Netzolin
☆

Mexico,
2015-01-05 19:06
(2294 d 11:53 ago)

Posting: # 14222
Views: 7,051

## IC90 vs IW90 [General Sta­tis­tics]

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

Thanks so much!
Helmut
★★★

Vienna, Austria,
2015-01-06 01:43
(2294 d 05:16 ago)

@ Netzolin
Posting: # 14223
Views: 6,127

## Forget Westlake’s symmetrical CI

Hi Netzolin,

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

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 CVintra (7.3%) but high CVinter (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.

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

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2015-01-06 14:38
(2293 d 16:20 ago)

@ Helmut
Posting: # 14225
Views: 5,875

## Forget Westlake’s symmetrical CI

Hi Hötzi,

» 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.

I love it, especially the middle one. It just does not strike me as being connected to the real world in any meaningful way
Quite possible it made sense to somebody. At some point. Perhaps. Or maybe not.

I wonder what the figures will look like for a drug which proves to be BE but with 1.00 not part of the conventional 90% CI?

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2015-01-07 00:41
(2293 d 06:17 ago)

@ ElMaestro
Posting: # 14231
Views: 5,991

## Forget Westlake’s symmetrical CI

Hi ElMaestro,

» […] It just does not strike me as being connected to the real world in any meaningful way
» Quite possible it made sense to somebody. At some point. Perhaps. Or maybe not.

I think it’s crap. I heard about it in the very early 1980s, when one of our sponsors suggested to report it as “additional information”. I said that’s rather “subtractive information” but he insisted. Life at a CRO is hard. A quote from the paper:*

This author's experience with bioequivalence trials suggests that most clinicians tend to make their equivalence statements in a symmetrical manner, stating, for example, that if the absolute (or possibly proportional) difference between µn and µs, is less than some spe­cified value, then N is therapeutically equivalent to S and if not, doubt as to therapeutic equi­va­lence exists.

» I wonder what the figures will look like for a drug which proves to be BE but with 1.00 not part of the conventional 90% CI?

I don’t understand. This is exactly my example above (BE, but 1 not within the conventional CI). Can you help my little brain?
Our 2,2,2 reference data sets in Phoenix/WinNonlin 6.3 (dropped in v6.4):

        90% CI        WL’s 90% CI   A   90.76 –  99.62   91.76 – 108.24 B   51.45 –  98.26   55.45 – 144.55 C   39.41 –  87.03   43.32 – 156.68 D   51.45 –  98.26   55.45 – 144.55 E   55.71 – 151.37   53.52 – 146.48 F   93.37 – 106.86   93.26 – 106.74 G   88.46 –  95.99   89.26 – 110.74 H   86.81 – 100.55   88.27 – 111.77

BTW, sometimes it is not possible to compute WL’s CI (see the paper).

• Westlake WJ. Symmetrical Confidence Intervals for Bioequivalence Trials. Biometrics. 1976;32(4):741–4. doi:10.2307/2529259.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
ElMaestro
★★★

Denmark,
2015-01-07 05:01
(2293 d 01:58 ago)

@ Helmut
Posting: # 14232
Views: 5,848

## My mistake

Hi Hötzi,

» » I wonder what the figures will look like for a drug which proves to be BE but with 1.00 not part of the conventional 90% CI?
»
» I don’t understand. This is exactly my example above (BE, but 1 not within the conventional CI). Can you help my little brain?

Sorry, you are absolutely right. I am a moron

Pass or fail!
ElMaestro
nobody
nothing

2015-01-07 12:16
(2292 d 18:42 ago)

@ ElMaestro
Posting: # 14235
Views: 5,788

## My mistake

What is really bizarre in my opinion is that such nonsense surfaces again after some decades... but why should pharmaceutics be more clever than, lets say, politics or so. Just recycling the old errors is part of the business, apparently

Kindest regards, nobody