## Non-Superiority [Design Issues]

Hi Dennis,

❝ The goal of an RCT is to compare the difference of complication rates of CVD surgery between two groups (group A and group B).

❝ The patients in group A will take medicine (traditionally treatment) and the patients in group B without taking medicine.

❝ Notably, we want to design the RCT as a non-inferiority trial. That is, the effect of complication rates of patients without taking medicine in group B is not worse than the patients in group A with take medicine.

Hhm.

❝ So, could we design the RCT as a non-inferiority trial?

The other way ’round.

Higher response is considered ‘better’ → Non-Inferiority
Lower response is considered ‘better’  → Non-Superiority

You hope that the complication rates in group A (with medicine) are lower than in group B (without medicine), right? Hence, that’s a Non-Superiority trial.

Note: x-axis in log-scale. $$\delta$$ made up out of thin air.

❝ Moreover, how to defining the non-inferiority margin at the situation?

You don’t need only to define the non-superiority margin $$\small{\delta}$$ but also assume the variability. No idea.
You are dealing with complication rates, which are $$\small{0\leq x \leq 1}$$. As an aside, you can’t use the function sampleN.noninf() of the -package PowerTOST, because it handles only lognormal $$(\small{x\in\mathbb{R^{+}}}$$) or normal $$(\small{-\infty\leq x+\infty}$$) distributed data. I’m sure, PASS has a fancy method for that.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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