How to properly analyze a non-inferiority study In my study I try to show that treatment A is not inferior to treatment B. With a delta margin of tolerance =-2. I had discussed the subject in a previous post, of which here is the link. For two-sided statistical tests I have this difference $\mu_A−\mu_B= -0,7$ $[-2,1; 0.8]$.
But in one-sided test I have $-0.7$ $[-1.9; +\infty)$.
If I conclude from the two-sided test, $H_0$ is not rejected. Non-inferiority is therefore not proven.
On the other hand, with respect to the one-sided test, non-inferiority is proven.
Which is more valid of the two analyses? Or do they interpret each other differently?  Or does the decision to use a one- or two-sided test depend on the objectives set beforehand, whether or not superiority is to be tested in the case of non-inferiority? I still don't understand in an operational way the unilateral or bilateral test.
 A: Both tests are valid, but they address different questions.
Two-sided tests are used to answer questions like:

*

*Is there any relationship between outcome and treatment? (existence)

*Treatment has no influence on the outcome whatsoever (nonexistence)

*Treatment has no relationship with the outcome (also nonexistence)

*The outcome in A is not any different than the outcome in B (nonexistence again)

One-sided tests come from directional questions:

*

*Is A better than B?

*Is doing X worse than doing Y?

*Is A better than B by at least k?

You should use the CI (or a p-value) that corresponds to the hypothesis you designed your experiment to test. If your goal was to show non-noninferiority, that means using the second CI/p-value.
A: Your significance levels (or confidence levels for the CIs) are not the same. You used 5% for the two-sided test and also 5% for the one-sided test. So that people don't game "the system" in such a "silly" way, it is usual (at least when we talk about a drug regulatory setting) that one-sided non-inferiority testing is done at half the significance level of two-sided testing. In that case, there's no inconsistency.
