84 CHAPTER 6 Hypothesis Testing
one - sided hypothesis with power function requirement at a fi xed δ. So
the approach is the same as in the Tendril DX lead example. Noninferiority
and equivalence are different and require more detailed explanations.
Briefl y for noninferiority, the null hypothesis becomes that the
treatment is worse than the control by at least a δ , called the noninfe-
riority margin. The alternative is that treatment may be better, but is at
least within the margin required to say that it is not inferior. Noninferiority
tests are one sided. Equivalence testing means that we want to show
that the treatment and control are essentially the same (i.e., within a
margin of equivalence δ ). So, equivalence tests are two - sided tests that
would simply reverse the null and alternative hypotheses if there were
no margin (i.e., δ = 0). The existence of a positive margin and the
reversal of the null with the alternative make equivalence testing a little
complicated, and it deserves a more detailed discussion also.
6.11.1 Superiority Tests
Not much needs to be said for superiority. It is the standard test that
fi ts in naturally to the Neyman – Pearson approach. The one - sided two -
sample t - test as described in Section 6.2.
6.11.2 Equivalence and Bioequivalence
Bioequivalence and equivalence are the same in terms of the formal
approach to hypothesis testing. The only difference is that bioequiva-
lence means that two drug formulations must be essentially the same
in terms of their pharmacokinetic and pharmacodynamic (PK/PD) char-
acteristics. This is common when developing a new formulation of a
treatment or developing a generic replacement for an approved drug
whose patent has expired.
When doing equivalence or bioequivalence testing, the conclusion
you want to reach is that the two treatments are nearly the same. This
is like trying to “ prove ” the null hypothesis. For a parameter of interest,
we want to show that the difference in the estimates for the subjects on
each treatment is within an acceptable range called delta. The Neyman –
Pearson approach fi xes the level of the test for the null hypothesis of
no difference and tries to use the data to reject this hypothesis. If we
reject, we have accepted the alternative because we controlled the type
II error with an adequately large sample size.