Non-inferiority trials: the 'at least as good as' criterion

To demonstrate in a clinical trial that a new or experimental therapy (et) is 'at least as good as' a standard therapy (st), a statistical test or confidence interval procedure must rule out clinical inferiority with a high probability. The term 'at least as good as' implies equivalent but not necessarily superior efficacy. As it is statistically impossible to demonstrate equivalence (that is, prove the null hypothesis of no difference), Blackwelder proposed a one-sided significance test to reject the null hypothesis that standard therapy is better than experimental therapy by a clinically acceptable amount, delta(BW). In this paper, Blackwelder's approach is redefined in terms of the ratio of two means (R(True)= mu(et)/mu(st)) based on a continuous variate with higher values denoting greater improvement. The ratio-based equivalents to Blackwelder's hypotheses will be shown. The ratio parameter has the benefit of being available as a dimensionless percentage, not tied to a specified difference in means. Thus, a study can be sized to assure, with high probability, that the experimental therapy is 'at least' (R(LB)x100) per cent 'as effective as' the standard therapy, where R(LB) is the selected lower bound on the percentage effectiveness. A practical rationale is given for defining non-inferiority as a high fraction or percentage of the standard drug's efficacy, both in terms of statistical efficiency and medical relevance. For most typical 'at least as good as' applications (when R(LB)<R(True) < or =1), the ratio formatted test of H(0):R(True)< or =R(LB) is shown to be more efficient than Blackwelder's test of H(0): mu(st) - mu(et) > or = delta(BW), thereby requiring smaller sample sizes to detect the directionally based non-null alternatives contained in H(1): mu(et)/mu(st)>R(LB) or, equivalently, mu(st) - mu(et)<delta(BW). Further, when R(True)= 1.0, tests of Blackwelder's hypotheses, their ratio-based equivalents and conventional superiority can be evaluated for comparative efficiency. Testing H(0):R(True)< or =R(LB) with single-sided critical region of size alpha, versus H(1):R(True)>R(LB), is shown to be more efficient than excluding R(LB) from the lower limit of a 100(1-2alpha) per cent two-sided symmetric confidence interval centred by R. Relevant examples will be presented.