I planed to extend nonWinferiority testing to one of my statistical notes, *Equivalence Testing and TOST (Two One-Sided Test)* since noninferiority test is simply half part of the equivalence test. Today I’m glad to find an even better explanation from

SAS Usage Note 48616: Design and analysis of noninferiority studies

You will love it if you are interested in this subject (bookmark this link since it looks like unfinished somehow). Few comments:

- It’s better not to use a two-side test for noninferiority testing. In PROC TTEST, you can add option like “side=U” or “side=L”.
- If you do like a two-side test for noninferiority testing, it’s OK but DO remember assign an alpha value of 0.1 since the default value is 0.05 (if you’re lost by this statement, read this post again). It’s pretty tricky and I saw lots of mistakes due to ignoring of this point.
- In note 48616, it is said only test of mean(s) is supported by PROC TTEST. Actually, PROC TTEST can also test ratios (a log-transformation will be applied) by a “dist=lognormal” option.
- To make decision in noninferiority, superiority, and equivalence testings, lower or/and upper limits are used to compare with the margin(s) rather than the P-value. They are of course equivalent but the former approach is much more accessible and meaningful for non-statistician researchers.