Introduction of likelihood methods for defining the non-inferiority margin and measuring the strength of evidence in non-inferiority trials. Likelihood methods are used to (1) evaluate and combine the evidence from historical trials and (2) assess and report the smallest non-inferiority margin supported by the data. This framework offers important theoretical and practical advantages such as eliminating the influence of sample spaces, and/or prior probabilities, while maintaining good frequentist properties. The methods are illustrated using data from six aspirin-controlled trials for acute coronary syndrome and the active-controlled trial 'Organization to Assess Strategies for Ischemic Syndromes' (OASIS-2). We also explore the evidence for potential violations of the constancy assumption in this framework.