Inclusion Criteria:
1. Patient must have a histologically confirmed diagnosis of uterine leiomyosarcoma obtained less than 8 weeks from the surgery
2. Eastern cooperative oncology group (ECOG) performance status (PS) 0 or 1
3. Patient was previously untreated with chemotherapy for a sarcoma, and did not receive anthracyclines and/or trabectedin for another cancer
4. Available Formalin Fixed Paraffin Embedded (FFPE) tumor blocks in sufficient quantity and quality to allow CINSARC NanoCind® qualification (low-risk or high-risk)
5. Age ≥ 18 years and ≤ 75 years
6. FIGO 2018 classification stage I (IA and IB), with complete resection (total hysterectomy and optional bilateral oophorectomy; possible ovarian preservation is feasible in selected cases)
7. No measurable disease, as assessed by the investigator: normal post-operative thoracic, abdominal and pelvic CT-scan or normal MRI of abdomen and pelvis + normal chest CT performed within 4 weeks prior to inclusion or randomization in the study
8. Signed informed consent form prior to any trial specific procedures consistent with international conference on harmonisation - good clinical practice (ICH-GCP) and local legislation
9. Patient must be affiliated to a social security system or in possession of equivalent private health insurance (according to local regulations for participation in clinical trials).
Additional inclusion criteria for randomization
10. Inclusion criteria checked at study entry are all still met at the time of randomization
11. High-risk CINSARC signature
12. Patient must have a diagnosis of uterine leiomyosarcoma confirmed by a local sarcoma expert pathologist from RRePS (Sarcoma Pathology Reference Network from NETSARC +) locally or by the study central RRePS expert pathologist.
13. Adequate hematologic organ function:
* absolute neutrophil count ≥ 1.5 Giga/ L
* hemoglobin ≥ 9 g/dL
* platelets ≥ 100 Giga/L
14. Adequate renal function: serum creatinine ≤ 1.5 mg/dL (≤ 132.6 µmol/L) or calculated creatinine clearance ≥60 mL/min (by the Cockcroft and Gault formula)
15. Adequate liver function: total bilirubin ≤ upper limit of normal (ULN), transaminases ≤ 2.5 x ULN, alkaline phosphatases ≤ 1.5 x ULN
16. Adequate cardiac function: cardiac ultrasound and/or isotopic ventriculography, shortening fraction (SF) \> 30%, Left Ventricular Ejection Fraction (LVEF) (per ultrasound or scintigraphy) \> 50%
17. Creatine phosphokinase (CPK) ≤ 2,5 x ULN
18. Albumin ≥ 25 g/L
19. Signed informed consent form for the randomized phase, consistent with ICH-GCP and local legislation.
Exclusion Criteria:
* Exclusion criteria:
1. All other histology types of uterine sarcoma (adenosarcoma, endometrial sarcoma, undifferentiated uterine sarcoma)
2. Prior or concurrent malignant disease diagnosed or treated in the last 5 years except for adequately treated in situ carcinoma of the cervix, basal or squamous skin cell carcinoma, or in situ transitional bladder cell carcinoma
3. Planned pelvic post-operative radiation therapy
4. Metastatic or measurable disease on CT-Scan
5. Known hypersensitivity to doxorubicin or trabectedin or to any of the excipients
6. Any contra-indication for the use of doxorubicin and/or trabectedin treatment
7. Participation in another therapeutic trial within the 30 days prior to inclusion in the study
8. Active viral hepatitis B or C or known human immunodeficiency virus (HIV) infection.
9. Prior anticancer therapy, including radiotherapy, endocrine therapy, immunotherapy, chemotherapy (CT) or other investigational agents within the last 4 weeks (6 weeks for nitrosoureas and mitomycin C)
10. Cardiovascular dysfunction:
* Congestive heart failure (New York Heart Association \[NYHA\]) ≥ 2)
* Myocardial infarction \<6 months before study
* Poorly controlled cardiac arrhythmias
* Uncontrolled hypertension
* Unstable (angina symptoms at rest) or new-onset angina (begun within the last 3 months) 11. Ongoing infection \> Grade 2 according to NCI-CTCAE v5.0 12. Breastfeeding woman 13. Patients unwilling or unable to comply with the medical procedures and follow-up required by the trial because of geographic, familial, social, or psychological reasons 14. Persons deprived of their liberty or under protective custody or guardianship.
Additional exclusion criteria for randomization 15. At least one of the exclusion criteria check at study entry is met at the time of randomization 16. Unknown risk for CINSARC signature 17. For patients who require a pathological review by the study central pathologist, failure to obtain a confirmed diagnosis at randomization 18. More than 13 weeks have elapsed since the surgery procedure. 19. Patient receiving phenytoin within 88 hours prior to randomisation and or live attenuated vaccines within 14 days prior to randomisation and or CYP3A4 inhibitors (e.g. oral ketoconazole, fluconazole, ritonavir, clarithromycin or aprepitant) and or strong CYP3A4 inducers (e.g. rifampicin, phenobarbital, St John's wort).
Criteria for continuing in the prospective cohort :
1. Patient must have a diagnosis of uterine leiomyosarcoma confirmed by a sarcoma expert pathologist or by the study central pathologist
2. Patients with a low-risk CINSARC signature
