Background: Patent foramen ovale (PFO) is a contributor to embolic stroke of undetermined source (ESUS). Subgroup analyses from previous studies suggest that anticoagulation could reduce recurrent stroke compared with antiplatelet therapy. We hypothesised that anticoagulant treatment with rivaroxaban, an oral factor Xa inhibitor, would reduce the risk of recurrent ischaemic stroke compared with aspirin among patients with PFO enrolled in the NAVIGATE ESUS trial. Methods: NAVIGATE ESUS was a double-blinded, randomised, phase 3 trial done at 459 centres in 31 countries that assessed the efficacy and safety of rivaroxaban versus aspirin for secondary stroke prevention in patients with ESUS. For this prespecified subgroup analysis, cohorts with...