Comparing the Safety and Efficacy of Apixaban and Rivaroxaban

* The trial will compare two anticoagulants ("blood thinners") that are currently used in the VA and are considered standard care to prevent strokes in patients with atrial fibrillation. The two most commonly-used anticoagulants will be compared: apixaban (Eliquis) and rivaroxaban (Xarelto). They are considered by many doctors to have similar benefits and risks, but no one knows for sure. * The trial only enrolls patients with a diagnosis of atrial fibrillation ("A Fib") or atrial flutter. Most participants will be age 65 or older, and should already be taking apixaban or rivaroxaban. * The investigators will measure, in about 10,000 VA patients nationally, whether the rates of stroke, major bleeding, or death differ between these two drugs. * The trial will last about 7 years, but after the first prescription, all information will be collected from electronic medical records.