Bioequivalence and Bioavailability Forum

Hi Netzolin,

❝ Does somebody know the difference to use IW90 (westlake intervals 90%) vs IC90 (Confidence Intervals 90%) for BE acceptancy.

Short answer: Yes.

Long answer: Westlake’s symmetrical confidence interval went to the statistical waste bin ages ago. No regulatory agency would accept it. In the latest release of Phoenix/WinNonlin it was removed from the output. Westlake’s CI is an information sink. His idea was: Physicians don’t feel comfortable with the 90% CI – which is asymmetrical around 100% – but after log-transformation symmetrical around ln(PE). In order to make their lives less miserable his rationale was: In the conventional CI we split the t-values symmetrical at 0.05. It should be possible (by an iterative procedure) to find two tails in such a way that they

• sum up to 0.1 and
  
• the limits of the CI are symmetrical around 1.
  
• The patient’s risk is maintained and their physicians are less confused.

Example: A drug with very low CV_intra (7.3%) but high CV_inter (54%). Let’s ignore the regulatory requirements (n ≥12); for such a low CV even six subjects are enough.

Subject Period Sequence Treatment Data
   1      1       TR        T     81.2
   2      1       RT        R     33.6
   3      1       TR        T     27.7
   4      1       RT        R     87.9
   5      1       RT        R     47.1
   6      1       RT        R     27.8
   7      1       TR        T     38.8
   8      1       TR        T     21.8
   1      2       TR        R     62.0
   2      2       RT        T     42.9
   3      2       TR        R     21.7
   4      2       RT        T     95.2
   5      2       RT        T     52.9
   6      2       RT        T     32.7
   7      2       TR        R     35.0
   8      2       TR        R     21.9

T/R: PE     116.40%
     90% CI 108.40 – 124.99%
     90% WL  77.30 – 122.70%
The test is BE (90% CI within 80–125%), though statistically significant different (the 90% CI does not include 100%). Even if the PE is not reported we can calculate it from \(\small{\sqrt{108.40\times124.99}}\).
Westlake’s CI leaves us out in the rain. In the original form it would have been reported as “with 90% probability the test is not more than ±22.70% different from the reference”. No way to even guess whether T was higher or lower than R. Physicians get the false impression that there is a 5% chance each to be ≥–22.7% and ≤+22.7% different to the reference.
Homework: Estimate the chance for a patient to have a BA of 77.3% or 122.7% of the reference.*

According to FDA’s definition (too lazy to search now) the procedure should be reversible; if T is BE to R, R should be BE to T as well. Let’s do that:

R/T: PE     85.91%
     90% CI 80.01 –  92.25%
     90% WL 81.50 – 118.50%
Fine with the conventional analysis. Note that 1/1.1640=0.8591, 1/1.2499=0.8001, and 1/1.0840=0.9225. If we compare the CI in the log-domain only the order or values and their signs switches (+0.08070, +0.22305 ⇒ –0.22305, –0.08070). Mission accomplished.
But hey, Westlake now tells us ±18.50%. Lesson learned: For any ratio ≠ 1, Westlake’s procedure is not reversible. Forget it.

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• ~0.001% and ~9.999%. A little bit different from the 5% the physician would expect at each side.