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) 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)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.

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An overview was conducted of all randomized, controlled studies comparing NaF to SMFP dentifrices in the prevention of caries development. Data from these separate trials were subjected to a pooling procedure, or meta-analysis, in order to obtain a more stable estimate of comparative treatment efficacy and to aid in interpreting the generalizability of results. Based on a pool of studies involving over 7,000 subjects, NaF was associated with a significantly greater reduction in caries development compared to SMFP. The increment in D(M)FS was reduced an average of 0.28 (95% confidence limits 0.10 to 0.46) with the use of NaF as compared to SMFP over a 2- to 3-year follow-up period. This difference represents a 6.4% reduction in the rate of caries development observed with SMFP. The numerical advantage conferred by NaF over SMFP in caries risk reduction must be judged clinically as to its public health implications. Alternative analytic techniques and rules for including studies in the pooling process yielded consistent conclusions. A similar analysis of data from dual-active studies indicated that NaF in combination with SMFP provides greater lowering of the D(M)FS increment (approx. 0.16 over 2-3 years) compared to SMFP at the same total fluoride dose, whereas the dual-active product demonstrated no advantage over NaF alone.

SUMMARYThe 'at least as good as' criterion, introduced by Laster and Johnson for a continuous response variate, is developed here for applications with dichotomous data. This approach is adaptive in nature, as the margin of non-inferiority is not taken as a ÿxed di erence; it varies as a function of the positive control response. When the non-inferiority margin is referenced as a high fraction of the positive control response, the procedure is seen to be uniformly more e cient than the ÿxed margin approach, yielding smaller sample sizes when sizing non-inferiority trials under identically speciÿed conditions. Extending this method to proportions is straightforward, but highlights special considerations in the design of non-inferiority trials versus superiority trials, including potential trade-o s in statistical e ciency and interpretability.