Currently, the recommendation for asymptomatic patients who have antiphospholipid antibody (regardless of titer) is that they not be treated. One retrospective study, conducted here at HSS, looked at women who had been identified because of fetal loss and were/were not treated with aspirin; the results suggested that aspirin protects against future clotting events. The primary author, Doruk Erkan, MD, is now engaged in a prospective study through the national registry (APSCORE) to verify the findings.
I don't believe that anyone would treat asymptomatic patients with warfarin or heparin. Michelle Petri, MD, of Johns Hopkins Medical Center, advises hydroxychloroquine.
With regard to the INR, the best information comes from the a double-blind, prospective study by Crowther in The New England Journal of Medicine in 2003, which stated that, for uncomplicated antiphospholipid syndrome patients who have not previously failed anticoagulation, an INR of 2.5 is as effective as are higher INRs. This paper reduces a recommendation previously made by Khamashta in 1995 for an INR of greater than 3,and a subsequent update raising (without justification, in this reviewer's mind) the recommended INR to 3.5. In the Crowther study, the recommendation applied equally to patients with venous and with arterial clots.
Many authorities also prescribe a baby aspirin as well.
 Erkan D, Merrill JT, Yazici Y, Sammaritano L, Buyon JP, Lockshin MD. High thrombosis rate after fetal loss in antiphospholipid syndrome: effective prophylaxis with aspirin. Arthritis Rheum. 2001 Jun;44(6):1466-7.
 Petri M. Treatment of the antiphospholipid antibody syndrome: progress in the last five years? Curr Rheumatol Rep. 2000 Jun;2(3):256-61.
 Khamashta MA, Hughes GR. Antiphospholipid antibodies and antiphospholipid syndrome. Curr Opin Rheumatol. 1995 Sep;7(5):389-94. Review.
 Ruiz-Irastorza G, Khamashta MA, Hunt BJ, Escudero A, Cuadrado MJ, Hughes GR. Bleeding and recurrent thrombosis in definite antiphospholipid syndrome: analysis of a series of 66 patients treated with oral anticoagulation to a target international normalized ratio of 3.5. Arch Intern Med. 2002 May 27;162(10):1164-9.
 Crowther M A, Ginsberg J S, Julian J, Denburg J, Hirsh J, et al. A Comparison of Two Intensities of Warfarin for the Prevention of Recurrent Thrombosis in Patients with the Antiphospholipid Antibody Syndrome. New Engl J Med 2003 Sep 18; 349:1133-1138.