Frequency of analyses (Randomized trial): Three interim analyses are planned. The first will occur after 200 patients have been enrolled. In this analysis, the statistician will not be aware of treatment allocation; the overall rate of bleeding for the entire population will be computed. Assuming balanced allocation, we anticipate the event rate will be 5.7 percent. If the observed rate of hemorrhage is more than 2.5 percent above or below 5.7 percent, a revised sample size will be calculated. If the revised sample size suggests an unfeasibly large study (defined by the need for more than 500 patients per arm), the statistician will determine whether limiting enrollment to patients with INR values of more than 6.0 will enrich the event rate sufficiently to allow completion of the study with less than 500 patients per arm. In these analyses, blinding to treatment allocation will be maintained and the sample size will be revised assuming a 60 percent reduction in the risk of bleeding in the vitamin K arm.