Bioequivalence and Bioavailability Forum

Hi ElMaestro,

THX for your explanation (especially the lucid last sentence).

I was puzzled by the “appropriate sample size calculation” [sic] in 4.1.3. If there are no safety issues I don’t see a reason why not any Xover BE study could be performed in a replicate design.¹ Sometimes the clinical capacity might come into play.²
Example: The “best guess” CV is 0.25. You are not sure. You have seen one study with a CV of 0.35. You want to play it safe with the GMR and assume 0.9. The CRO houses 32 beds. Given all that, you opt for a 4-period full replicate. If the CV turns out to be correct, chances for reference-scaling are not very high. But, who knows?
My question: Is a CV of 0.25 “close enough” to the magic 0.30 which would justify a replicate design + optional scaling (GL: “applicant suspects that…”) or do you have to stick to a 2×2 (GL: “If two for­mu­lations are compared, a randomised, two-period, two-sequence single dose crossover design is re­com­mended.”)? That would mean 56 subjects compared to 28 in the replicate design (equal number of ad­mi­nis­trations, similar study costs). Stupid enough the former is beyond the capacity of the CRO. Two groups, etc. etc.
Try:

library(PowerTOST)
CV     <- seq(0.2, 0.4, 0.01)
CV.exp <- 0.25
GMR    <- 0.90
cap    <- 32
des    <- "2x2x4"
n1     <- vector("numeric", length=length(CV))
n2     <- n1
n3     <- n1
for (j in seq_along(CV)) {
  n1[j] <- sampleN.TOST(CV=CV[j], theta0=GMR, design="2x2x2",
    print=F)[["Sample size"]]
  n2[j] <- sampleN.TOST(CV=CV[j], theta0=GMR, design=des,
    print=F)[["Sample size"]]
  n3[j] <- sampleN.scABEL(CV=CV[j], theta0=GMR, design=des,
    print=F, details=F)[["Sample size"]]
}
plot(CV, n1, pch=0, col="red", ylim=c(12, max(c(n1, n2, n3))),
  ylab="sample size", las=1)
points(CV, n2, pch=2, col="black")
points(CV, n3, pch=6, col="blue")
abline(v=0.3, col="red", lty=1)
abline(v=CV.exp, col="blue", lty=3)
abline(h=12, col="red", lty=1)
abline(h=cap, lty=3)
legend("topleft", pch=c(0, 2, 6), col=c("red", "black", "blue"),
  legend=c("2x2x2: ABE", paste(des, "ABE"), paste(des, "ABEL")))

---

1. Alfredo told me (in Bonn, 2013): “IMHO, all BE studies should be performed in a 4-period full replicate design. From a statistical perspective replicate designs are superior to two-way cross­overs.”
   Could not agree more.
   
2. Anyone can run a computer program to calculate how many subjects are needed for a BE study. […]
   The first question one should ask Clinical in designing a bioequivalence trial is, ‘How many formu­la­tions and doses need to be involved?’ The next question to ask Clinical is, ‘How many beds does the clinical have, and how many subjects can be scheduled?’ (also known as, ‘How many spots are avail­able?’).
      Scott Patterson and Byron Jones
      Bioequivalence and Statistics in Clinical Pharmacology
      Boca Raton 2006. Chapman & Hall / CRC. pp160–1