Bioequivalence and Bioavailability Forum

Hi roman_max,

❝ within this code in PowerTOST

❝ 100*CVfromCI(alpha=0.05, lower=0.8450985339, upper=1.104975299, n=c(5,5), design="2x2x4")

❝ if design is "parallel" it is a CVtotal? Am I right?

Yes, you are.

For the record:

1. Any replicate design: \(\small{CV_\text{intra}}\), assuming homoscedasticity (\(\small{s_\text{wT}^2\equiv s_\text{wR}^2}\)).
   
2. Any crossover and a paired design: \(\small{CV_\text{intra}}\).
   
3. Parallel design: \(\small{CV_\text{total}}\), assuming homoscedasticity (\(\small{s_\text{T}^2\equiv s_\text{R}^2}\)).

Note that the \(\small{s^2}\) components in #1 and #3 cannot be calculated from the confidence interval. You need the raw data.

library(PowerTOST)
CI      <- c(0.85, 1 / 0.85)
n       <- 24
designs <- known.designs()[c(1, 13, 3:6, 8:9, 12, 7, 10:11), c(2:3, 9)]
res     <- data.frame(design = designs$design, name = designs$name,
                      n = rep(n, nrow(designs)), df = designs$df,
                      lower = CI[1], upper = CI[2], CV = NA,
                      type = c("total", rep("intra", nrow(designs) - 1)))
for (j in 1:nrow(designs)) {
  res$CV[j] <- sprintf("%.2f%%", 100 * CI2CV(lower = res$lower[j],
                                             upper = res$upper[j], n = n,
                                             design = res$design[j]))
}
print(res, row.names = FALSE, right = FALSE)

 design   name                        n  df    lower upper    CV     type
 parallel 2 parallel groups           24 n-2   0.85  1.176471 23.50% total
 paired   paired means                24 n-1   0.85  1.176471 33.75% intra
 2x2x2    2x2x2 crossover             24 n-2   0.85  1.176471 33.69% intra
 3x3      3x3 crossover               24 2*n-4 0.85  1.176471 34.47% intra
 3x6x3    3x6x3 crossover             24 2*n-4 0.85  1.176471 34.47% intra
 4x4      4x4 crossover               24 3*n-6 0.85  1.176471 34.73% intra
 2x2x4    2x2x4 replicate crossover   24 3*n-4 0.85  1.176471 50.60% intra
 2x4x4    2x4x4 replicate crossover   24 3*n-4 0.85  1.176471 50.60% intra
 2x2x2r   Liu's 2x2x2 repeated x-over 24 3*n-2 0.85  1.176471 50.62% intra
 2x2x3    2x2x3 replicate crossover   24 2*n-3 0.85  1.176471 40.20% intra
 2x3x3    partial replicate (2x3x3)   24 2*n-3 0.85  1.176471 40.20% intra
 2x4x2    Balaam's (2x4x2)            24 n-2   0.85  1.176471 16.50% intra

You can calculate \(\small{CV_\text{wR}}\) from the upper expanded limit (irrespective of the design and sample size):

U <- 1.4319
cat(sprintf("%.2f%%", 100 * U2CVwR(U)), "\n")
50.00%