What about the risk of bleeding on anticoagulant therapy?  There are many factors affecting anticoagulation-related bleeding complications: advanced age, uncontrolled hypertension, history of myocardial infarction or ischemic heart disease, cerebral vascular disease, anemia or history of bleeding, and of course the concomitant use of other drugs such as antiplatelet agents.  The notable feature of these elements, however, is that almost all of these factors are also risk factors for increased risk of stroke; the patients at the highest risk of stroke are also at highest risk of bleeding, and yet the benefit of prevention of stroke with anticoagulation therapy almost always outweighs the risk of a bleed. 

Rothman SA. Am J Med 2013; 126: 00-00.