Confidence intervals for equivalence

The next step is to undertake the trial and calculate the 95 per cent confidence interval for the difference in the means (mean increase in PEF on new inhaler (pi) - mean increase in PEF on existing inhaler ( 2))- As a first example, suppose that this confidence interval is (-71/min, 121/min). In other words, we can be 95 per cent confident that the true difference, pj — P2, is between 71/min in favour of the existing inhaler and 121/min in favour of the new inhaler. 

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. 

Note that there are no conventional p-values here. Such p-values have no role in the evaluation of equivalence establishing equivalence is based entirely on the use of confidence intervals. 

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

The confidence intervals we have used to date are all two-sided. We will talk later about one-sided confidence intervals. 

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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. ... 

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