A Study of Ramucirumab in Participants With Gastric, Esophageal, and Gastroesophageal Cancer

Inclusion Criteria: * Histologic or cytologic confirmation of adenocarcinoma of the esophagus, gastroesophageal junction (GEJ), or stomach * Metastatic or locally advanced, unresectable disease at time of study entry * Provided signed informed consent and is amenable to compliance with protocol schedules and testing * Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0-1 at study entry * Adequate renal, hematological, and hepatic function * Measurable or non-measurable disease at the time of study entry * Resolution to Grade less than or equal to 1 by the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE), Version 4.0, of all clinically significant toxic effects of prior locoregional therapy, surgery, or other anticancer therapy, except where otherwise mentioned in the eligibility criteria * Eligible participants of reproductive potential (both sexes) must agree to use adequate contraceptive methods (hormonal or barrier methods) during the study period and at least 12 weeks after the last dose of study therapy * Life expectancy of greater than or equal to 3 months * Willingness to provide blood and tissue samples for research purposes. Submission of tumor specimen is mandatory for participation in this study, if a histologic, paraffin-embedded specimen exists (either from a surgical resection or biopsy); submission of paraffin block or a minimum of 8 unstained slides is required if sufficient sample. NOTE: If insufficient additional tissue exists (that is, all tissue has been utilized for prior diagnostic purposes), participation in the study is allowable without the requirement for an additional biopsy; this situation must be discussed with the study principal investigator and/or the ImClone medical monitor or designee. Exclusion Criteria: * The participant has received prior first-line systemic therapy for advanced/unresectable and/or metastatic disease (prior adjuvant or neo-adjuvant therapy is permitted) * Previous or concurrent malignancy except for basal or squamous cell skin cancer and/or in situ carcinoma of the cervix, or other solid tumors treated curatively and without evidence of recurrence for at least 3 years prior to study entry * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the investigator would make the participant ineligible for entry into this study * The participant is receiving chronic therapy with nonsteroidal anti-inflammatory agents (NSAIDs; for example, indomethacin, ibuprofen, naproxen, or similar agents) or other antiplatelet agents (for example, clopidogrel, ticlopidine, dipyridamole, anagrelide). Aspirin use at doses up to 325 milligrams per day (mg/day) is permitted. * The participant has significant third-space fluid retention (for example, ascites or pleural effusion), and is not amenable for required repeated drainage * The participant is pregnant or breastfeeding * Uncontrolled intercurrent illness including, but not limited to, active or uncontrolled clinically serious infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, uncontrolled thromboembolic, or hemorrhagic disorder, psychiatric illness/social situations, or other co-morbid systemic illnesses, or other severe concurrent disease * Immunocompromised participants including participants known to be human immunodeficiency virus (HIV) positive. * Progressive disease less than or equal to 12 months of completing platinum or 5-FU treatment, including capecitabine, if given previously in the perioperative (adjuvant or neoadjuvant) setting * Current or recent (within 28 days prior to randomization) treatment with an investigational drug that has not received regulatory approval for any indication at the time of study entry, or participation in another interventional clinical trial. Participants participating in surveys or observational studies are eligible to participate in this study. * Are currently enrolled in, or discontinued within the last 28 days from, a clinical trial involving ramucirumab drug product (DP), or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Received prior therapy with an antiangiogenic agent (including but not limited to bevacizumab, sunitinib, or sorafenib) * Major surgical procedure or significant traumatic injury less than 28 days prior to randomization, or anticipation of need for elective or planned major surgical procedure during the course of the study. Subcutaneous venous access device placement within 7 days prior to randomization * Clinically significant peripheral neuropathy at the time of registration * Known central nervous system metastases that are symptomatic or untreated * New York Heart Association (NYHA) classification III-IV congestive heart failure * Greater than normal risk of bleeding or coagulopathy in the absence of therapeutic anticoagulation; Grade 3/4 gastrointestinal bleeding within 3 months prior to registration; active bleeding (that is, within 14 days prior to first dose of study therapy); or pathological condition present that carries a high risk of bleeding (for example, tumor involving major vessels or known varices) * Participant has experienced any arterial thromboembolic events, including but not limited to myocardial infarction, stroke, transient ischemic attack (TIA), cerebrovascular accident, or unstable angina, less than or equal to 6 months prior to registration * Clinically significant vascular disease (for example, aortic aneurysm, aortic dissection) for which more than minimal intervention is being administered or planned * History of hypertensive crisis or hypertensive encephalopathy or current poorly-controlled hypertension despite standard medical management * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess less than 6 months prior to registration * Known hypersensitivity to any of the treatment components of modified FOLFOX6 (mFOLFOX6) (oxaliplatin, 5-FU, and leucovorin) or ramucirumab DP