Equivalence Margin

As seen in Figure 12.1, this confidence interval is completely contained between the equivalence margins —151/min to 151/min and all of the values for the treatment difference supported by the confidence interval are compatible with the definition of clinical equivalence we have established equivalence as defined. 

In contrast, suppose that the 95 per cent confidence interval had turned out to be (—171/min, 121/min). This interval is not entirely within the equivalence margins and the data are supporting potential treatment differences below the lower equivalence margin. In this case we have not established equivalence. 

Statistical analysis is generally based on the use of confidence intervals. For equivalence trials, two-sided confidence intervals should be used. Equivalence is inferred when the entire confidence interval falb within the equivalence margins. ... 

Although conventional p-values have no role to play in equivalence or noninferiority trials there is a p-value counterpart to the confidence intervals approach. The confidence interval methodology was developed by Westlake (1981) in the context of bioequivalence and Schuirmann (1987) developed a p-value approach that was mathematically connected to these confidence intervals, although much more difficult to understand It nonetheless provides a useful way of thinking, particularly when we come later to consider type I and type II errors in this context and also the sample size calculation. We will start by looking at equivalence and use A to denote the equivalence margins. 

Operationally, this is equivalent to the method of using two simultaneous one-sided tests to test the (composite) null hypothesis that the treatment difference is outside the equivalence margins versus the (composite) alternative hypothesis that the treatment difference is within the margins. ... 

The equivalence margins for bioequivalence specified by both the FDA (2001) Statistical Approaches to Establishing Bioequivalence and the CPMP (2001) Note for Guidance on the Investigation of Bioavailability and Bioequivalence require that the ratio of the geometric means, for the two treatments lie between... 

Having seen why the hypothesis testing used in superiority trials is inappropriate for equivalence trials, the appropriate approach in this context is now discussed. The first step in this approach is to establish the equivalence margin for the trial. 

In this case, the research hypothesis states that the two drugs are equivalent, and the null hypothesis states that they are not equivalent. The locations of the lower and the upper limit of the 95% Cl determine whether or not the null hypothesis is rejected. If both the lower limit and the upper limit lie within the equivalence margin, we reject the null hypothesis and the new drug and the reference drug are declared to be equivalent. If either the lower limit or the upper limit lies outside the equivalence margin or if both limits lie outside, we fail to reject the null hypotheses, and the drugs are not declared to be equivalent. 

Fortical s PD equivalence was shown in a double-blind, active-controlled, 24-week study in 134 postmenopausal women randomized to Fortical (200IU per day) or Miacalcin (200IU per day). The primary outcome measure was change in serum beta-CTx from baseline. The results fell within prespecified PD equivalence limits (-0.08 to 0.06ng/mL equivalence margin of 0.2ng.mL) and indicated Fortical was not inferior to Miacalcin. 

The equivalence margin would be selected such that the two treatments were considered equivalent. If two antihypertensive therapies were compared in this manner, an equivalence margin might be 5 mmHg (a trivial difference). The inferential statistical analysis for equivalence trials typically involves the calculation of a (1 -a)% confidence interval for the difference in population means. If the lower and upper bounds of the confidence interval are both within the equivalence margin, the conclusion is that we are (1 -a)% confident that the true difference in population means does not exceed equivalence e conclusions that Can be drawn from an equivalence trial are displayed in Figure 12.3. 

All the aspects of discrete distributions have continuous equivalents. Marginal distributions by analogy... 

Conversely, given the wetting-liquid saturation, or equivalently P of the permeable medium, the locus of marginally stable states... 

Reference pricing was not introduced in Spain until December 2000. The fact that it is applied exclusively to bio-equivalent products leads, in the opinion of the authors, to the assumption that its effect on expenditure is limited, as a major market share is acquired by recently introduced drugs. The level at which the reference price is fixed is an important factor. For non-patented products, price competition should push the price towards the marginal cost, and therefore a reference price that is clearly higher than the cheapest generic could actually become a barrier to price competition in this case. 

Profit II is then the equivalent of the contribution margin II used to evaluate long-term profitability... 

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