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Statin dosage in patients with acute myocardial infarction (AMI) and concomitant kidney dysfunction is a clinical dilemma. We studied discontinuation during the first year after an AMI and long-term outcome in patients receiving high versus low–moderate intensity statin treatment, in relation to kidney function. For the intention-to-treat analysis (ITT-A), we included all patients admitted to Swedish coronary care units for a first AMI between 2005 and 2016 that survived in-hospital, had known creatinine, and initiated statin therapy (N = 112,727). High intensity was initiated in 38.7% and low–moderate in 61.3%. In patients with estimated glomerular filtration rate (eGFR) < 60 mL/min/1.73 m², 25% discontinued treatment the first year; however, the discontinuation rate was similar regardless of the statin intensity. After excluding patients who died, changed therapy, or were nonadherent during the first year, 84,705 remained for the on-treatment analysis (OT-A). Patients were followed for 12.6 (median 5.6) years. In patients with eGFR 30–59 mL/min, high-intensity statin was associated with lower risk for the composite death, reinfarction, or stroke both in ITT-A (hazard ratio [HR] 0.93; 95% confidence interval, 0.87–0.99) and OT-A (HR 0.90; 0.83–0.99); the interaction test for OT-A indicated no heterogeneity for the eGFR < 60 mL/min group (P = 0.46). Similar associations were seen for all-cause mortality. We confirm that high-intensity statin treatment is associated with improved long-term outcome after AMI in patients with reduced kidney function. Most patients with reduced kidney function initiated on high-intensity statins are persistent after 1 year and equally persistent as patients initiated on low–moderate intensity.