A Phase 2 Study of Ramucirumab (LY3009806) in Participants With Gastric or Gastroesophageal Junction (GEJ) Cancer

Inclusion Criteria: * The participant has a histopathologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction (GEJ). * The participant has documented disease progression during or within 4 months after the last dose of first-line chemotherapy for metastatic disease, or during or within 6 months after the last dose of neoadjuvant or adjuvant therapy. * The participant received combination chemotherapy prior to disease progression. * Prior chemotherapy regimens must include a platinum and/or a fluoropyrimidine component and must not include a taxane or antiangiogenic agent. * The participant has metastatic disease or locally advanced disease that is measurable or nonmeasurable, but is evaluable disease by radiological imaging per Response Evaluation Criteria in Solid Tumors, Version 1.1 (RECIST 1.1). * Patients are eligible if they are considered not appropriate, for whatever reason, for treatment with ramucirumab in combination with paclitaxel. * The participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * The participant has adequate organ function, including: * Total bilirubin 1.5 × the upper limit of institutional normal (ULN) and alanine aminotransferase (ALT) and aspartate aminotransferase (AST) 3 × ULN. If the liver has tumor involvement, AST and ALT \<5 × ULN are acceptable. * Serum creatinine 1.5 × ULN or calculated creatinine clearance (per the Cockcroft-Gault formula or equivalent and/or 24-hour urine collection) 60 milliliters/minute (mL/min). * Urinary protein is \<2+ on dipstick or routine urinalysis. * Absolute neutrophil count 1.5 × 10\^9/Liter (L), platelets 100 × 10\^9/L, and hemoglobin 9 g/deciliter (dL) (5.58 millimoles/Liter). * International normalized ratio 1.5 × ULN or prothrombin time 5 seconds above ULN. * Partial thromboplastin time 5 seconds above ULN. * The participant has an estimated life expectancy of 12 weeks in the judgment of the investigator. * The participant, if female and of child-bearing potential, must have a negative serum or urine pregnancy test within 7 days prior to randomization. Exclusion Criteria: * The participant has squamous cell or undifferentiated gastric cancer. * The participant is receiving chronic therapy with any of the following within 7 days prior to randomization: * Nonsteroidal anti-inflammatory agents (NSAIDs; such as indomethacin, ibuprofen, naproxen, or similar agents), or * Other anti-platelet agents (such as clopidogrel, ticlopidine, dipyridamole, or anagrelide). Aspirin use at doses up to 325 milligrams (mg)/day is permitted. * The participant received radiotherapy within 14 days prior to randomization. * The participant received \>1 line of prior therapy for the treatment of locally advanced and unresectable or metastatic gastric or GEJ (Siewert Types I-III) adenocarcinoma. * The participant received previous treatment with agents targeting the vascular endothelial growth factor (VEGF)/VEGF receptor 2 signaling pathway. * The participant has documented brain metastases, leptomeningeal disease, or uncontrolled spinal cord compression. * The participant experienced any arterial thromboembolic event, including myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack, within 6 months prior to randomization. * The participant has symptomatic congestive heart failure (New York Heart Association II-IV) or symptomatic or poorly controlled cardiac arrhythmia. * The participant has uncontrolled hypertension, as defined in Common Terminology Criteria for Adverse Events (CTCAE) Version 4.0, prior to initiating study treatment, despite antihypertensive intervention. * The participant underwent major surgery within 28 days prior to randomization or central venous access device placement within 7 days prior to randomization. * The participant has a history of gastrointestinal perforation or fistula within 6 months prior to randomization. * The participant has any condition (for example, psychological, geographical, or medical) that does not permit compliance with the study and follow-up procedures or suggests that the participant is, in the investigator's opinion, not an appropriate candidate for the study.