You ask if it is the best treatment and I focussed on stroke :). Warfarin is best suited, in areas of slowly-running blood, such as in veins and the pooled blood behind artificial and natural valves, and pooled in dysfunctional cardiac atria. So common clinical indications for warfarin use are atrial fibrillation, the presence of artificial heart valves, deep venous thrombosis (clots), and pulmonary embolism (where the embolized clots first form in veins).
Many people don't want an artificial heart valve because there requires periodic testing for the optimum effectiveness. If it is medication for a prior heart attack, or some other heart issues many doctors prescribe aspirin and that is what I take. But that would be your doctor's decision. Take care.
Hopefully you are having blood tests periodically to establish your INR is correct? this is how quickly your blood can clot. The lower the number, the quicker your blood clots. The reason blood tests are important is because of diet. Vitamin K, present in most green foods such as broccoli, spinach, lettuce etc, affect the performance of Warfarin because this medication relies on a fairly constant vitamin K level in the Liver to work properly.
Warfarin is an anti-platelet medciation that helps prevent blood clots or prevent the clot from growing larger and is appropriate and adequate medication for the intended purpose. However, a stroke can occur from hard plaque that breaks away from the vessel lining, etc. (low probability of happening)
Hope this helps and thanks for the question. Take care.