The main purpose of this study is to provide dose-guiding information by assessing the safety and tolerability of 4 different dosing regimens of an extended-release (ER) formulation of AZD0837 compared with well-controlled, dose-adjusted Vitamin-K antagonists (VKA) (aiming for an international normalized ratio (INR) 2.0 to 3.0) in patients with non-valvular atrial fibrillation (AF) with one or more additional risk factors for stroke.