Blood thinners, such as warfarin, prevent blood clots from forming, thereby reducing the risk of a stroke or heart attack. When people undergo surgery or certain procedures, they must stop using warfarin to prevent too much bleeding during and after the surgery or procedure. Some doctors prescribe a different blood thinner, one that works more quickly and wears off more quickly, to bridge the gap between starting and stopping warfarin. However, this short-term treatment is expensive, may increase the risk of bleeding, and has not been proven effective. This study will determine whether a bridging blood thinner called dalteparin is helpful or harmful for people with atrial fibrillation who stop taking warfarin in preparation for surgery or a procedure.