The hazard ratios account for age, sex, prior myocardial infarction, diabetes, hypertension, hyperlipidemia, prior stroke or transient ischemic attack, smoking status, index event (stroke vs transient ischemic attack), atrial septal aneurysm on transesophageal echocardiography (definition in eAppendix 5 and eTables 3 and 4 in the Supplement), patent foramen ovale shunt size (large vs small, definition in eAppendix 5 and eTables 3 and 4 in the Supplement), and superficial infarction on neuroimaging (present vs absent). Two-year absolute risk reductions calculated as differences in Kaplan-Meier event rates at 2 years. Median time to the primary outcome of recurrent ischemic stroke was 13.7 months (IQR, 4.8-29.7; n = 121). RoPE indicates Risk of Paradoxical Embolism (definition provided in Table 1); PASCAL, PFO-Associated Stroke Causal Likelihood.