I always have trouble making sense of noninferiority studies. If treatment B is noninferior to A, I can understand that. But when it says B is NOT noninferior to A, why can’t they just say B is inferior to A? What’s the difference?
Example of such a trial: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(22)00537-2/fulltext
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The study was designed from the start as a non-inferiority study. That means there is a single yes/no question at the heart of the statistical analysis: “Is B non-inferior to A?” For this study, “non-inferior” means “B is at least 88% as good as A.” It’s actually *less* confusing to consistently use the terminology “non-inferior / not non-inferior” especially because we’ll also be talking about p-values and confidence intervals.
When we measure the value of anything, there’s always some uncertainty. We can’t ever say a drug is exactly 84.0% effective; we can only say that we’re 95% confident that it’s between 80% and 88%, say. In a study like this, we’ve measured two numbers – the effect for A and the effect for B – both with some degree of uncertainty. Let’s say we think A is between 80% and 90% effect, and we think B is between 85% and 95% effective. Is B *better* than A? We can’t say for sure; their confidence intervals overlap too much. The p-value of the hypothesis test that the difference in means is not exactly zero would be around 0.25, higher than the 0.05 usually used in scientific papers, so we wouldn’t be able to reject the null hypothesis. Or, in other words, even though B *seems* better than A, the difference is too small to be statistically significant. However, if we ask the question, Is B *non-inferior* to A, then we can get a clear-cut “yes” to our question with a p-value less than 0.05.
So when they say “B is NOT non-inferior to A”, they’re not saying B is *definitely* inferior to A, they’re saying they weren’t able to prove beyond a reasonable doubt that B is non-inferior to A because the difference wasn’t statistically significant. Maybe that means B is inferior to A, but maybe it just means the study was underpowered and needs to be repeated with a larger sample size.
The most common reason to use a non-inferiority study design is that you suspect both interventions have roughly the same effect, but one has other desirable qualities, such as being a lot cheaper, having fewer side effects, or being tolerable to patients who have an adverse reaction to the other. In these cases, it’s not necessary to prove beyond a reasonable doubt that B is statistically significantly better than A, or even as good as – if it’s even in the same ballpark, it’s good enough. The non-inferiority design requires considerably smaller sample size and is therefore cheaper and faster to conduct.
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