Standard statistical analyses of randomized clinical trials fail to provide a direct assessment of which treatment is superior or the probability of a clinically meaningful difference. A Bayesian analysis permits the calculation of the probability that a treatment is superior based on the observed data and prior beliefs. The subjectivity of prior beliefs in the Bayesian approach is not a liability, but rather explicitly allows different opinions to be formally expressed and evaluated. The usefulness of this approach is demonstrated using the results of the recent GUSTO study of various thrombolytic strategies in acute myocardial infarction. This analysis suggests that the clinical superiority of tissue-type plasminogen activator over streptokinase remains uncertain.