RCT: estimation of total sample size knowing only the percentage of occurrence

Dear all,

I was asked to estimate the minimum sample size to set up a RCT comparing a standard dose technique to detect recurrence of disease vs low-dose technique. It seemed to be reasonably to me to think about differences in sensitivity and to suggest a noninferiority trial comparing the sensitivity of standard dose (active control) for diagnose of recurrence to low dose, where enrolled patients are to be allocated to either group at a 1:1 ratio. Since clinically acceptable noninferiority margin would be 5% and knowing the sensitivity of standard dose, I applied the formula

n = 2[(Za+Zb)^2P(1-P)/2], where P was the sensitivity of standard dose.

Clinicians assessed that their real endopoint would be differences in time to detect suspicious recurrence (es. lung nodules) between standard vs low dose techniques, and told me that in 3 years, about 40% of patients will present recurennce. However, how do I estimate sample size with those indications? I thought about a comparison between two proportions, applying the following formula:

n > [Za x (sqrt(2(P1-P2/2)(1-(P1-P2/2))) + Zb x (sqrtP1(1-P1)+P2(1-P2))/P1-P2]^2

where P1 is 0.4 (the percentage of occurrence), P2 is 0.35, the percentage of detection considering a non-inferiority limit of about 5%.

However, I am not sure this is the proper way to test for difference in time to detect... and I am also not sure this is the best way to compare standard to low dose.

Thanks for discussing and helping with this issue.