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I'm projecting the number of patients needed for a clinical trial. Specifically, I'm using this model (https://www.sealedenvelope.com/power/binary-noninferior), and setting the variables as: (1) alpha = 2.5%, (2) 1-beta = 80%, (3) %success in control group = 99%, (4) %success in experimental group = 99%, and (5) d= 3%.

When I keep assumptions #3 and #4 the same (% success in control vs. experimental), why does the "n" sample size required for a clinical trial decline as the "success rate" of standard therapy decreases towards 50%? I'd expect that, as the standard of care improves, more patients are needed to show that your new therapy is not inferior to it?

Many, many thanks for your help.

Best, Evan

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I guess that you have reversed what is success and what's failure.

You want to test if the experimental treatment is non-inferior to the control treatment. By setting the %success to 99 in both groups you assume that there is no true difference between the treatments. When you decrease the %success in the control group you assume that the experimental group is superior to the control group. Hence, you need fewer subjects to show non-inferiority.

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