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 norm…