In their answer to Question 24 from the first paper of 2018, the college describes a non-inferiority trial as "an active control trial which tests whether an experimental treatment is not worse than the control treatment by more than a specified margin". This is almost exactly the first sentence of an excellent article by Steven Snapinn (2000), which is therefore the most sensible single reference to be recommended to time-poor exam candidates. The college question also asked for details of why one might run a non-inferiority trial, and what the limitations of such a trial might be. The objective of this chapter is to render this difficult topic into small chunks for easy storage, for the 95.9% of exam candidates who couldn't answer Question 24 in the second paper of 2018, or for the 95.5% who couldn't answer the very similar Question 23 from the first paper of 2019. It appeared again as Question 10 from the cursed first paper of 2021, but because at the time of writing we do not have official pass rates from the Plague Year, it is impossible to say whether the pass rate is getting better.
In superiority trials, the hypothesis is that the experimental treatment is different (better) to the standard treatment, and two-sided statistical tests are used to test the null hypothesis (because the experimental treatment could be better or worse). The null hypothesis is therefore that there really is no difference. In equivalence trials the null hypothesis is that the treatments are significantly different, by a specified margin (the "equivalence margin"). In non-inferiority trials the null hypothesis is that the experimental treatment is worse than the standard treatment - and the equivalence margin determines how much worse.
The diagram below is borrowed and modified from Ian A Scott (2009), and demonstrates the results and confidence interval ranges expected of the three different types of trials, when they have demonstrated that the null hypothesis is false.
Superiority trials have to have their results well over to the "favours experimental treatment" side, usually by a pre-specified margin. Equivalence trials need to have their results and confidence intervals within that margin to confirm that the two treatments are in fact equivalent. Non-inferiority trials also need to have their results within that margin, but there is no need to prove that the treatment is superior (i.e the confidence intervals and results simply need to remain within the not much worse margin, the "+1%" line in the diagram).
Obviously, those margins are under the control of the investigators, and therefore it would be easy to force the results into successful publishable trial territory by manipulating the equivalence margin.
A non-inferiority trial is appropriate when:
Snapinn, Steven M. "Noninferiority trials." Trials 1.1 (2000): 19.
Lesaffre, Emmanuel. "Superiority, equivalence, and non-inferiority trials." Bulletin of the NYU hospital for joint diseases66.2 (2008): 150-154.
Murray, Gordon D. "Switching between superiority and non‐inferiority." British journal of clinical pharmacology 52.3 (2001): 219-219.
Scott, Ian A. "Non-inferiority trials: determining whether alternative treatments are good enough." Med J Aust 190.6 (2009): 326-330.
Piaggio, Gilda, et al. "Reporting of noninferiority and equivalence randomized trials: extension of the CONSORT 2010 statement." Jama 308.24 (2012): 2594-2604.
Garattini, Silvio. "Non-inferiority trials are unethical because they disregard patients' interests." The Lancet 370.9602 (2007): 1875-1877.
Fleming, Thomas R. "Current issues in non‐inferiority trials." Statistics in medicine 27.3 (2008): 317-332.