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

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

Here is the SAS code for the analysis of ABE with fully replicate design data.

PROC MIXED; CLASSES SEQ SUBJ PER TRT; MODEL Y = SEQ PER TRT/ DDFM=SATTERTH; RANDOM TRT/TYPE=FA0(2) SUB=SUBJ G; REPEATED/GRP=TRT SUB=SUBJ; ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1;

Q2: When should I write 1 -1 and when should I write -1 1 in estimate statements?

Here is the covariance output from SAS

 Covariance Parameter Estimates Cov Parm  Subject       Group         Estimate FA(1,1)   subject                     0.2001 FA(2,1)   subject                     0.1263 FA(2,2)   subject                     0.1507 Residual  subject   formulation Ref   0.01495 Residual  subject   formulation Test  0.03265 G(1,1) = 0.04005, G(2,1)=G(1,2)=0.02527, G(2,2)=0.03866

In replicate design, the intra-subject variabilities are still calculated from the residuals as in a 2-way crossover, using:
IntraCV_T = 100%*sqrt(exp(sig_WT^2)-1)
IntraCV_R = 100%*sqrt(exp(sig_WR^2)-1)

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? If I want to get CVwt and CVwr based on confidence interval, how can I do it using R package

Q4: I try to use the formula 100%*sqrt(exp(sig_W^2)-1) where sig_w^2 = (sig_wt^2+sig_wr^2)/2 to get the same CV(25.24456) based on the covariance output above, but the value is different. Is my calculation wrong? If so, can anyone please tell me the right way to get same CV?

Many thanks!  Ing. Helmut Schütz 