Justifying the sample size in an equivalence study (created 2010-11-02).

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One of the projects I have been asked to work on is a study trying to establish equivalence between two treatments. How do you justify the sample size in a study of equivalence?

In order to show equivalence, you need to demonstrate that the 95% confidence interval lies entirely inside the range of clinical indifference. If the width of the confidence interval is 90 and the width of the range of clinical indifference is 60, then the sample size is clearly inadequate. It will never fit inside the range of clinical indifference no matter where the difference in means lies.

So first thing is to insure that the expected width of the confidence interval is sufficiently narrow. Making it exactly the width of the range of clinical indifference is also problematic because you will never in a million years be so lucky that the difference in sample means will lie exactly at zero.

You have to specify a bit of wiggle room within the range of clinical indifference. So it takes a bit more thinking to get the sample size for equivalence. For both traditional testing and equivalence testing, you need a measure of the variability of your outcome. For both you have to think about the range of clinical indifference (or the flip side of the coin, the minimum clinically important difference). But in equivalence you need to think about where within the range of clinical indifference, you think the mean difference is likely to fall.