * Must have confirmed disease progression based on investigator's judgment prior to study enrollment * Measurable disease according to RECIST v 1.1 criteria * Tumor lesions situated in a previously irradiated area, or in an area subjected to other loco-regional therapy, are usually not considered measurable unless there has been demonstrated progression in the lesion * Formalin fixed paraffin embedded tumor blocks or representative hematoxylin/eosin slides (preferably both) available (local histopathological diagnosis will be accepted for trial entry) * No prior anticancer therapy for this disease * No prior anthracycline * Non-anthracycline therapy for nonmetastatic disease is acceptable * No known history of CNS metastases or leptomeningeal tumor spread PATIENT CHARACTERISTICS: * WHO performance status 0-1 * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Hemoglobin ≥ 9 g/dL * Platelet count ≥ 100 x 10\^9/L * Bilirubin normal * ALT/AST ≤ 2.5 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 2.5 times ULN, (if alkaline phosphatase \> 2.5 times ULN, hepatic isoenzymes 5-nucleotidase and/or GGT must be within the normal range) * Albumin \> 30 g/L * Serum creatinine ≤ 1.5 times ULN * Creatinine clearance ≥ 30 mL/min * Creatine phosphokinase (CPK) ≤ 2.5 times ULN * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception (double barrier method for men) 2 weeks prior to, during, and for 3 months (women) or 5 months (men) after completion of study therapy * LVEF normal by MUGA scan or ECHO * 12-lead ECG normal (without clinically significant abnormalities) * None of the following unstable cardiac conditions: * Congestive heart failure * Angina pectoris * Myocardial infarction within the past year * Uncontrolled arterial hypertension, defined as BP ≥ 150/100 mm Hg despite optimal medical therapy * Clinically significant arrhythmias * No active or uncontrolled infections or serious illnesses or medical conditions, including a history of any of the following: * Chronic alcohol abuse * Hepatitis * HIV * Cirrhosis * No history of malignancy within the past 5 years, except soft tissue sarcoma, basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the cervix, resected incidental prostate cancer (staged pT2 with Gleason score ≤ 6 and postoperative PSA \< 0.5 ng/mL) * Patients with any history of malignancies who are disease-free for more than 5 years are eligible * a history of malignancy and disease-free for more than 5 years * No psychological, familial, sociological, or geographical condition potentially hampering compliance with the study protocol and follow-up schedule * No concurrent alcohol consumption PRIOR CONCURRENT THERAPY: * See Disease Characteristics * At least 28 days since prior and no concurrent anticancer therapy including systemic therapy, radiotherapy, or surgery * At least 28 days since prior and no other concurrent investigational agents * No concurrent phenytoin, live attenuated vaccines, or yellow fever vaccine