## What do you want to achieve? [General Sta­tis­tics]

Hi Victor,

I tried to reconstruct your original post as good as I could. Since it was broken before the first “$$\mathcal{A}$$”, I guess you used an UTF-16 character whereas the forum is coded in UTF-8. Please don’t link to large images breaking the layout of the posting area and forcing us to scroll our viewport. THX.

I think that your approach has same flaws.
• You shouldn’t transform the profiles but the PK metrics AUC and Cmax.
• The Null hypothesis is bioinequivalence, i.e.,
$$H_0:\mu_T/\mu_R\notin \left [ \theta_1,\theta_2 \right ]\:vs\:H_1:\theta_1<\mu_T/\mu_R<\theta_2$$ where $$[\theta_1,\theta_2]$$ are the limits of the acceptance range. Testing for a statistically significant difference is futile (i.e., asking whether treatments are equal). We are interested in a clinically relevant difference $$\Delta$$. With the common 20% we get back-transformed $$\theta_1=1-\Delta,\:\theta_2=1/(1-\Delta)$$ or 80–125%.
• Nominal $$\alpha$$ is fixed by the regulatory agency (generally at 0.05). With low sample sizes and/or high variability the actual $$\alpha$$ can be substantially lower.
• Since you have to pass both AUC and Cmax (each tested at $$\alpha$$ 0.05) the intersection-union tests keep the familywise error rate at ≤0.05.
• For given design, sample size, variability, and point estimate calculation of $$\alpha$$ and $$\beta$$ is straightforward. R-code for the package PowerTOST at the end.
• tmax follows a discrete distribution and hence, should be assessed by a nonparametric test.

library(PowerTOST) design <- "2x2x2" # for others, see known.designs() n      <- 24 CV     <- 0.25 PE     <- 0.95 alpha  <- power.TOST(CV = CV, n = n, theta0 = 1.25, design = design) beta   <- 1 - power.TOST(CV = CV, n = n, theta0 = PE, design = design) cat("alpha =", alpha,     "\nbeta  =", beta, "\n"

Gives
alpha = 0.04999527 beta  = 0.2608845

Dif-tor heh smusma 🖖
Helmut Schütz

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