Statistics - explanations and formulas

"If the intent of a study is to demonstrate that an experimental treatment is not substantially worse than a control treatment, the study is known as a noninferiority trial" (Hahn, 2012). 

"In a noninferiority trial, the null hypothesis (to be rejected) is that the treatment is inferior, whereas the alternative hypothesis (to be proven) is that the treatment is non-inferior. The type I and type II errors are hence reversed, if compared with superiority trials" (Ruste, 2022).

In traditional superiority trials, the null hypothesis indicates that treatments are similar until proven otherwise (there's no statistical difference). Whereas, in noninferiority trials, the standard treatment is considered superior to the new treatment unless proven equivalent or otherwise.

When looking to prove the "absence of an effect that is large enough to be worthwhile to examine," researchers can test for equivalence (Lakens, 2017). An equivalence range is determined for the highest and lowest acceptable size; this is the predetermined equivalence range (). If the results fall within this range, the treatment is considered equivalent. There are several approaches to determining :

• Clinical notion of minimally important effect (subjective)

• Historical effect of active control in placebo trials

• Regulatory requirements

• Disease severity

• At times, one treatment can even be a bit worse than the other tx so long as it falls within the equivalence range

Researchers need to use different statistical analysis to determine superiority; may or may not be able to do so from the same study depending on the power.