Equivalence testing is important, if you expect a
new treatment to be equally efficaceous as the standard treatment.
This new treatment may still be better suitable for practice, if it
has fewer adverse effects or other ancillary advantages.
For the purpose of equivalence testing we need to
set boundaries of equivalence prior to the study. After the study
we check whether the 95% confidence interval of the study is
entirely within the boundaries.
As an example, in a blood pressure study a
difference between the new and standard treatment between −10 and
+10 mm Hg is assumed to smaller than clinically relevant. The
boundary of equivalence is, thus, between −10 and +10 mm Hg. This
boundary is a priori defined in the protocol.
Then, the study is carried out, and both the new
and the standard treatment produce a mean reduction in blood
pressure of 10 mm Hg (parallel-group study of 20 patients) with
standard errors 10 mm Hg.
The standard errors of the mean differences = 10
mm Hg
This result is entirely within the a priori
defined boundary of equivalence, which means that equivalence is
demonstrated in this study.