An evidential approach to non-inferiority clinical trials.

We present likelihood methods for defining the non-inferiority margin and measuring the strength of evidence in non-inferiority trials using the 'fixed-margin' framework. Likelihood methods are used to (1) evaluate and combine the evidence from historical trials to define the non-inferiority margin, (2) assess and report the smallest non-inferiority margin supported by the data, and (3) assess potential violations of the constancy assumption. Data from six aspirin-controlled trials for acute coronary syndrome and data from an active-controlled trial for acute coronary syndrome, Organisation to Assess Strategies for Ischemic Syndromes (OASIS-2) trial, are used for illustration. The likelihood framework offers important theoretical and practical advantages when measuring the strength of evidence in non-inferiority trials. Besides eliminating the influence of sample spaces and prior probabilities on the 'strength of evidence in the data', the likelihood approach maintains good frequentist properties. Violations of the constancy assumption can be assessed in the likelihood framework when it is appropriate to assume a unifying regression model for trial data and a constant control effect including a control rate parameter and a placebo rate parameter across historical placebo controlled trials and the non-inferiority trial. In situations where the statistical non-inferiority margin is data driven, lower likelihood support interval limits provide plausibly conservative candidate margins.