Confidence interval: A confidence interval \((a,b)\) is the result
of a procedure that independently of the sample will contain the value of
the target parameter in most of the cases (say, for instance, in the 95% of the cases).
Then, given a particular sample, the values \((a,b)\) can be taken has containning, with
a degree of confidence, the true value of the parameter. Different samples will produce
different confidence interval values. Thus, conclusions based on a confidence interval
should be taken with caution.
Equivalence range: \(\Delta\) indicates the value for which
the absolute difference \(|\pi_1-\pi_2|<\Delta\) leads to consider that
both probabilities are clinically equivalent.
Consider that the confidence interval obtained is CI:\((a,b)\)
\( -\Delta < (a,b) <\Delta \): Clinically equivalent results
\( 0 > a > -\Delta \) and \( b > \Delta \): Non-inferior results
\( a > 0\) and \( a < \Delta \): Superior results
\( a > \Delta \): Clinically superior results
You can explore this interpretation in the tab: Equivalence and non-inferiority