A p-value approach

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. 

Within the framework of hypothesis testing, the null and alternative hypotheses of interest for equivalence when dealing with means are as follows  

In this case, the alternative hypothesis states that the two treatments are clinically equivalent the null hypothesis is saying that the two treatments are not equivalent. Note that the alternative encapsulates the objective we are trying to disprove the null in order to establish equivalence. 

The hypotheses stated above can be expressed as two separate sets of hypotheses corresponding to the lower and upper ends of the equivalence range  

ICH E9 (1998) Note for Guidance on Statistical Principles for Clinical Trials  

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