Bioequivalence and Bioavailability Forum

Hi Mittyri,

❝ There is a discontinuity at CV=0.3. I cannot figure out the reason.

You introduced it yourself with the highlighted parts of the code:

❝   if (x1[j] > 0.3) {


❝     y1[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[1], reg="EMA")
❝     y2[j] <- power.scABEL(CV=x1[j], theta0=GMR, n=n, des=des[2], reg="EMA")
❝   }
❝   if (x1[j] <= 0.3) {
❝     y1[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[1])
❝     y2[j] <- power.TOST(CV=x1[j], theta0=GMR, n=n, des= des[2])
❝   }

If you indend to go with reference-scaling you have to state that in the protocol. Based on that you perform the sample size estimation, but always with sampleN.scABEL(). Once the study is done, you may scale or not (dependent on CV_wR). Hence, the only fair comparison would be ABE (power.TOST if you don’t intend to scale) with ABEL (power.scABEL) over the entire range of CVs, like this:

library(PowerTOST)
CV       <- seq(0.25, 0.55, 0.01)
pwr.ABEL <- vector()
pwr.ABE  <- pwr.ABEL
for (j in seq_along(CV)) {
  pwr.ABEL[j] <- power.scABEL(CV=CV[j], theta0=0.95,
                              n=48, design="2x2x3")
  pwr.ABE[j]  <- power.TOST(CV=CV[j], theta0=0.95,
                            n=48, design="2x2x3")
}
plot(CV, pwr.ABEL, type="l", col="blue", lwd=2,
  ylim=c(0.90, 1), ylab="power", las=1)
lines(CV, pwr.ABE, col="red", lwd=2)
abline(v=c(0.3, 0.5), lty=3)
legend("topright", legend=c("ABEL", "ABE"),
  col=c("blue", "red"), lwd=rep(2, 2))

or


With your code you would jump at 0.30 from the red line (ABE) to the blue line (ABEL). Note that even at CV 0.25 power of ABEL is slightly larger than the one of ABE since there is small chance that you are allowed to scale. That’s the tricky part with reference scaling. The simulation – as the scaling model itself* – is based on the true (but unknown) θ₀ and σ_wR. By pure chance (CV_wR >0.30) you will be allowed to scale although the drug is not highly variable (σ_wR ≤0.2936). This is the (main?) reason behind the inflation of the type I error. Another story.

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• ln(0.80) / σ_w0 ≤ [ln(μ_T) – ln(μ_R)] / σ_wR ≤ ln(1.25) / σ_w0
  Only parameters here, not their estimates…