Bioequivalence and Bioavailability Forum

Dear AB!

❝ PE is 100 and the number of subjects completed in the study were 70, the resulting CI was well within 80-125 with ISCV of 47%.

❝ could i suspect something wrong went in analysis?

I’m not a friend of post-hoc power calculations, but your result is not surprising:

library(PowerTOST)
power.TOST(theta0=1.00, CV=0.47, n=70, design="2x2x4")
[1] 0.9872979

According to Endrényi & Tóthfalusi, Table A2 (see there), you would have needed only 25 subjects (50% CV, PE 1.00) to show BE with 90% power.

❝ on the other hand if every thing was correct why do we need widening of CI?

You should follow the protocol. See the GL Section 4.1.10:

The request for widened interval must be prospectively specified in the protocol.

• If you did not intend to scale: The acceptance range remains at 80.00–125.00% and since your 90% CI is within ⇒ BE.
  
• If you intended to scale the widened AR is:
  library(PowerTOST)
exp(-0.76*CV2se(0.47)); exp(+0.76*CV2se(0.47))
[1] 0.7121033
[1] 1.404291
  Since your 90% CI is within 71.21–140.43% and the PE is within 80.00–125.00% ⇒ BE.

No worries; you wasted only money.

Dear AB

❝ The data provided is of Cmax from the study.

❝ PE is 100 and the number of subjects completed in the study were 70, the resulting CI was well within 80-125 with ISCV of 47%.

❝ could i suspect something wrong went in analysis?

See this post for a (simple) formula to use for the 90% CI in case of a fully replicate design.
The standard error s in this post is obtained via s=sqrt(log(CV*CV+1)), CV as ratio, not percent.

Your givings thus should result in
CI = 91.56 ... 109.22%
If the exact result you have is reasonable near this result (within the accuracy of the givings) you don't have to be afraid. All went right in your analysis .

❝ on the other hand if every thing was correct why do we need widening of CI?

You have obtained your result with an extraordinary high number of subjects. At least extraordinary high within the context of BE studies, especially considering the replicate design . I had seldom seen such a high number of subjects in BE studies during my over 30 years career .

The widening of the acceptance range in case of ISCV >30% (of reference) has the purpose of avoiding such a high numbers of subjects under study.
See this recent thread for sample size tables for scaled average bioequivalence, including the EMA and the FDA analysis methods.

These tables give you a necessary sample size of N=20 for the EMA evaluation, assuming target power = 80%, GMR=1 and an ISCV=50% (Table A2 of the paper). Even if you follow the recommendation of the two Laszlo's and assume a GMR=0.90 the sample size necessary is N=28.
Thus you could have saved your sponsor quite a lot of money. But on the other hand your company did earn lesser money .
Moreover you could had prevented your volunteers from a lot of blood losses (Someone may call your study unethically). But on the other hand they were of course poorer of the volunteer fee .
One's owl is another one's nightingale.

---

Sorry. Seen just now after submitting that some points were doubled with Helmut.