Bioequivalence and Bioavailability Forum

Hi Smog,

❝ The point estimate for the Cmax was 116.97. CI is: LL 95,28, UL 146,01 in the pilot study.

Hhm, I get \(PE = \sqrt{0.9528 \times 1.4601} = 1.1795 \; {\color{Red} \neq 1.697} \). Are your numbers correct?

❝ The drug is not HVD.

Correct if we believe that the CV is “carved in stone”.
By means of R / package PowerTOST:

library(PowerTOST)
n  <- c(6, 5) # my assumption: 6 in one sequence and 5 in the other
LL <- 0.9528
UL <- 1.4601
PE <- sqrt(LL*UL)
CV <- CVfromCI(lower=LL, upper=UL, design="2x2x2", n=n)
cat(sprintf("%s %.2f%%%s", "estimated CV:", 100*CV, "\n"))
estimated CV: 27.70%

But the CV is an estimate and its precision depends on the sample size. The “true” CV might as well cross the border of a HVD(P). Let’s assume a “producer’s risk” of 20%:

CVupper <- CVCL(CV=CV, df=sum(n)-2, side="upper", alpha=0.20)[["upper CL"]]
cat(sprintf("%s %.2f%%%s", "upper CL of the CV:", 100*CVupper, "\n"))
upper CL of the CV: 36.29%

❝ Is there any sence to go forward with pivotal study in case of such GMR? If so which GMR to use: 0,95 or 1,1697?

0.95 is already outside the 90% CI of the pilot study! The 90% CI means that the true (but unknown) T/R-ratio lies with p ≤ 0.05 below the lower CL and with p ≤ 0.05 above the upper CL. In other words your odds would be less than 1:20. Very bad idea. See also Fuglsang¹ for the transition from pilot to pivotal studies in BE and some old stuff² for background.
On the other hand, if you assume that both the PE and CV from the pilot are “true” values sample sizes would be extreme (274 for 80% power in a 2×2×2 for ABE and still 136 in a 2×2×4 for ABEL). I would be very wary to proceed. Think about reformulation.

---

1. Fuglsang A. Pilot and Repeat Trials as Development Tools Associated with Demonstration of Bioequivalence. AAPS J. 2015;17(3):678–83. doi:10.1208/s12248-015-9744-6.
   
2. Browne RH. On the use of a pilot sample for sample size determination. Stat Med. 1995;14(17):1933–40. doi:10.1002/sim.4780141709.

Hi Smog,

❝ I have a little question regarding the pilot study (2x2x2, 11 subjects). The point estimate for the Cmax was 116.97. CI is: LL 95,28, UL 146,01 in the pilot study. The drug is not HVD.

❝ Is there any sence to go forward with pivotal study in case of such GMR? If so which GMR to use: 0,95 or 1,1697?

Those were wise words from Helmut even though he is quoting some very dubious sources . I am a tiny bit less certain than he is, I must admit; like Helmut I am also leaning towards reformulation. Using a GMR of 0.95 for sample size calculation is functionally -in terms of sample size- exactly the same as using 1/0.95 (=1.053) and that is nicely within your confidence interval and could perhaps be used. Eyeballing it, the chance that the true GMR is 1.053 or better appears smaller than the chance (risk) that the true GMR is completely outside the acceptance range. So chances are not much in your favour, I'd say.
But I am not at all very certain about anything in this case.