## CV limbo [Regulatives / Guidelines]

Hi j_kevin,

for background about variances accessible in different designs see there.

❝ In simple 2*2*2 cross over design, Can we still get Swr or Swt?

No. We get only the within subject variance $$\small{s_\text{w}^2}$$ (and, of course, the between subject variance $$\small{s_\text{b}^2}$$ as well).
As an aside, the model for BE assumes homoscedasticity $$(\small{s_\text{wT}^2\equiv s_\text{wR}^2})$$. Bad luck, if $$\small{s_\text{wR}^2>s_\text{wT}^2}$$. The ‘good’ test product will be punished by the ‘bad’ referrence.

❝ Or we can only get those two values in replicate design? Is RSABE method can only be applied in replicate design?

Yes and yes.

❝ 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.

If you have data of a previous study in a parallel design, you get just the total CV anyway. Only if you have a crossover study ($$\small{CV_\text{w}}$$ and $$\small{CV_\text{b}}$$) you have to pool variances in order to estimate the sample size of a study in a parallel design.

❝ 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.

Correct.

❝ However, the calculation of confidence intervcal is based on Sw instead of Swt or Swr.

See the applicable decision scheme (i.e., whether to use ABE or RSABE). For obscure reasons the FDA does not use $$\small{s_\text{wR}}$$ estimated from the mixed-effects model, but from intra-subject contrasts of the reference treatment with sequence as a factor. See this post for an example.

❝ 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?

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Helmut Schütz

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