If you choose to join this study, we will schedule you for a "baseline" visit that you can do in-person or over the phone or computer. If we determine that you are eligible to continue in the study, you will get a random assignment (like a coin flip) to 1 of 2 study groups. Depending on your assignment, you will either:

• Take an 81 mg dose of aspirin every day; OR
• Take a 5 or 2.5 mg dose of apixaban twice per day (your dose will depend on your age, weight, and kidney function)

The study is "blind," which means you will not know your group assignment. Everyone in the study will take a combination of real pills and placebo (inactive "sugar pills") every day. The combination will either be legitimate aspirin and placebo or legitimate apixaban and placebo. However, if it ever becomes medically necessary to know your group assignment, the research team can unblind your assignment and let you and your doctor(s) know what you are taking. Participation in the study will last for up to 3 years. You will have check-up visits with the study doctor and study team every 3 months while you are in the study. These visits will take 15-30 minutes. If in-person visits are not possible, you can do the visits over the phone or computer. Activities at these routine follow-up visits will include:

• Assessing for any strokes or adverse events since your last visit
• Assessing how well you are taking your study medications
• Assessing your physical health
• Assessing what other medications you are taking
• Assessing your blood pressure
• Providing you with a re-supply of the study medications

If a follow-up visit is not done in-person for any reason, your new supply may be mailed to your home from the site pharmacy. The study staff will still need to collect all unused study medication, so please save all bottles and unused medication until they can be returned.