If we have a balanced factorial designed experiment where each variable is taken in 2 levels (+1,-1) and we don't have estimates of each proportion for each factor level combination like we did in this question: Simulation of logistic regression power analysis - designed experiments, what is the best approach for determining sample size? Can we consider the baseline proportion (say 0.0005) and how large a deviation we care to detect (say 0.00005) and then simply run a two sample difference in proportions power analysis? That is:
power.prop.test(n=NULL, p1=0.0005, p2=0.00055, power=0.8)
which in this case suggests the total sample size required is 6589596 (3294798 *2 from the output of the R function), and divide this sample size between each design point? So if there are 4 factors at 2 levels each then each "cell" gets (6589596 / 16)?
The thinking: Given a factorial design, each effect (main as well as interactions) will use 1/2 of the total sample for (+ levels) and the other half for (- levels) if we say we only care about effects that are at least a certain size, this approach should work regardless of the number of 2 level factors and works for both main effects and interactions.
Is this correct?