6.11 Special Tests in Clinical Research 85In equivalence testing, we want to accept the null hypothesis. To
do this in the Neyman – Pearson framework so that the type II error is
controlled, we simply switch the roll of the null and alternative hypoth-
eses. Often, in equivalence testing, it is feasible to do cross - over
designs, which remove subject - to - subject variability by allowing each
subject to act as their own control.
Example: You want to show that a generic drug or a new formula-
tion of an approved drug is basically the same as the approved drug
with respect to PK and PD characteristics. At Auxilium Pharmaceuticals
Inc., we had a testosterone gel that was approved and trademarked as
Testim ®. We wanted to see if we could show that a new formulation
with a better odor was equivalent in terms of the PK parameters, area
under the curve (AUC), time of maximum concentration (Tmax), and
value of maximum concentration (Cmax). For each of the parameters,
there is a test of bioequivalence that can be performed. We designed a
cross - over trial to perform these tests.
Steps in Equivalence Testing
- Pose a clinically important difference δ.
2. State a pair of null hypotheses: H 0L : d < − δ and H OH : d > δ ,
where d is the observed mean difference. The alternative hypoth-
esis is then H 1 : − δ ≤ d ≤ δ.
3. Choose a signifi cance level α.
4. Find the appropriate critical value (usually from the standard
normal or the t - distribution).
5. Calculate the appropriate test statistics for the two tests of null
hypotheses.
6. Compare these test statistics to their critical values, and if both
null hypotheses are rejected, you have rejected nonequivalence
or accepted equivalence at the level α.
In the case where the data are normally distributed, we can use
Schuirmann ’ s two one - sided t - tests. The same idea can be used with
other tests when the data are not normally distributed. We next describe
Schuirmann ’ s test.
When each test of the null hypotheses is a one - sided Student ’ s t -
test, it is called Schuirmann ’ s two one - sided t - tests (TOST). A simple