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.