Aims Using Scandinavian population-based registries, we assessed risk of stroke/systemic embolism (SE) and bleeding with non-vitamin K antagonist oral anticoagulants compared with warfarin in anticoagulation-naive patients with atrial fibrillation (AF). Methods and results This historical cohort study included 219 545 AF patients [median age 74 years; 43% women; mean CHA(2)DS(2)-VASc (congestive heart failure, hypertension, age >= 75 years, diabetes mellitus, stroke or transient ischaemic attack, vascular disease, age 65-74 years, sex category) score 3.3] initiating apixaban, dabigatran, rivaroxaban, or warfarin in Denmark, Norway, and Sweden (1 January 2013 to 31 December 2016). The primary endpoints were stroke/SE and major bleeding. The median follow-up times were 9.7 (3.9-21.5) months for stroke/SE and 9.6 (3.8-21.3) months for bleeding. Apixaban and warfarin initiators were older and had higher CHA(2)DS(2)-VASc scores compared with dabigatran and rivaroxaban initiators. After 1:1 propensity score matching, three cohorts were created: apixaban-warfarin (n = 111 162), dabigatran-warfarin (n = 56 856), and rivaroxaban-warfarin (n = 61 198). Adjusted hazard ratios (HRs) were estimated using a Cox regression. For stroke/SE, adjusted HRs against warfarin were 0.96 [95% confidence interval (CI): 0.87-1.06] for apixaban, 0.89 (95% CI: 0.80-1.00) for dabigatran, and 1.03 (95% CI: 0.92-1.14) for rivaroxaban. For major bleeding, the HRs against warfarin were 0.73 (95% CI: 0.67-0.78) for apixaban, 0.89 (95% CI: 0.82-0.97) for dabigatran, and 1.15 (95% CI: 1.07-1.25) for rivaroxaban. The results in the dabigatran cohort did not hold in all dose-defined subgroups. Conclusion In this large Scandinavian study among AF patients initiating oral anticoagulation, those initiating dabigatran, apixaban, and rivaroxaban had similar rates of stroke/SE to patients initiating warfarin. Rates of major bleeding were lower with apixaban and dabigatran and higher with rivaroxaban, each compared with warfarin.