## FDA's HVD SAS Code / Stan­dard Error / CV [Regulatives / Guidelines]

Dear Helmut,

❝ ❝ Q1: May I ask why in 2*2*2 cross over design, SE = sqrt(MSE)*sqrt(2/N)?

❝ Correct is $$SE=\sqrt{\frac{MSE}{2}\left(\frac{1}{n_1}+\frac{1}{n_2}\right),}\tag{1}$$

❝ where $$\small{n_1}$$ and $$\small{n_2}$$ are the number of subjects in sequences $$\small{1}$$ and $$\small{2}$$, respectively.*

If and only if sequences are balanced ($$\small{n_1=n_2\to N=n_1+n_2}$$) you can use \eqalign{SE&=\sqrt{\frac{2\,MSE}{N}}\\&=\sqrt{MSE}\,\cdot\,\sqrt{\frac{2}{N}}}\tag{2}

❝ instead. In order to avoid falling into a trap (i.e., using $$(2)$$ if $$\small{n_1\neq n_2}$$), I strongly recommend to use always $$(1)$$.

New Q1: May I ask the formula to calculate SE in a 2*2*4 replicated design? I read your lection but I only find the formula to calculate in 2*2*2 design. Thanks.

❝ ❝ The data include 10 subjects and 5 in seq 1 and 5 in seq2. This is a 2*2*4, 2 sequence 2 treatment and 4 period design, 90% CI of T/R is (0.8450984199, 1.104975448) and point estimate is 0.9663400049.

❝ ❝ I tried to use CVfromCI function from R package PowerTOST to calculate CV, and here is my r code:

❝ ❝ 100*CVfromCI(alpha=0.05, lower=0.8450985339, upper=1.104975299, n=c(5,5), design="2x2x4")

❝ ❝ and I get CV = 25.24456.

❝ ❝

❝ ❝ Q3: Is this CV a pooled CV?

❝ Correct, since the 90% CI is based on it.

New Q3: (1) When we talk about CV, do we usually mean CVwr(within-subject variability of the reference treatment)? Because we need to use whether CVwr > 30% (Swr>0.294) or not to determine which bioequivalence method should use.
(2) If the answer of (1) is yes, then why we need to calculate pooled CV from 90% CI if we only care about CVwr? Or if pooled CV is important, when will we need to use pooled CV to make any decision?
(3) What's the relationship among CV(Sw), CVwr(Swr), CVwt(Swt)? For 2*2*2 design, is that S^2w = (S^2wr + S^2wt)/2, and CV=100*sqrt(exp(S^2w)-1)? Will this formula change in 2*2*4 design? If it will change, could you please write the formula in 2*2*4 design? Thanks.