Bioequivalence and Bioavailability Forum

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 C_max.
  
• 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 C_max (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.
  
• t_max 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