Bioequivalence and Bioavailability Forum

AngusMcLean
★★

USA,
2010-11-07 15:55
(5303 d 16:00 ago)

Posting: # 6111
Views: 15,799

reference scaled bioequivalence [RSABE / ABEL]

Sunday November 7, 201:

I discovered this slide from a presentation from Pharsight

From: 80-125% to ± 1.25^σ(Ref)/0.25

Reference Intra-CV < 30% → BE-range: 80 to 125%
Reference Intra-CV = 35% → BE-range: ≈ 77 to 130%
Reference Intra-CV = 40% → BE-range: ≈ 74 to 135%
Reference Intra-CV = 45% → BE-range: ≈ 71 to 141%
Reference Intra-CV = 50% → BE-range: ≈ 68 to 147%

I understand it is an interpretation of the direction of FDA thinking relating to extending the criteria for means ratio and confidence intervals for BE of highly variable drugs. ;-)

The observed ratio must be within 80-125%; the study design must be partially or fully replicated.

What do you think of it?

Angus

Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2010-11-07 17:08
(5303 d 14:48 ago)

@ AngusMcLean
Posting: # 6112
Views: 14,194

reference scaled bioequivalence

Post reply

Hi Angus!

❝ Sunday November 7, 201:

It’s not necessary to date your posts. But if you do so – do you have a time-machine? ;-)

❝ I discovered this slide from a presentation from Pharsight

Well, do you have a link?

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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AngusMcLean ★★ USA, 2010-11-08 23:22 (5302 d 08:34 ago) @ Helmut Posting: # 6115 Views: 14,105	reference scaled bioequivalence Post reply
	Helmut: there is a link; here it is. I am interested in what folks think of this expansion of the confidence intervals.

Helmut
★★★

Vienna, Austria,
2010-11-09 03:13
(5302 d 04:43 ago)

@ AngusMcLean
Posting: # 6116
Views: 15,138

RSABE: FDA vs. EMA

Post reply

Hi Angus!

❝ I am interested in what folks think of this …

Well, I have no idea what Pharsight calculated here – I get other values. ;-)

See also a comparison with Table I of Tóthfalusi et al. (2009).

CV%  Pharsight slide 15    FDA’s limits       EMA’s limits

30       80% - 125%      [77.0% - 129.9%]    80.0% - 125.0%

35       77% - 130%       73.9% - 135.3%     77.2% - 129.5%

40       74% - 135%       71.0% - 140.9%     74.6% - 134.0%

45       71% - 141%       68.2% - 146.5%     72.2% - 138.6%

50       68% - 147%       65.7% - 152.3%     69.8% - 143.2%

55                        63.3% - 158.0%    [67.7% - 147.8%]

60                        61.0% - 163.8%    [65.6% - 152.4%]

Values in red: The calculated limits at CV=30% are not applicable with FDA's method; 80%-125% are used instead. Expanded limits for CV>50% are not allowed by the EMA; the limits for CV=50% are used instead.

❝ … expansion of the confidence intervals.

<nitpicking>

The confidence interval is the same – the acceptance range (bioequivalence limits) is expanded.

</nitpicking>

It’s important to note that FDA’s and EMA’s approaches are different; FDA’s leads to a discontinuity of the acceptance range at CV=30%, because the scaling CV is 25% – but only applied at CV >30%: See the following two plots (lin and log scale):

[image]

The dotted red lines demonstrate FDA’s procedure: from their formula scaling would start at CV 25%, but is only allowed for >30% – with the scaling factor of 25%. Therefore this nice step. So far about global harmonization.
Orange dots are Pharsight’s values. A vendor-specific ‘compromise’ across the Atlantic? :confused:

For some background see

Haidar SH, Davit B, Chen M-L, Conner D, Lee LM, Li QH, Lionberger R, Makhlouf F, Patel D, Schuirmann DJ, and LX Yu
Bioequivalence Approaches for Highly Variable Drugs and Drug Products
Pharm Res 25(1), 237–41 (2008)
DOI 10.1007/s11095-007-9434-x
free online resource
Endrényi L and L Tóthfalusi
Regulatory Conditions for the Determination of Bioequivalence of Highly Variable Drugs
J Pharm Pharm Sci 12(1), 138–49 (2009)
online abstract, free online resource
Tóthfalusi L, Endrényi L and A García-Arieta
Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence
Clin Pharmacokinet 48(11), 725–43 (2009)
online Abstract

Personally I would prefer EMA’s approach, because no ‘sudden jump’ is introduced at CV=30%. Unfortunatelly EMA restricted scaling to CV ≤50% (higher CVs are to be treated as if CV=50%) for political reasons. No scaling for AUC is scientifically nonsense, IMHO.
If you have to deal with the FDA, simply follow the progesterone guidance from April 2010.

The restriction on the point estimate (GMR) of 80–125% in both regulations is statistically not justified, but entirely political.

P.S.: Search the forum for RSABE, reference scaled bioequivalence, or HVD – a lot of stuff is waiting for you.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes
★★★

Berlin, Germany,
2010-11-09 11:42
(5301 d 20:13 ago)

@ Helmut
Posting: # 6118
Views: 13,872

Farside CV relabelling

Post reply

Dear Helmut,

❝ Well, I have no idea what Pharsight calculated here ...

Me too. Their formula given on the slide
+1.25^{(sigma_Ref/0.25)}
is clearly nonsense. It would give negative lower bounds!
The correct one is
exp(+log(1.25)*sigma_Ref/0.25)
I think.

Taking the numbers for the widened acceptance ranges given, they seems to have a label problem.
(In German: Wo 35% draufsteht sollte auch 35% drin sein!)
Label their CV=35% with 30%, their CV=40% with 35% and so on and you have perfect coincidence with your values within rounding error :cool:

.
Eventually one should remind the author of the slides that labelling falls under the policy of GMP :-D

.

Full ACK to all other of your points.

BTW:
<nitpicking> ------------------
I get for the FDA's widened limits:

CV 30% 76.95 - 129.96 35% 73.83 - 135.45 40% 70.90 - 141.04 45% 68.16 - 146.71 50% 65.60 - 152.45 55% 63.20 - 158.23 60% 60.96 - 164.04

using R-2.12.0 64bit on my new Intel Core i3 machine with Windows 7 Prof.
</nitpicking> ------------------ :wink:

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2010-11-09 16:10
(5301 d 15:46 ago)

@ d_labes
Posting: # 6121
Views: 13,867

Farside CV relabelling

Post reply

Dear D. Labes!

❝ ❝ Well, I have no idea what Pharsight calculated here …

❝

❝ Me too. Their formula given on the slide

❝ +1.25^{(sigma_Ref/0.25)}

❝ is clearly nonsense. It would give negative lower bounds!

Sure. But note that the upper bound is OK, maybe the have calculated L=1/U?

❝ The correct one is

❝ exp(+log(1.25)*sigma_Ref/0.25)

❝ I think.

Right – as always. :cool:

❝ Taking the numbers for the widened acceptance ranges given, they seems to have a label problem.

Oh no!

❝ Eventually one should remind the author of the slides that labelling falls under the policy of GMP :-D .

I have linked this thread to Pharsight’s Extranet ten hours ago…

❝ BTW:

❝ <nitpicking> ------------------

❝ I get for the FDA's widened limits: [...]

❝ </nitpicking> ------------------

Me too – even with bloody M$-Excel (excuse me, Martin). Don’t know what László has done here. Was too late to produce a nice looking plot in R…

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes ★★★ Berlin, Germany, 2010-11-09 17:46 (5301 d 14:10 ago) @ Helmut Posting: # 6122 Views: 13,857	Laszlo's constant Post reply
	Dear Helmut! ❝ Me too - even with bloody M$-Excel (excuse me, Martin). Don’t know what László has done here … He has taken `log(1.25)/0.25 ~ 0.89 exact is 0.892574205...` — Regards, Detlew

AngusMcLean
★★

USA,
2010-11-09 18:12
(5301 d 13:44 ago)

@ d_labes
Posting: # 6123
Views: 13,821

Farside CV relabelling

Post reply

The reason for the confusion is we do not know the calculation that is being made by Pharsight. Consequently we do not know conceptually it is incorrect or if there is an error in it.

I had difficulty getting the same number you got so I must not be interpreting your equation correctly.
exp(+log(1.25)*sigma_Ref/0.25)

For sigma = 0.30 I get 1.3221 for above calculation (when exp(+log(1.25) is used. Am I misunderstanding the parenthesis used? First I evaluated e^log1.25= 1.101761

That is (1.101761)*0.3/0.25 =1.3221

Please can you advise as to my error,

Angus

Edit: Full quote removed. Please delete anything from the text of the original poster which is not necessary in understanding your answer; see also this post! [Helmut]

d_labes
★★★

Berlin, Germany,
2010-11-09 20:48
(5301 d 11:08 ago)

@ AngusMcLean
Posting: # 6124
Views: 13,803

Widened calculations step by step

Post reply

Dear Angus,

❝ Please can you advise as to my error,

Lets try it step by step:

First evaluate log(1.25)/0.25 = 0.892574205....

Second: Convert the CV to the within-subject standard error for Reference:
sigma_Ref=sqrt(log((CV/100)²+1))
gives for CV=30%
sigma_Ref=0.293560379....

Third: Calculate
exp(+0.892574205*sigma_Ref
Should give you for the lower bound
exp(-0.892574205*0.293560379)=0.769492231
and for the upper bound
exp(+0.892574205*0.293560379)=1.29955828.

Fouth: Change the numbers to percent is left to you. :-D

BTW: I think you could figure out this all by your self in a couple of minutes if you remember your high school math. Or didn't you sympathize with your math teacher? :cool:

Hope this helps.

—
Regards,

Detlew

AngusMcLean
★★

USA,
2010-11-09 21:46
(5301 d 10:10 ago)

@ d_labes
Posting: # 6127
Views: 13,905

Widened calculations step by step

Post reply

Many Thanks! At highschool in the UK log(1.25)/0.25 =0.096910013/0.25
=0.38764. In other words the the term "log" pertained to a logarithm to the base 10.

Now for a log to the base e (otherwise known as a natural logarithm or Napierian logarithm) we were taught to use the term "ln". They were first used by John Napier, who was a Scottish mathematician (late 17^th century).

So ln(1.25)/0.25=0.892574205, which is what you have.

On the calculators here in the US there are log and ln functions to use as appropriate.

So now I realize that in future when I read an equation that I have to look out for this difference in notation. :ponder:

Angus

Helmut
★★★

Vienna, Austria,
2010-11-09 23:07
(5301 d 08:49 ago)

@ AngusMcLean
Posting: # 6130
Views: 14,101

ln vs. log

Post reply

Lá maith, Angus!

❝ At highschool in the UK [...] the term "log" pertained to a logarithm to the base 10.

❝ Now for a log to the base e (otherwise known as a natural logarithm or Napierian logarithm) we were taught to use the term "ln". They were first used by John Napier, who was a Scottish mathematician (late 17^th century).

Yeah! I guess you’re still a patriot – even after your move to the former colonies!

BTW, in my posts I’ve used ln rather than log in order to avoid any ambiguities (see also the label of the y-axis in my second plot above). I guess Detlew used log assuming to be evident from the following exp which kind is meant. In SAS and R/S+ log() calls the natural logarithm – so we might be excused.

Since I was trained as a chemical engineer, I’m used to switch my brain. In mechanical engineering and (in-)organic technology we used solely log₁₀, because it’s easy to guess a value from the part before the decimal point: a log₁₀ of 3.69897 means something between 10³ and 10⁴. Only an idiot savant can tell 10^3.69897=5000… In physical chemistry we used mainly ln; like in PK solving systems of differential equations is much easier in the ‘world’ of e. Well known exceptions in chemistry, where the decadic log is used are pK-values. Neutral pH means –log₁₀([H₃O⁺])=7 or 10^-7 molar H₃O⁺.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes
★★★

Berlin, Germany,
2010-11-10 09:31
(5300 d 22:25 ago)

@ AngusMcLean
Posting: # 6134
Views: 13,881

ln on US calculators!

Post reply

Dear Angus!

❝ On the calculators here in the US there are log and ln functions to use as appropriate.

Thanks for pointing at this. Since I do not own an US calculator I was not aware of this distinction.
My use of log() as synonym of the natural logarithm's aka ln() came from the fact that all programming languages, spreedsheets and statistical systems I came across so far (and this are more than 2 :cool:

) use the function log() for that and eventually log10() for the logs to base 10.

That leads me to the opinion that english-like speaking people use log() always in that context. So I must abandon this opinion.
"Man wird alt wie eine Kuh und lernt immer noch dazu" was a slogan of my grandma (One gets old as an cow and learns still thereto) :-D

.

BTW: For the Napierian logarithm you may find this interesting.

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2010-11-10 14:42
(5300 d 17:14 ago)

@ d_labes
Posting: # 6137
Views: 13,821

Spreadsheet addiction

Post reply

Dear D. Labes!

❝ spreedsheets […] use the function log() for that and eventually log10() for the logs to base 10.

Not quite. M$-Excel, OpenOffice-Calc:
LN(EXP(1)) natural (Napierian)
LOG10(10^1)) decadic
LOG(10^1)) no base given, fallback to decadic
LOG(10^1,10)) base 10, same as LOG10()
LOG(2^1,2) base 2 (logarithmus dualis)
LOG(PI()^1,PI()) crazy, but working

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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Helmut
★★★

Vienna, Austria,
2010-11-09 21:11
(5301 d 10:44 ago)

@ AngusMcLean
Posting: # 6125
Views: 14,119

CV vs. sigma

Post reply

Dear Angus!

❝ The reason for the confusion is we do not know the calculation that is being made by Pharsight. Consequently we do not know conceptually it is incorrect or if there is an error in it.

Right.
I would say both.
Five more hours have passed. I'm still waiting for a response at the Extranet (it's a bright day across the pond, isn't it?)...

❝ I had difficulty getting the same number you got so I must not be interpreting your equation correctly.

❝ exp(+log(1.25)*sigma_Ref/0.25)

❝

❝ For sigma = 0.30 I get 1.3221 for above calculation (when exp(+log(1.25) is used. Am I misunderstanding the parenthesis used? [...]

Don’t know, but let's see how to get this right. I didn’t check your parentheses business, but mainly you mixed up CV_WR with sigma_WR, in other words you plugged in CV_WR, whereas a conversion to sigma_WR is required first. See one of my lectures (slides 34pp): sigma_WR=sqrt(ln(CV_WR²+1)).
For example (including all intermediate steps):
CV_WR: 0.30
CV_WR²: 0.09
CV_WR²+1: 1.09
ln(CV_WR²+1): 0.86178
sqrt(ln(CV_WR²+1)): 0.29356 (Hurrah, that’s sigma_WR!)
ln(1.25): 0.22314 (Aha – the usual suspect: upper limit in log-scale.)
ln(1.25)*sigma_WR/0.25: 0.26202 (Scaled limit in log scale; note FDA’s magic 0.25…)
exp(±ln(1.25)*sigma_WR/0.25): 0.7695-1.2996 (Welcome back to the linear world.)

A word about the magic 0.25 in FDA’s method. Note that this value does not correspond to a theoretical start of switching of CV_WR 25%, but corresponds to a CV_WR=sqrt(exp(0.25²)-1)) 25.396% (sigma_WR 0.25). That’s the CV where the dashed lines in my plots intersect the conventional limits. If I recall it right, this value was chosen for convenience (if you are masochistic, follow the links here). Haidar et al. suggested 0.25 in their paper without any justification.

[image]

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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

AngusMcLean ★★ USA, 2010-11-09 21:57 (5301 d 09:58 ago) @ Helmut Posting: # 6128 Views: 13,856	CV vs. sigma Post reply
	Helmut: Thank you for your elegant outline. Please see my new post. It seems that Log X can mean Lnx (otherwise know as log_eX. You see I was taught that Log X means Log₁₀X and for Log_eX we differentiate and use Ln X. Angus

Helmut
★★★

Vienna, Austria,
2010-11-09 22:31
(5301 d 09:24 ago)

@ AngusMcLean
Posting: # 6129
Views: 14,093

log(e) vs. log(10)

Post reply

Hi Angus!

Yes, I saw your post already. I guessed that also, but concentrated on CV vs. sigma – which may make one’s life miserable. In PK (with a few exceptions) ln is used, because it comes handy dealing with the calculus. It’s much easier with base e than with base 10. Of course any base can be used, even the logarithmus dualis (ld – base 2); not uncommon in the IT world. As long as you are consistent, everything is fine.

Some anecdotes: I once saw an application for Australia, where log₁₀ was used. So far, so good. But next they fiddled around with a posteriori power (sigh!). In calculating the CV_intra they used the common formula, ignoring that their MSE was in log₁₀ rather than log_e scale and got stuck. Gotcha! I also saw an enquiry from the Malaysian authority, asking whether log₁₀ or log_e was used in the analysis. Obviously they had a good reason to ask.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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SDavis
★★

UK,
2010-11-19 19:02
(5291 d 12:54 ago)

@ Helmut
Posting: # 6178
Views: 13,828

slide 15 of the Pharsight presentation

Post reply

Angus, Helmut, et al.

Apologies for the delay, been a busy few weeks; the authors are going to look at that slide in the presentation next week and hopefully I/they can post some clarification shortly; thanks for bringing it to our attention.

Have a good week-end,
Simon.

—
Simon
Senior Scientific Trainer, Certara™
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yjlee168
★★★

Kaohsiung, Taiwan,
2010-11-30 08:16
(5280 d 23:40 ago)

@ Helmut
Posting: # 6251
Views: 13,795

one more ref. for the ref. list of RSABE

Post reply

Dear Helmut,

I would like to add one more links for your RSABE ref. list.

BASS XVII Presentations.

And Endrenyi & Tothfalusi's presentation slides (Title: SCALED AVERAGE BIOEQUIVALENCE: AN APPROACH TO RESOLVE A DIFFICULT PROGRAM, pdf) can be found there. BASS website also has many nice presentations.

—
All the best,
-- Yung-jin Lee
bear v2.9.2:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
Download link (updated) -> here

Helmut ★★★ Vienna, Austria, 2010-11-30 16:44 (5280 d 15:12 ago) @ yjlee168 Posting: # 6257 Views: 13,567	Great! Post reply
	Dear Yung-jin, THX, nice presentations! — Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes

reference scaled bioequivalence [RSABE / ABEL]

reference scaled bioequivalence

reference scaled bioequivalence

RSABE: FDA vs. EMA

Farside CV relabelling

Farside CV relabelling

Laszlo's constant

Farside CV relabelling

Widened calculations step by step

Widened calculations step by step

ln vs. log

ln on US calculators!

Spreadsheet addiction

CV vs. sigma

CV vs. sigma

log(e) vs. log(10)

slide 15 of the Pharsight presentation

one more ref. for the ref. list of RSABE

Great!