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Stopping rules for a placebo controlled clinical trial of anticoagulants after acute myocardial infarction were evaluated by means of computer simulation for the case of five interim analyses. The trial will be terminated and the null hypothesis of no treatment effect rejected when the one-sided P-value (logrank test) is lower than 0.005, 0.005, 0.005, 0.014, and 0.023 at the respective interim analyses, and 0.032 at final evaluation. This implies a total size alpha = 0.05 and a power close to that of fixed sample size testing. The trial will also be terminated, without rejecting the null hypothesis, when the one-sided P-value exceeds 0.95, 0.88, 0.81, 0.74, and 0.67 at the respective interim analyses. This modification hardly affects size and power.