A Study of Ramucirumab (LY3009806) in Combination With Paclitaxel in Participants With Gastric Cancer

Inclusion Criteria:

* The participant has a diagnosis of gastric or GEJ adenocarcinoma.
* The participant has disease progression during or within 4 months after last dose of first-line chemotherapy or during or within 6 months after the last dose of neoadjuvant or adjuvant therapy.
* The participant received combination chemotherapy, which must include a platinum and/or a fluoropyrimidine and must not include a taxane or antiangiogenic agent.
* The disease is evaluable by imaging per Response Evaluation Criteria in Solid Tumors 1.1.
* The participant has an Eastern Cooperative Oncology Group performance status of 0 or 1.
* The participant has adequate organ function:

  * Total bilirubin ≤1.5 × the upper limit of normal (ULN) and alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3 × ULN. If the liver has tumor involvement, AST and ALT \<5 × ULN.
  * Serum creatinine ≤1.5 × ULN or calculated creatinine clearance ≥50 milliliters/minute.
  * Urinary protein is \<2+.
  * Absolute neutrophil count ≥1.5 × 10\^9/liter (L), platelets ≥100 × 10\^9/L, and hemoglobin ≥9 grams/deciliter (5.58 millimoles/L).
  * International normalized ratio ≤1.5 × ULN and partial thromboplastin time ≤5 seconds above ULN.
* The participant has an estimated life expectancy of minimum 12 weeks.
* The participant has resolution to Grade 1 or less by Common Terminology Criteria for Adverse Events Version 4.0, of all clinically significant toxic effects of previous therapy.
* The participant, if male, is sterile or agrees to use a reliable method of birth control.
* The participant, if female, is surgically sterile, is postmenopausal, or agrees to use a highly effective method of birth control.
* The participant, if female and of child-bearing potential, must have a negative pregnancy test.

Exclusion Criteria:

* The participant is receiving therapy with any of the following:

  * Nonsteroidal anti-inflammatory agents.
  * Other anti-platelet agents; 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 previous chemotherapy with a cumulative dose of \>900 mg per meter squared (mg/m\^2) of epirubicin or \>400 mg/m\^2 of doxorubicin.
* The participant has documented brain metastases or leptomeningeal disease.
* The participant has a significant bleeding disorder or vasculitis.
* The participant experienced any arterial thromboembolic event within 6 months.
* The participant has symptomatic congestive heart failure or symptomatic cardiac arrhythmia.
* The participant has uncontrolled hypertension, despite antihypertensive intervention.
* The participant underwent major surgery within 28 days.
* The participant has a history of gastrointestinal perforation or fistula within 6 months.
* The participant has a history of inflammatory bowel disease or Crohn's disease requiring medical intervention within 12 months.
* The participant has bowel obstruction or history of chronic diarrhea that is considered clinically significant.
* The participant has either of the following:

  * Child-pugh B or C cirrhosis.
* The participant has a serious illness or medical condition including:

  * Human immunodeficiency virus infection.
* The participant has a concurrent active malignancy other than the following:

  * Nonmelanomatous skin cancer.
  * In situ carcinoma of the cervix or other noninvasive carcinoma or in situ neoplasm.
* The participant has a serious nonhealing: (a) wound, (b) peptic ulcer, or (c) bone fracture.
* The participant experienced any Grade 3 or 4 venous thromboembolic event that is not adequately treated.