Compared with aspirin alone, warfarin plus aspirin decreased annual rates of heart attacks, ischemic strokes, and heart artery procedures. Warfarin plus aspirin increased annual rates of major bleeding. Patients with several risk factors, such as older age, diabetes, heart failure, and decreased kidney function, had the highest risks for heart attacks and strokes. Older patients who previously had a stroke, gastrointestinal bleeding episode, kidney disease, or atrial fibrillation were at higher risk for bleeding. Numbers of deaths did not differ between treatments. In patients with low or average risk for bleeding, the numbers of heart and stroke events prevented with combination therapy exceeded the numbers of major bleeding episodes that it caused.