## CV limbo [Regulatives / Guidelines]

Dear Helmut,

Please neglect my previous first question and I change it a little bit. Looking forwatd to your reply. Thanks.

❝ When we talk about the CV in a crossover (simple 2×2×2, Higher-Order, or replicate) design, generally the intra-subject CV (CVw) is meant. In parallel designs it’s the total CV (pooled from CVw and CVb). Only in reference-scaling we are interested in the intra-subject CVs of treatments (CVwT and CVwR) as well. Of course, both are only accessible in full replicate designs. In the bloody partial replicate design we get only the latter. The former is nice to know (esp. in pilot studies when we want to estimate the sample size for a pivotal study; see there for an example).

Question:
In simple 2*2*2 cross over design, Can we still get Swr or Swt? Or we can only get those two values in replicate design? Is RSABE method can only be applied in replicate design?
In parallel design, CV is the total(pooled) CV (pooled from CVw and CVb). Why we need to calculate pooled CV in parallel design? Will we use that pooled CV to calculate sample size? Or we only need to use CVw to calculate sample size.

❝ ❝ To complicate things: CVwT and CVwR could be directly estimated from the FDA’s mixed-effects model (as you did in your OP).

❝ ❝ If the study is balanced, correct. Otherwise we would have to weigh the variances by the degrees of freedom. See also this post.

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;

Question: If the design is replicated design and based on the code provided by FDA, I can get two seperate residuals which are Swt and Swr. However, the calculation of confidence intervcal is based on Sw instead of Swt or Swr. Hence, I should first determine whether the design is balanced or not, and then find appropriate way to calculate Sw based on Swt and Swr. Then use Sw to calculate CVw, then use CVw to calculate confidence interval. Are those steps correct? Thanks.