This randomized, open-label, parallel-group, multicenter study will evaluate the rate of cardiovascular events with tocilizumab in comparison to etanercept in participants with rheumatoid arthritis (RA). Participants will be randomized to receive intravenous (IV) 8 milligrams per kilogram (mg/kg) tocilizumab every 4 weeks or subcutaneous 50 milligrams (mg) etanercept weekly, with or without non-biologic disease-modifying anti-rheumatic drug (DMARD).