Non‐inferiority trials: the ‘at least as good as’ criterion

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Abstract
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, δBW. In this paper, Blackwelder's approach is redefined in terms of the ratio of two means (RTrue=μet/μst) 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’ (RLB×100) per cent ‘as effective as’ the standard therapy, where RLB 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 RLB<RTrue ⩽1), the ratio formatted test of H0:RTrue⩽RLB is shown to be more efficient than Blackwelder's test of H0:μst ‐ μet ⩾ δBW, thereby requiring smaller sample sizes to detect the directionally based non‐null alternatives contained in H1:μet/μst>RLB or, equivalently, μst ‐ μet<δBW. Further, when RTrue= 1.0, tests of Blackwelder's hypotheses, their ratio‐based equivalents and conventional superiority can be evaluated for comparative efficiency. Testing H0:RTrue⩽RLB with single‐sided critical region of size α, versus H1:RTrue>RLB, is shown to be more efficient than excluding RLB from the lower limit of a 100(1–2α) per cent two‐sided symmetric confidence interval centred by R̂. Relevant examples will be presented. Copyright © 2003 John Wiley & Sons, Ltd.

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