People taking the blood-thinning drug warfarin who monitor their own blood and adjust their dosage can reduce the risk of blood clots by half, British researchers report. Warfarin (Coumadin, Jantoven) is taken to prevent potentially deadly clots in patients with conditions such as atrial fibrillation -- an abnormal heart rhythm -- or a mechanical heart valve. But if the blood is thinned too much, serious bleeding can occur. Keeping the drug in check requires monthly monitoring and frequent doctors visits.