At the professional workshop that I attended, we were told by the presenter that the anticoagulation properties of
warfarin are most likely present down to an
INR of about 1.6. The reason doctors don't like their patients to go below 2.0 (or in some cases 2.5) is to provide a cushion of safety. Also, a bleeding incident attributable to warfarin would not be expected to happen at an INR of 4.0. Some people, such as those who have two mechanical heart valves, have a prescribed range of 3.