Aspirin is a very old drug, and in recent years physicians have moved toward drug combinations, such as aspirin and another antiplatelet agent, clopidogrel.  Two trials have looked at this combination in patients with AFib: the ACTIVE W trial, which included patients who were randomized to either aspirin plus clopidogrel or warfarin,[72] and the ACTIVE A trial, in a group of patients deemed to be at too high a risk to receive anticoagulant therapy using warfarin, and who were therefore randomized in aspirin with clopidogrel versus aspirin alone.[73]

On the right-hand side of the Figure we see that for vascular events and stroke, the combination of clopidogrel and aspirin was indeed superior to that of aspirin alone, but at the expense of a higher risk of bleeding.  On the left-hand side, however, there is a clear benefit in efficacy with warfarin versus the combination of aspirin and clopidogrel, and more importantly there was no significant difference in major bleeding within these two groups.  

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

[ACTIVE = Atrial fibrillation Clopidogrel Trial with Irbesartan for prevention of Vascular Events A (aspirin) / W (warfarin)]