I am trying to calculate the sample size for a trial in which I wish to compare two rare proportions. I know that in the control group, the proportion is 0.07, while in the treatment group the proportion is expected to be 0.04. Using the Fisher's Exact Test for two proportions, I get that in order to achieve a power of 80%, for the 5% significance level, I need 971 subjects from each group.
I tried calculating the sample size for using the Odds Ratios. The OR, according to the proportions mentioned above, is 1.8. I calculated the sample size, and got 545 per group, for the same power and significance level.
I don't understand why I need so many less subjects to test the hypothesis that the OR=1, vs testing the hypothesis that P1-P2=0 ?
Why would anyone use proportion difference then ? And people do !
Can I simply use the logistic regression to test for the OR instead of using Fisher's exact test ? Will regulatory bodies such as the FDA accept it ? It feels like cheating in a way.
Can you please help me to put things in order here ? Thank you !
P.S Sample sizes were calculated using a sample size software, so I take it they are correct