Bioequivalence and Bioavailability Forum

Hi Shawn,

❝ I think intra-subject CV is an inherent characteristic of a drug. is it right?

Only if you are talking about an intravenous dose. Otherwise, it is mixture of the properties of the drug (influenced by transporters, pre-systemic and first-pass metabolism, clearance) and the formulation / physiology (absorption, lag-time due to gastric emptying). See my nitpicking paragraph in this post.

❝ If it not, does anyone can reduce it by any ways?

I can’t imagine how.^1,2 In a crossover design every subject acts as its own control. Imagine you have a very high between-subject variability (e.g., extensive and poor metabolizers or one is stupid enough to include only ballerinas and sumo-wrestlers in a study). The within-subject variability will not be affected.
Try it: Use the data of any study and multiply results of half of the subjects by two (mimicking the ballerinas with low volumes of distribution) and divide the other half by two (mimicking the sumo-wrest­lers). What do you get?

In a simple crossover CV_intra is pooled from CV_wT and CV_wR (i.e., one common variance is assumed in the model). If CV_wT < CV_wR (the reference is a lousy product), the CI is inflated and we are punished by a higher sample size. All too bad that we don’t know the CVs in a simple 2×2 crossover. We need one the full replicate designs (see also this post) and reference-scaling for a potential incentive in the sample size.
An example: CV_wT and CV_wR 0.3–0.5, theta0 0.95, targetpower 0.8. sampleN.TOST() does not support different CVs. Makes sense, since only CV_w is part of the model. We can misuse the function sampleN.scABEL() after ‘switching off’ all scaling conditions. Does it help? Not at all. Only ABEL can be nice.

library(PowerTOST)
CV.lo     <- 0.30
CV.mid    <- 0.40
CV.hi     <- 0.50
CVwR      <- CVwT <- seq(CV.lo, CV.hi, 0.1)
res       <- data.frame(CVwT=rep(CVwT, each=length(CVwR)),
                        CVwR=rep(CVwR, length(CVwT)), CVw=NA,
                        n.ABE=NA, n.ABE.sim=NA, n.ABEL=NA)
res$CVw   <- mse2CV((CV2mse(res$CVwT)+CV2mse(res$CVwR))/2)
# remove all scaling conditions
reg       <- reg_const("USER", r_const=log(1.25)/CV2se(0.3),
                       CVswitch=0.3, CVcap=0.3, pe_constr=FALSE)
for (j in 1:nrow(res)) {
  res$n.ABE[j] <- sampleN.TOST(CV=res$CVw[j], theta0=0.95, design="2x2x4",
                               print=FALSE, details=FALSE)[["Sample size"]]
  res$n.ABE.sim[j] <- sampleN.scABEL(CV=c(res$CVwT[j], res$CVwR[j]),
                                     theta0=0.95, design="2x2x4",
                                     regulator=reg, print=FALSE,
                                     details=FALSE)[["Sample size"]]
  res$n.ABEL[j] <- sampleN.scABEL(CV=c(res$CVwT[j], res$CVwR[j]),
                                  theta0=0.95, design="2x2x4",
                                  regulator="EMA", print=FALSE,
                                  details=FALSE)[["Sample size"]]
}
print(res[with(res, order(CVw, CVwT)), ], row.names=FALSE)

 CVwT CVwR       CVw n.ABE n.ABE.sim n.ABEL
  0.3  0.3 0.3000000    20        20     18
  0.3  0.4 0.3527824    26        26     16
  0.4  0.3 0.3527824    26        26     24
  0.4  0.4 0.4000000    34        34     20
  0.3  0.5 0.4089765    34        34     16
  0.5  0.3 0.4089765    34        34     32
  0.4  0.5 0.4518401    42        42     18
  0.5  0.4 0.4518401    42        42     24
  0.5  0.5 0.5000000    50        50     22

Lesson learned: Even if we would know that the reference is a lousy product, in ABE we suffer.

---

1. I once heard about a Russian CRO claiming that “our volunteers have a lower CV_intra and studies at our site can be smaller than usual”. What the heck are they doing? Include mo­no­zycotic twins or have access to human clones? Would violate the assumption of independence in the model. I guess, they are just fabricating data.
   
2. Some people claim that extreme standardization (BMI, …) will also help to reduce CV_intra. I strongly doubt that since the between- and within-variance components are mutually independent.