## Confidence intervals vs. point estimators [Regulatives / Guidelines]

Dear Dan,

» AUC:  98.57-124.33%, 68.58-103.22%, 100.95-122.94%, 91.56-105.70%
» Cmax: 99.69-134.01%, 78.49-116.04%, 102.67-125.98%, 89.06-106.49%

Thanks - now much more clear and improves your chances.

» "The applicant's response does not resolve the objections concerning the bioequivalence issue. The first formulation of the Test product in the study showed bioinequivalence in comparison to the Reference product (Cmax outside of the widened acceptance range of 75-133%) and furthermore the ...

No, here the assessor is outright wrong. The CI's for Cmax above do not show bioINequivalence. Bioinequivalence is when the the CI has no point in common with the acceptance range. You can even argue that with increased sample sizes the studies would all be expected to be acceptable.
It is often forgotten that bioequivalence studies have at least three outcome: Equivalent, not conclusive, inequivalent. Studies 1 and 3 are inconclusive but do not indicate inequivalence. Dr. Dan vs Regulator 1-0.

» ...values for the point estimates for the ratio of the geometric means (AUC0-t, AUC0-inf and Cmax) were all over 100%. Afterward the formulation of the Test product was changed and a new BE-study was conducted which again showed a bioinequivalence (AUC0-t and AUC0-inf outside of the acceptable range of 80-125%), with the point estimates all under 100%. The same test batch and the same formulation was investigated in a third BE-study, in which Cmax was out of the normally accepted range of 80-125% and all the point estimates were again over 100%, excluding the value 100%itself. Another batch of the same formulation of the Test product was then investigated in a fourth Replicate-BE-study which this time showed acceptable results for AUC0-t, AUC0-inf and Cmax (all in the normally acceptable range of 80-125%) but again the point estimates were only closely to 100%.
» Even if it should be assumed that the first two BE-studies were only pilot studies and hence not suitable for statistical inclusion and taking into consideration that the formulation of the Test product was changed after the first BE-study, it still remains unclear why the same formulation of the Test product in the following three performed BE-studies shows varying values concerning point estimates in these studies (all values were lower, then higher and then again lower than 100% successively). This fluctuation can not be explained through the "intra-subject variability" as the latter influences Cmax and hence justifies the widening of the acceptance range for Cmax but not the fluctuating point estimates which are independent of this variability
» This fluctuation is also independent of the number of subjects in the studies.

I think the assessor is implicitly making the assumption that the test product does not vary between batches. Dan vs. Regulator 2-0. The wording highlighted in red lacks qualification. Variability, whenever present, causes fluctuations.

» The Applicant is stating that the differences in point estimates in the four conducted BE-studies might result among others from different test batches. This is exactly the major objection raised by DE that the bioequivalence of the future batches of this formulation is not warranted."

This is certainly not a good comment. The only way to ensure this would be to do the mixed model with batch as random. Bioequivalence by today's definitions require two batches tested against each other and showing equivalence. If the rules change tomorrow, then ok, take that comment into consideration, otherwise just keep your cool and await the referral.

Pass or fail!
ElMaestro