Bioequivalence and Bioavailability Forum

Dear Helmut!

❝ Had to have a break. Let’s see what I got from n 12, CV 6%, 10⁶ sim’s:

❝ 50331 studies passed when BE was defined as the unrounded upper CL ≤1.25 (α_emp n.s.). 50503 studies passed based on round(CLhi,4) ≤1.25 (α_emp sign. >0.05). In increasing order (skipping 170):

❝     Unrounded.lo     Unrounded.hi  Rd.lo  Rd.hi

❝ 1.14406215516423 1.25000008857710 1.1441 1.2500

❝ …

❝ 1.16009942086582 1.25004974319996 1.1601 1.2500

❝ and

I'm not certain if I understand your numbers given. How do the above correspond to below? Numbers from cases which were judged BE if rounded and not BE if not rounded?

❝     Unrounded.lo         Unrounded.hi         Rounded.lo         Rounded.hi

❝ Min.   :1.11998223   Min.   :1.25000009   Min.   :1.12000000   Min.   :1.25

❝ 1st Qu.:1.14730961   1st Qu.:1.25001184   1st Qu.:1.14730000   1st Qu.:1.25

❝ Median :1.16346327   Median :1.25002528   Median :1.16345000   Median :1.25

❝ Mean   :1.16222013   Mean   :1.25002554   Mean   :1.16221977   Mean   :1.25

❝ 3rd Qu.:1.17608605   3rd Qu.:1.25003838   3rd Qu.:1.17610000   3rd Qu.:1.25

❝ Max.   :1.20299871   Max.   :1.25004974   Max.   :1.20300000   Max.   :1.25

❝ If I round I get more significant results.

❝ Mr X will tell me “Nice simulations proving the patient’s risk is not maintained.”

Augmented with the reply “If and only if one uses your (assuming Mister X to be a regulator) f*#*g rule of rounding the CI's.”

BTW: My original question was more concerned with empirical alpha>0.05 significant without rounding. I wouldn't expect such cases to be real. Otherwise the theory behind our BE statistics is wrong.

BTW2: There is a question that bothers me, every time I think about it:
assuming BE if
   0.8 ≤ lCL and uCL ≤ 1.25 (I)
or better
   0.8 < lCL and uCL < 1.25  (II).
At least in formulating the bioequivalence alternative hypothesis it is always written:
   Θ1< µT/µR < Θ2
and the corresponding two one-sided t-statistics have to be t_l < -t(1-α,df) and t_u > t(1-α,df). Does this transform really to (I) for the confidence interval inclusion rule? The EMA guidance is here clear: "To be inside the acceptance interval the lower bound should be ≥ 80.00% when rounded to two decimal places and the upper bound should be ≤ 125.00% when rounded to two decimal places." But the regulatory point of view is not necessarily the scientific one as we noticed more than once.

In case of no rounding this doesn't make much difference since lCL=0.8 and uCL=1.25 (without rounding) are obtained with probability of nearly zero. But in case of rounding ...