Bioequivalence and Bioavailability Forum

Dear Helmut,

IMHO generally it would be "Good mathematical practice" not to round intermediate results. At least I was teached this in my very first courses during studying chemistry. Maybe statisticians in England or wherever have another view arosen from their daily handling of errors of all kind .

Theoretical statistician. A second class mathematician who imagines that he is a first class statistician.
Applied statistician. A second class statistician who imagines that he is a first class scientist.
Medical statistician. A second class scientist without any imagination.
Guernsey McPearson's Drug Development Dictionary

❝ From the table in the GL, it’s clear that 0.760 – rather than ln(1.25)/sqrt(ln(0.3²+1)) – should be used.

Seems right, beside the fact that the differences to the 'exact' formula are only marginal (+1 in the last decimal if % is used) and should not have any practical impact.

May be the whole story is a bit hair-splitting as always with us.
The guideline does not adress at any time that k is connected to the scaling standard error s₀ or CV₀ via the well known formula you give above. Eventually they even don't know this formula . They formulate the widening via Boddy's formula exp(+k*s_WR).
In that sense they haven't defined a regulatory s₀ or CV₀ but rather a regulatory k. Thus rounding is spirited off in a magical way if we accept this view.

Take k=0.760 to make your regulator feel confident that you accept his competence to define it that . Don't forget the zero in reporting k!

BTW: The Americans are a little bit smarter or nearer to the theory in defining a s₀=0.25 and using log(1.25)/s₀ as BEL for
-BEL < (µT-µR)/sWR < BEL .
Aside from the fact that the value 0.25 is not so well chosen in leading to the already discussed discontinuity at CV=30%.
BTW2: In the literature about scABE you can find our s₀ to various degrees of precision f.i. 0.29, 0.294 or 0.2936. This in turn leads to k=0.769, 0.759 or 0.760 with 3 decimals.

❝ Should we round another two times (both the CL and the acceptance limits to two decimal places) – in analogy to Section 4.1.8?

I would do so if 0.760 is accepted.

Dear HS,

in practice this will make a difference to very few studies. Never say never, of course, but the difference in acceptance range that the different options allow for the constant will only seldomly change the regulatory decision.

But if you insist, then I will take this view on it:
The guideline says:
"(...) For these parameters the 90% confidence interval for the ratio of the test and reference products should be contained within the acceptance interval of 80.00-125.00%."
Look closer. Did you see it? If EMA's wish is to work with two decimals on the acceptance range then so be it. Then they could have chosen to write that constant with two decimals. However, working with "X decimals" is in itself dubious to some. In a mathematical sense when uncertainty is involved it might make a bit more sense to work with X significant digits. The EMA could have said they want the CI's with X signif. digits on both ends and hence also specified the constant with X significant digits. This would at least follow some stringency.
Coincidentially the last digit in the constant is 0 so specifying with two or three decimals (or sigdigs) does not make much of a difference anyway.