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.

Inclusion Criteria: In order to be eligible to participate in this study, an individual must meet all of the following criteria: 1. Male or female Veteran, aged 22 years or older 2. Diagnosis of atrial fibrillation (AF) or atrial flutter (AFL) and currently taking either apixaban or rivaroxaban. 3. CHA2DS2-Vasc of 3 or more 4. Ability to take oral medication and self-reported willingness to adhere to the prespecified apixaban or rivaroxaban regimen Exclusion Criteria: An individual who meets any of the following criteria will be excluded from participation in this study; notably use of antiplatelet agents or prior OAC use will not be an exclusion criterion: 1. Current use of oral or injectable anticoagulation, without ability to switch to the assigned study medication 2. Another indication for anticoagulation, such as pulmonary embolism 3. Contraindication to oral anticoagulation 4. Known bleeding diathesis 5. Documented current pregnancy or lactation in the EHR or self-reported current pregnancy or lactation 6. Known allergic reactions or intolerance to apixaban or rivaroxaban 7. Most recent estimated glomerular filtration rate (eGFR) is \< 30 mL/minute/1.73m2. An eGFR result must have been obtained within 18 months before randomization. 8. Known mechanical heart valve 9. Known moderate-severe mitral stenosis 10. Known history of left atrial occlusion, excision, or ligation 11. Current or planned use of systemic ritonavir, itraconazole, or ketoconazole (topical use of ketoconazole only is allowed) 12. Cardiac or thoracic surgery in the past 3 months