A Study of Trabectedin or Dacarbazine for the Treatment of Patients With Advanced Liposarcoma or Leiomyosarcoma

Inclusion Criteria:

   - Histologically proven, unresectable, locally advanced or metastatic liposarcoma
   (dedifferentiated, myxoid round cell, or pleomorphic) or leiomyosarcoma. Participants
   must have a pathology report indicating the diagnosis of liposarcoma or leiomyosarcoma
   that has been reviewed by the sponsor before randomization may occur

   - Treated in any order with at least: an anthracycline and ifosfamide containing
   regimen, or an anthracycline containing regimen and 1 additional cytotoxic
   chemotherapy regimen

   - Measurable disease at baseline in accordance with RECIST Version 1.1

   - Pathology specimens (example [e.g.], tumor blocks or unstained slides) for potential
   centralized pathology review and biomarker studies

   - ECOG Performance Status score of 0 or 1

   - Adequate recovery from prior therapy, all side effects (except alopecia) have resolved
   to Grade 1 or less according to the National Cancer Institute - Common Terminology
   Criteria of Adverse Events (NCI-CTCAE) Version 4.0

   - Adequate organ function as evidenced by the following peripheral blood counts or serum
   chemistry values: hemoglobin 9 gram per deciliters (g/dL), absolute neutrophil count
   (ANC) 1,500/L, platelet count 100,000/L, serum creatinine 1.5*the upper limit of
   normal (ULN), creatine phosphokinase (CPK) 2.5 Upper Limit of Normal [ULN]

   - Adequate hepatic function as evidenced by the following serum chemistry values: total
   bilirubin, ULN. If total bilirubin is greater than (>) ULN, measure indirect bilirubin
   to evaluate for Gilbert's syndrome (if direct bilirubin is within normal range,
   participant may be eligible) ALP 2.5 x ULN; Trabectedin: if the ALP is >2.5 x ULN,
   then an ALP liver fraction or 5-nucleotidase must be obtained and ULN, AST and ALT 2.5
   ULN

   - Negative pregnancy test (urinary or serum beta-HCG) at screening (applicable to women
   of child bearing potential who are sexually active)

   - Female participants must be postmenopausal (no spontaneous menses for at least 2
   years), surgically sterile (have had a hysterectomy or bilateral oophorectomy, tubal
   ligation, or otherwise be incapable of pregnancy), abstinent (at the discretion of the
   investigator), or if sexually active, be practicing an effective method of birth
   control. Male participants must agree to use an adequate contraception method as
   deemed appropriate by the investigator (e.g., vasectomy, double-barrier, partner using
   effective contraception) and to not donate sperm for a minimum of 5 months after
   treatment discontinuation

Optional Extension Phase (OEP) Phase:

   - Documentation for inclusion criteria histologically proven, unresectable, locally
   advanced or metastatic liposarcoma (dedifferentiated, myxoid round cell, or
   pleomorphic) or leiomyosarcoma. Participants must have a pathology report indicating
   the diagnosis of liposarcoma or leiomyosarcoma that has been reviewed by the sponsor
   before randomization may occur and treated in any order with at least: an
   anthracycline and ifosfamide containing regimen, or an anthracycline containing
   regimen and 1 additional cytotoxic chemotherapy regimen do not need to be reviewed by
   the Sponsor

   - Collection of the specimen: Pathology specimens (example (e.g.), tumor blocks or
   unstained slides) for potential centralized pathology review and biomarker studies is
   not applicable

   - Documentation of inclusion criteria adequate organ function as evidenced by the
   following peripheral blood counts or serum chemistry values: hemoglobin 9 gram per
   deciliters (g/dL), absolute neutrophil count (ANC) 1,500/L, platelet count 100,000/L,
   serum creatinine 1.5*the upper limit of normal (ULN), creatine phosphokinase (CPK)
   2.5*ULN and adequate hepatic function as evidenced by the following serum chemistry
   values: total bilirubin, ULN. If total bilirubin is greater than (>) ULN, measure
   indirect bilirubin to evaluate for Gilbert's syndrome (if direct bilirubin is within
   normal range, participant may be eligible) ALP <= 2.5*ULN; Trabectedin: if the ALP is
   >2.5*ULN, then an ALP liver fraction or 5-nucleotidase must be obtained and ULN, AST
   and ALT 2.5 ULN will be reviewed by the Sponsor before enrollment in the OEP may occur

Exclusion Criteria:

   - Potential participants who meet any of the following criteria will be excluded from
   participating in the study: Prior exposure to trabectedin or dacarabazine, less than 3
   weeks from last dose of systemic cytotoxic therapy, radiation therapy, or therapy with
   any investigational agent, other malignancy within past 3 years. Exceptions: basal or
   nonmetastatic squamous cell carcinoma of the skin, cervical carcinoma in situ, or
   Federation Internationale de Gynecologie et d'Obstetrique (FIGO) Stage 1 carcinoma of
   the cervix

   - Known central nervous system metastasis

   - Known significant chronic liver disease, such as cirrhosis or active hepatitis
   (potential participants who test positive for hepatitis B surface antigen or hepatitis
   C antibodies are allowed provided they do not have active disease requiring antiviral
   therapy)

   - Myocardial infarct within 6 months before enrollment, New York Heart Association Class
   II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular
   arrhythmias, clinically significant pericardial disease, or electrocardiographic
   evidence of acute ischemic or active conduction system abnormalities

   - Uncontrolled intercurrent illness including, but not limited to, poorly controlled
   hypertension or diabetes, ongoing active infection, or psychiatric illness/social
   situation that may potentially impair the participant's compliance with study
   procedures

   - Unwilling or unable to have a central venous catheter

   - Known allergies, hypersensitivity, or intolerance to trabectedin, dacarbazine,
   dexamethasone, or their excipients

   - Pregnant or breast-feeding

   - Any condition that, in the opinion of the investigator, would compromise the
   well-being of the participant or the study or prevent the participant from meeting or
   performing study requirements

OEP phase:

   - Potential participants who meet any of the following criteria will be excluded from
   Participating in the study: Prior exposure to trabectedin, less than 3 weeks from last
   dose of systemic cytotoxic therapy, radiation therapy, or therapy with any
   investigational agent, other malignancy within past 3 years. Exceptions: basal or
   nonmetastatic squamous cell carcinoma of the skin, cervical carcinoma in situ, or
   Federation Internationale de Gynecologie et d'Obstetrique (FIGO) Stage 1 carcinoma of
   the cervix does not apply

   - Treated in any order with at least: an anthracycline and ifosfamide containing
   regimen, or an anthracycline containing regimen and 1 additional cytotoxic
   chemotherapy regimen with less than 3 weeks from last dose of systemic anticancer
   therapy, radiation therapy, or therapy with any investigational agent

   - Known allergies, hypersensitivity, or intolerance to dacarbazine does not apply