A Study of Olaratumab (LY3012207), Doxorubicin, and Ifosfamide in Participants With Advanced or Metastatic Soft Tissue Sarcoma

Inclusion Criteria: * Have a histological diagnosis of advanced STS (by local pathology review), for which treatment with doxorubicin, ifosfamide and mesna is deemed appropriate by the investigator. * Have measurable or nonmeasurable but evaluable disease as defined by the Response Evaluation Criteria in Solid Tumors (RECIST 1.1). * Have adequate hematologic, organ and coagulation function within 2 weeks (14 days) prior to enrollment. * Have a performance status of 0 to 1 on the Eastern Cooperative Oncology Group scale. * Have received no prior lines of systemic therapy and are suitable to receive doxorubicin, ifosfamide and mesna. All previous anticancer treatments must have completed ≥3 weeks (21 days) prior to the first dose of study treatment. * Have left ventricular ejection fraction (LVEF) ≥50% assessed within 28 days prior to enrollment. * Have resolution of Adverse Events (AEs), with the exception of alopecia, and of all clinically significant toxic effects of prior locoregional therapy, surgery or radiotherapy to ≤Grade 1, by National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) Version 4.0. * Have sufficient available material from archived formalin-fixed paraffin-embedded tumor tissue for biomarker-related studies. If such tissue is not available, a newly obtained core or excisional biopsy of a tumor lesion must be performed. * If male, must be sterile or agree to use an effective method of contraception or a highly effective method of contraception during the study and for at least 12 weeks following the last dose of study treatment. * If female and of child-bearing potential, must: 1. have a negative serum pregnancy test at the time of enrollment, 2. have a negative urine pregnancy test within 24 hours prior to the first dose of study treatment, and 3. agree to use a highly effective method of contraception during the study and for 3 months following the last dose of study treatment. * Have a life expectancy of at least 3 months, in the opinion of the investigator. Exclusion Criteria: * Are currently enrolled in a clinical trial involving an investigational product or any other type of medical research judged not to be scientifically or medically compatible with this study. * Have participated within the past 30 days in a clinical trial involving an investigational product. If the previous investigational product has a long half-life, 3 months or 5 half-lives (whichever is longer) should have passed. * Have previously completed or withdrawn from any study investigating olaratumab. * Have received prior treatment with olaratumab, doxorubicin, or ifosfamide, or have participated in other trials investigating olaratumab. * Have received prior radiotherapy of the mediastinal/pericardial area or whole pelvis radiation. * Have known urinary outflow obstruction, or inflammation of the urinary bladder (cystitis). * Are diagnosed with gastrointestinal stromal tumor or Kaposi sarcoma. * Have active central nervous system (CNS) or leptomeningeal metastasis (brain metastasis) at the time of enrollment. Participants with a history of CNS metastasis (previously treated with curative intent \[for example, stereotactic radiation or surgery\]) that has not progressed on follow-up imaging, have been asymptomatic for at least 60 days, and are not receiving systemic corticosteroids and/or anticonvulsants are eligible. Participants with signs or symptoms of neurological compromise should have appropriate radiographic imaging performed before enrollment to rule out brain metastasis. * Have a history of another primary malignancy, with the exception of: 1. curatively treated non-melanomatous skin cancer 2. curatively treated cervical carcinoma in situ * Have an active fungal, bacterial and/or known viral infection including human immunodeficiency virus or viral (A, B, or C) hepatitis (screening is not required). * Have Grade 3 or 4 peripheral neuropathy per NCI-CTCAE Version 4.0. * Have a serious cardiac condition. * Have a resting heart rate of \>100 beats per minute (bpm). * Have a Fridericia's QT corrected interval (QTcF) interval of \>450 milliseconds (msec) for males and \>470 msec for females on screening electrocardiogram (ECG) utilizing Fridericia's correction. * Have uncontrolled intercurrent illness including, but not limited to, an ongoing/active infection requiring parenteral antibiotics. * Have a psychiatric illness/social situation that would limit compliance with study requirements. * Have electively planned or will require major surgery during the course of the study. * Are females who are pregnant or breastfeeding.