ratnakar1811
★    

India,
2013-03-05 08:30
(2876 d 00:51 ago)

Posting: # 10151
Views: 24,819
 

 AUCt not covering at least 80% of AUCinf [Regulatives / Guidelines]

Dear All,
As per EMA guideline AUC(0-t) should cover at least 80% of AUC(0-∞) but in one of my study I have got this percentage more than 20% and the % in the study is around 31%.

Is there any way by which I can justify this issue? Anybody has any such experience with the European regulators’?
Your views are highly appreciated.

Best Regards,

Ratnakar
d_labes
★★★

Berlin, Germany,
2013-03-05 11:12
(2875 d 22:09 ago)

@ ratnakar1811
Posting: # 10153
Views: 18,140
 

 AUCt not covering at least 80% of AUCinf

Dear ratnakar,

the 80% coverage of AUC(0-tlast) in relation to AUC(0-inf) is specified further in the EMA guidance under the heading "Reasons for exclusion":
"As stated in section 4.1.4, AUC(0-t) should cover at least 80% of AUC(0-∞). Subjects should not be excluded from the statistical analysis if AUC(0-t) covers less than 80% of AUC(0-∞), but if the percentage is less than 80% in more than 20% of the observations then the validity of the study may need to be discussed."

I interpret the 20% of observations as 20% of AUC values i.e. 2xsubjects in a classical 2x2x2 crossover.

Don't ask me how the validity of the study may be discussed. Duno.

Regards,

Detlew
ratnakar1811
★    

India,
2013-03-06 08:50
(2875 d 00:30 ago)

@ d_labes
Posting: # 10157
Views: 17,955
 

 AUCt not covering at least 80% of AUCinf

Dear d_labes/forum members,

Yes, in more than 20% of observations AUCinf has been extrapolated for more than 20% and i have received a query from EMA to discuss the validity of the study.

I am just thinking what all points should be considered for the justification and further is there any way by which it can be justified?

Best Regards,

Ratnakar
ElMaestro
★★★

Denmark,
2013-03-06 11:10
(2874 d 22:11 ago)

@ ratnakar1811
Posting: # 10158
Views: 18,035
 

 AUCt not covering at least 80% of AUCinf

Hello Ratnakar,

» Yes, in more than 20% of observations AUCinf has been extrapolated for more than 20% and i have received a query from EMA to discuss the validity of the study.

From EMA? I guess you mean from one or more of the national agencies?

» I am just thinking what all points should be considered for the justification and further is there any way by which it can be justified?

Try and tell why this happened in the first place. If it was not intended then I guess your study could be argued to be slightly badly planned for which there are no obvious and acceptable excuses. On the other hand if you deliberately shortened sampling time for some reason (PI opinion, ethics, ADME-tox properties) then please give a little further info and let's see.

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ElMaestro
Helmut
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2013-03-06 14:35
(2874 d 18:46 ago)

@ ElMaestro
Posting: # 10162
Views: 17,915
 

 ADME-tox?

Hi ElMaestro!

» […] if you deliberately shortened sampling time for some reason (PI opinion, ethics, ADME-tox properties) then please give a little further info and let's see.

No sure what you mean by ↑ that. Shortening the sampling wouldn’t help.

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ElMaestro
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Denmark,
2013-03-06 16:40
(2874 d 16:41 ago)

@ Helmut
Posting: # 10164
Views: 17,926
 

 ADME-tox?

Hi HS,

» No sure what you mean by ↑ that. Shortening the sampling wouldn’t help.

Sorry, this was a dumb formulation, you are absolutely right. If the tox properties are unfavourable then one might need to dose so low that the drug is adme'd away by the time one for some reason or other would like to measure. Erm... Heh... even this sounds dumb now. Does bebac offer language courses?

PS: I don't mean to indicate this would be an excuse in itself, rather it could be a cause.

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Helmut
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2013-03-06 17:19
(2874 d 16:01 ago)

@ ElMaestro
Posting: # 10165
Views: 17,843
 

 OT

Servus!

» Does bebac offer language courses?

Depends. I’m far from being competent in standard German although I could offer counseling in its Austrian variant. The only language I really master is Viennese. Are you interested? Free lodging included. Visiting my favorite Heurigen mandatory.

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ElMaestro
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Denmark,
2013-03-07 17:19
(2873 d 16:01 ago)

@ Helmut
Posting: # 10171
Views: 17,790
 

 OT

Hi H.,

» Depends. I’m far from being competent in standard German although I could offer counseling in its Austrian variant. The only language I really master is Viennese. Are you interested? Free lodging included. Visiting my favorite Heurigen mandatory.

Austrian German is a funny kind of Mickey Mouse language. I like the sound of it.
Let's go and visit that place of yours next time I am in the area. Oh and haven't you heard? I converted to the Vegetophysticiologists. We only drink cabbage juice and eat mung beans.

Pass or fail!
ElMaestro
Helmut
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2013-03-07 17:26
(2873 d 15:55 ago)

@ ElMaestro
Posting: # 10172
Views: 17,568
 

 OT

Hi ElMaestro!

» Austrian German is a funny kind of Mickey Mouse language. I like the sound of it.

Yep. For me it’s always amazing that native speakers of English love the Austrian’s accent whereas they hate the Kraut’s. Both sound awful to me.

» […] I converted to the Vegetophysticiologists. We only drink cabbage juice and eat mung beans.

Go to Gujarat. Next step Breatharianism.

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Helmut
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2013-03-06 14:30
(2874 d 18:51 ago)

@ ratnakar1811
Posting: # 10161
Views: 17,973
 

 Science vs. regulations

Dear Ratnakar,

EMA’s opinion [sic] that AUCt is a reliable estimate of extent of absorption only if AUCt ≥ 80% of AUC is scientifically questionable if (!) IR formulations are concerned (absorption practically completed at 2–4× tmax). Therefore, we need more information.
  • IR or MR formulation? If MR, DR or CR?
  • Pilot studies performed? If yes, outcome?
  • Sampling planned based on average t½ from the literature? If yes, please give x±SD and sample size in your study.
  • Observed t½ (x±SD, range)?
  • tmax, tlast?

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cakhatri
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India,
2013-03-10 08:59
(2871 d 00:22 ago)

@ Helmut
Posting: # 10179
Views: 17,158
 

 Science vs. regulations

Dear All,

This is interesting topic as I too have had similar situation where in the ratio of AUC0-t / AUC0-inf was less than 80% in several cases.

Can anyone clear my doubt on this, does this apply to the untransformed or Ln transformed data

The ratios were fine with the Ln transformed data.

Regards
Chirag
Helmut
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2013-03-11 01:17
(2870 d 08:04 ago)

@ cakhatri
Posting: # 10181
Views: 17,272
 

 ratio = difference of logs!

Dear Chirag,

» […] does this apply to the untransformed or Ln transformed data
»
» The ratios were fine with the Ln transformed data.

Raw data! You need the ln-transformed data only in the BE-statistics. You would have to calculate the difference of logs and backtransform to get % covered. Example:

AUCt 375, AUC 500, covered: 100×375/500=75%.
lnAUCt 5.9269, lnAUC 6.2146, covered: 100×ℯ5.9269–6.2146=75%.

A ratio of logs (95.37%) is nonsense.

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Helmut
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2013-03-11 03:17
(2870 d 06:03 ago)

@ Helmut
Posting: # 10182
Views: 17,429
 

 Science vs. (EMA) GL aka PK primer

Dear all,

replying myself to clarify things. Starter: Scheerans et al. (2008).1 tmax in a monoexponential model is the root of the first derivative of the concentration-time curve and given by

\(\small{t_{max}=\log(k_a / k_{el}) / (k_a-k_{el})}\)

The inflection point tinpt where the sign of the curvature changes (or the tangent moves from above to below the curve) is the root of the second derivative and given by

\(\small{t_{inpt}=2\cdot \log(k_a / k_{el}) / (k_a-k_{el})}\)

If you want to play around yourself I suggest to convert the Bateman-function (with volume, fraction absorbed, and rate constants) to a sum of expo­nen­tials, i.e.,

\(\small{f(x)=A(e^{-k_{el}\cdot x}-e^{-k_a\cdot x})}\).

The first and second derivatives are

\(\small{f'(x)=A(-k_{el}\cdot e^{-k_{el}\cdot x}+k_a\cdot e^{-k_a\cdot x})}\) and
\(\small{f''(x)=A(k{_{el}}^{2}\cdot e^{-k_{el}\cdot x}-k_{a}^{2}\cdot e^{-k_a\cdot x})}\).

The percentage absorbed is given by

\(\small{\%\; abs = 100(1-e^{-k_a \cdot x})}\)

AUC in the interval [0, a] is given as the definite integral of ƒ(x) by

\(\small{A \left ( (e^{k_a \cdot a}-1)/k_a - (e^{k_{el}\cdot a}-1)/k_{el} \right )}\)

Example: A 400, ka 1.3863 (t½a 0.5), kel 0.6931 (t½el 1). Although Scheerans et al. recom­mended their procedure for ka ≥ 3kel in order to avoid problems with flip-flop PK (which is unlikely for IR formulations) I used a ratio of 2 in order to get nice numbers.

[image]

At tmax 75% are absorbed (AUCt/AUC 25%) and at tinpt already 93.75% (AUCt/AUC 56.25%). When do we have a ratio of 80%? At 3.244 (where 98.89% are absorbed). That’s a very, very conservative value. Note that tinpt equals four absorption half-lives (alternative method for the calculation of % absorbed: 100 – 100/24·t½a = 93.75%). If one wants to be more conservative and follow the logic of the GL (wash-out, saturation to steady state) and use five half-lives one could stop at 2.5.

tlast        % abs  % AUC
1.0 = tmax   75.00  25.00
2.0 = tinpt  93.75  56.25
2.161        95.00  60.28
2.5 = 5×t½a  96.88  67.77
3.244        98.89  80.00
3.322        99.00  81.00

So why a cut-off of 80%?* Since tinpt is a reasonable starting point for the estimation of λz (forget max. R²adj including earlier time points since elimination is contaminated by absorption), it should be possible to have ≥3 data points in the interval [tinpt, tlast]. We can expect to get a reliable estimate of λz. But what’s the use of it? The EMA’s metric for extent of absorption is AUCt. We could reliably estimate it with an earlier cut-off as well!2,3 Are we comparing λz of test and reference? No. On the contrary – we assume identical inter-occasion clearances (or V + kel if you belong to the other church).
IMHO, the cut-off of 80% is scientifically not justified for monoexponential models (including ones with a lag-time: homework). Would only make sense if we would use AUCs corrected by kel,4 which seems not to be acceptable by EMA (at least). It’s strange to judge the validity of a study based on eli­mi­na­tion rather than essentially complete absorption.

Unfortunately it is not that easy for multicompartimental models – or even worse – profiles with multiple peaks, though absorption will follow the same time course. MR (CR in particular) is another cup of tea. We might be in flip-flop limbo and personally I would not use AUCt as the main metric at all. I’m curious what the draft MR GL will tell us… I will propose AUC with an extrapolated area of well below 20%.

@Ratnakar: If you want help it would be a good idea to answer all of the questions in my previous post (see the Forum’s policy).


  1. Scheerans C, Derendorf H, Kloft C. Proposal for a Standardised Identification of the Mono-Exponential Terminal Phase for Orally Administered Drugs. Biopharm Drug Dispos. 2008;29:145–57. doi:10.1002/bdd.596.
  2. Midha KK, Hubbard JW, Rawson MJ. Retrospective evaluation of relative extent of absorption by the use of partial areas under plasma concentration versus time curves in bioequivalence studies on conventional release products. Europ J Pharm Sci. 1996;4:381–4. doi:10.1016/0928-0987(95)00166-2.
  3. Midha KK, Hubbard JW, Rawson MJ, Gavalas L. The application of partial areas in assessment of rate and extent of absorption in bioequivalence studies of conventional release products: Experimental evidence. Europ J Pharm Sci. 1994;2(5–6):351–63. doi:10.1016/0928-0987(94)00062-X.
  4. Abdallah HY. An Area Correction Method To Reduce Intrasubject Variability In Bioequivalence Studies. J Pharm Pharmaceut Sci. 1998;1(2):60–5. [image] free resource.

  • Note that the FDA – although both AUCt and AUC are required – doesn’t have such a cut-off.

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qualityassurance
☆    

Jordan,
2020-04-23 14:11
(269 d 20:10 ago)

@ Helmut
Posting: # 21345
Views: 9,483
 

 Science vs. regulations

Dear Helmut and all,

Hope everyone is good and safe.

The same query raised by MoH and i want to answer. Could you help me?

» IR or MR formulation? If MR, DR or CR?
IR

» Pilot studies performed? If yes, outcome?
No

» Sampling planned based on average t½ from the literature? If yes, please give x±SD and sample size in your study.
The last two time point was 24.00 & 48.00. It was planned based on PARs (12.00 & 24.00 was the last time point in two PARs). 36 subjects

» Observed t½ (x±SD, range)?
For reference (10.03 ±4.09, 3.5-19.0)
For test (9.2 ±2.96, 3.22-17.0)

» tmax, tlast?
For reference: Tmax: 0.67, Tlast: 28.25
For test: Tmax: 0.50, Tlast: 23.91

Forgive me for the formatting. I tried my best.
Regards.
Helmut
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2020-04-23 17:32
(269 d 16:49 ago)

@ qualityassurance
Posting: # 21347
Views: 9,467
 

 Science vs. regulations

Hi qualityassurance,

that’s an interesting case.

» » Observed t½ (x±SD, range)?
» For reference (10.03 ±4.09, 3.5-19.0)
» For test (9.2 ±2.96, 3.22-17.0)
»
» » tmax, tlast?
» For reference: Tmax: 0.67, Tlast: 28.25
» For test: Tmax: 0.50, Tlast: 23.91

I played around with your data. Such an early tmax means that this IR product acts practically like a solution (absorption t½ 10–15 minutes). However, there is an extreme between-subject variability in elimination. That’s why you missed the 80% rule in some subjects.
In retrospect it would have been better to opt for truncated AUC0–72. Then you would not have to worry about extrapolation.
However, think about the subject line of the post. At 2×tmax absorption is practically complete (~96.12%). You could even take a very conservative approach with 4×tmax (~99.85%). We are interested in comparing the performance of the formulations, not to assess its well-known PK, right?
Hence, scientifically the large extrapolated AUC you see in some subjects is not relevant at all. Kamal Midha showed this nice example of partial AUCs. Once absorption is essentially complete, later T/R-ratios are extremely stable – only their variability increases.
If the assessor prefers to “tick-the-box-in-the-form”, cards are stacked against you. Sorry.

» Forgive me for the formatting. I tried my best.

No worries; I edited your post a bit.

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Achievwin
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US,
2020-05-07 22:59
(255 d 11:22 ago)

@ Helmut
Posting: # 21404
Views: 7,942
 

 Science vs. regulations

Good discussions:

» » For reference: Tmax: 0.67, Tlast: 28.25
» » For test: Tmax: 0.50, Tlast: 23.91

Aren't we lost in pure numbers and forgot to look at the individual curves?
In order to have accurate AUC estimations you need to have at least two measurable concentrations (non-BQL) before Tmax and as many time points as possible on either side of Tmax.

With 067 and 0.50 hours as Tmax how many blood draws you can practically take (assuming this is an oral formulation) may be we have to go to IV blood sampling schedule.

I saw somewhere blood samples were taken 24 and 48 hrs (assuming these are ambulatory samples there will be lot of time variation.), Hardly we completed 1 or 2 half lives. and we expect to cover 80% AUC?

Even assuming we covered AUC there is always some bad apples, in my experience due to some bad data points in the extremes you may tend to have all kinds of elimination patterns (positive slope, bad two many missed blood draws or BQL values… so it is not surprising that AUC% is less than 80% in more than 30% subjects what is that 30% in 12 or 18 subjects?

If i am designing study I take following precautions (everyone knowns these things but I am listing)
  1. see you heavy sampling either side of your Tmax (this covers majority of the AUC and accurately determines Cmax).

  2. Ensure you have at least two blood draws for every half life

  3. Capture blood draws up to 4 half lives, if your assay permits your half life is not long

Then a priori in the protocol SAP include limitations on reporting AUCinf and %Extrp.
  • R2>0.800
  • AUC% Extrp should be more than 80%
  • if two consecutive blood draws are BQL and hen you see a reportable value in elimination phase no kEL, t1/2 aucINF % etrp will not be reported , at least FDA understands that AUCinf some times is skewed and excluding some subjects is always allowed with proper explanation.

Hope this helps.


Edit: Please don’t shout[Helmut]
Helmut
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2020-05-07 23:54
(255 d 10:27 ago)

@ Achievwin
Posting: # 21405
Views: 7,926
 

 Science vs. regulations

Hi Achievwin,

» Then a priori in the protocol SAP include limitations on reporting AUCinf and %Extrp.
» 1. R2>0.800

Why this – arbitrary – number? Given, I have seen it in lots of SAPs.
\(\small{R^2}\) (strongly!) depends on the number of time points \(n\) (see this rather old thread). \(\small{R_{\textrm{adj}}^{2}}\) is better though still not independent from \(n\) (that’s a misconception sold by software vendors).
If clearance is variable and/or the analytical variability is high, a low correlation may be perfectly fine, whereas in the opposite case even 0.9 may indicate a poor fit. Unless you have data of a previous study with the same analytical method, IMHO, a pre-specified cut-off does not make sense.
Furthermore, never trust in results of a silicon-based life-form. Visual inspection of the fit is mandatory.

PS: 0.8 with three significant digits: 0.8005 is OK and 0.8004 not. Really?

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Brus
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Spain,
2018-11-20 13:01
(789 d 20:20 ago)

(edited by mittyri on 2018-11-20 14:25)
@ ratnakar1811
Posting: # 19644
Views: 12,733
 

 AUCt not covering at least 80% of AUCinf

Dear Ratnakar,

How did you justify the clarification?

How can it be justified that the extrapolated AUC is greater than 20%?

Best Regards,

Brus


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Mittyri]
Astea
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Russia,
2020-06-05 19:05
(226 d 15:15 ago)

@ Brus
Posting: # 21501
Views: 6,100
 

 AUCt not covering at least 80% of AUCinf

Dear Friends!
I've got I question concerned to this issue.
Until now I thought that the rule of 80% AUCinf was invented in order to demonstrate that the total duration of sampling is sufficient. But consider a following case:
IR drug with T1/2=12-18 hours (according to literature data).
The last sampling time in the protocol was choosen to be 48 hours with a large step before, like: ..8 hours, 12 hours, 24 hours and 48 hours.
For several subjects the PK curves were like this:

[image]
The concentration in the last point was below LLOQ, however AUClast didn't cover 80% of AUCinf.
So I may conclude, although the rule was not followed, the duration of the sampling time was sufficient. In this case the rule may indicate: too large distance between sample time points (48-24=24) that is an error in study planning or too large LLOQ. Am I right in this conclusion? How can regulators interpret this issue?

"Being in minority, even a minority of one, did not make you mad"
Helmut
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2020-06-06 12:02
(225 d 22:19 ago)

@ Astea
Posting: # 21502
Views: 5,954
 

 So what?

Hi Nastia,

» Until now I thought that the rule of 80% AUCinf was invented in order to demonstrate that the total duration of sampling is sufficient.

Read the entire thread again. ;-)
I’m referring to the EMA’s guideline. Too lazy to Google-translate the ones in Russian.
The phrase in the EMA’s guideline “The sampling schedule should also cover the plasma concentration time curve long enough to provide a reliable estimate of the extent of exposure…” is nonsense. Why it was invented [sic] is beyond my intellectual reach.
  • We are interested in comparing the in vivo characteristics (ƒ, ka, tlag) to detect potential biopharmaceutical differences of formulations. Differences in ƒ are reflected in AUC and all three* in Cmax.
  • However, what happens once absorption is complete, is a property of the drug and hence, not relevant in BE (we are assuming identical clearances). Therefore, the FDA does not have such a bizarre “AUC0–t ≥ 80% AUC0–∞ rule”.

» But consider a following case: […]

The tmax is ≤ 1 h and hence, t½,a ≤ 30 minutes. It means that at four hours ≥ 99.6% were already absorbed. That’s what we are interested in. What follows shows that we have a two-compartment model (and possibly additional enterohepatic recycling). Nice to know, but already described by the innovator, right?
Any () AUC after 2–4times tmax is a reliable estimate of the extent of exposure. Full stop.

» So I may conclude, although the rule was not followed, the duration of the sampling time was sufficient. In this case the rule may indicate: too large distance between sample time points (48-24=24) that is an error in study planning or too large LLOQ. Am I right in this conclusion?

EMA: “Subjects should not be excluded from the statistical analysis if AUC0–t covers less than 80% of AUC0–∞, but if the percentage is less than 80% in more than 20% of the observations then the validity of the study may need to be discussed.”

OK, discuss it. It’s quite possible that even with an additional sampling point at 36 h (≥ LLOQ) you would have ended with < 80% AUC0–∞ as well. For an IR formulation you could have sampled longer and with AUC0–72 this entire extrapolation business would disappear.
Let’s play the devil’s advocate. IR formulation, drug has a fast distribution and long elimination, the LLOQ is sufficient to measure all samples at the last sampling time t; two studies:
  1. t = 71 h → AUC0–71 (< 80% AUC0–∞ in all cases):
    Problem (why?).
  2. t = 72 h → AUC0–72 (assessment of AUC0–t/AUC0–∞ not required):
    No problem (why not?).

» How can regulators interpret this issue?

Can or will? Regulators have the whip hand and therefore, can do whatever they like. If the assessor is a “checkbox-bureaucrat”, cards are stacked against you. If the assessor is a scientist, IMHO, good chances.

Science should always be the basis
of regulatory requirements.

    Joachim Röhmel (former head of biostatistics/BfArM)
    30th Annual Conference of the International Society fo Clinical Biostatistics.
    Prague, August 25th, 2009.




  • Cmax is a composite metric (influenced by ƒ) and hence, does not unbiased represent the absorption characteristics (ka, tlag). Cmax/AUC would be a better metric. Lots of publications, ignored in guidelines.

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Astea
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Russia,
2020-06-06 21:11
(225 d 13:09 ago)

@ Helmut
Posting: # 21503
Views: 5,904
 

 Carrot and whip

Dear Helmut! I'm grateful for your reply!

» Read the entire thread again. ;-)

Ok, my HW was not perfect :-) No I reread it. Still don't understand what to argue to the assessors...

By the way, there is a typo in f' (the graph is correct), first term should be with minus:

\(\small{f'(x)=A(-k_{el}\cdot e^{-k_{el}\cdot x}+k_a\cdot e^{-k_a\cdot x})}\)}

and for AUC as the integral from 0 to a, "a" should go instead of x:

\(\small{A \left ( (e^{k_a \cdot a}-1)/k_a - (e^{k_{el}\cdot a}-1)/k_{el} \right )}\)


» I’m referring to the EMA’s guideline. Too lazy to Google-translate the ones in Russian.

Do not bother yourself, EAEC experts had already translated it: "Количество отобранных образцов также должно быть достаточным, чтобы обеспечить надежную оценку длительности экспозиции. Это достигается, когда AUC(0–t) перекрывает не менее 80 процентов от AUC(0–∞)."
Though the statement is not scientifically based it is still in the list of regulator's requirements. So in case if some problems with the "80% covering rule" we have to justify somehow that the validity of the study should not be called into question - that's what I've asked about.

» Therefore, the FDA does not have such a bizarre “AUC0–t ≥ 80% AUC0–∞ rule

By the way, was this question ever discussed on the conferences on harmonization?

» ...71 h → AUC0–71...

Usually the last sampling point divides completely by 12, so I may expect 48 to be the last sampling point or may be 60, but who is so crazy to leave 71 as the last point?
But there arising another interesting situation: imagine there is a IR drug with T1/2 equals to 18 hours. 4*T1/2=72 so we can leave 72 hours as the last sampling point. Which of the two parameters AUClast or AUC72 should be used to choose the best strategy to confirm BE in this case? At first sight they should be equal but this is not true. The NCA software (like Phoenix) uses AUCpartial to calculate AUC72, so for 72 hours it would be equal to AUCall but not AUClast! For some subjects the last sample could be below LLOQ, for them AUCall>AUClast with an area of triangle.

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2020-06-07 12:41
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@ Astea
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 Gedanken­experi­ment

Hi Nastia,

» […] Still don't understand what to argue to the assessors...

You could refer to the papers of Scheerans et al. and Midha et al. (see this post). Again: Scientifically there is no point on measuring that long (IR only, of course) and the regulatory “≥80%-rule” is made out of thin air.
As you rightly stated previously: It’s an invention (Who is to blame – the CHMP’s PKWP?) and lacks any \(\small{\frac{\textrm{evidence}}{\textrm{justification}}}\).

If you have a lot of time and nothing better to do, perform simulations. On my to-do list for ages. Currently in the “dead dogs” folder of my machine.
Concept: Simulate studies for various PK models (1-, 2-compartments [different ratios of distribution/elimination rate constants], with/without lag-times). Have a range of T/R-ratios (say 0.85–1). Power the studies for AUC0–t (or AUC0–72?). Contaminate the data with missings at the end (mimicking BLQs). Calculate serial partial AUCs starting from tmax to the end (say, pAUC0–2, pAUC0–3, …, pAUC0–72). Assess each one for BE. Record the PE, CV, and fraction of studies passing (post hoc power). Additionally calculate the %RE of the PE to the “true T/R-ratio”.
My preliminary results (trivial and already shown by Kem Midha with real data sets): The CV of partial AUCs decreases with time and their PE stabilizes towards the true value pretty early (guess when).

In Table 1 of Kem’s 1996 paper he reported results of nine studies (22 analytes – parent and metabolites with t½ 1 – 656 h); sampling up to 1,848 (‼) hours (:waving: hy­droxy­chloro­quine) and concluded

[…] a sampling period of 24 h would have given the same bioequivalence decisions as AUClast […].

The last two sentences:

In bioequivalence, the issue is do deal with formulation differences. Once absorption is over, formulation differences no longer apply.

Sigh. Regulators, are you reading along?

» By the way, there is a typo in f' and for AUC …

Oh dear! I’m not sooo bad in basic calculus but in translating my original text to MathJax.
Original post corrected. THX!

» "Количество отобранных образцов также должно быть достаточным, чтобы обеспечить надежную оценку длительности экспозиции. Это достигается, когда AUC(0–t) перекрывает не менее 80 процентов от AUC(0–∞)."
» Though the statement is not scientifically based it is still in the list of regulator's requirements. So in case if some problems with the "80% covering rule" we have to justify somehow that the validity of the study should not be called into question - that's what I've asked about.

… должно быть ≈ should be or must be? :-D
In guidelines commonly “should be” is used. What’s your interpretation of the Russian original? Does it smell of a recommendation or rather a requirement?

» » Therefore, the FDA does not have such a bizarre “AUC0–t ≥ 80% AUC0–∞ rule
»
» By the way, was this question ever discussed on the conferences on harmonization?

Not that I recall. For IR products the main discussion (Amsterdam 2015, Rockville 2016) was about whether the FDA \(\small{\frac{\textrm{should}}{\textrm{will}}}\) drop the additional AUC0–∞.

» » ...71 h → AUC0–71...
»
» Usually the last sampling point divides completely by 12, so I may expect 48 to be the last sampling point or may be 60, but who is so crazy to leave 71 as the last point?

Yes but you go me wrong. For sure you know the correspondence between Einstein and Bohr about the Copenhagen interpretation of quantum mechanics? My example was a Gedanken­experiment to point out how absurd this requirement can be.
Let’s heighten the absurdity. We want to submit to two agencies, A and B, where B accepts a study with a foreign reference product. Both agencies have GLs asking for AUC0–t. We write the SAPs accordingly. Before the study starts, agency A allows AUC0–72. We write an amendment for agency A. Study performed. We have one (!) data set and will have no problems with agency A but likely receive a deficiency letter from agency B.

» […] imagine there is a IR drug with T1/2 equals to 18 hours. 4*T1/2=72 so we can leave 72 hours as the last sampling point. Which of the two parameters AUClast or AUC72 should be used to choose the best strategy to confirm BE in this case?

Since this is an IR formulation, AUC0–72. Stated in the protocol and no problems with extrapolation.

» At first sight they should be equal but this is not true. The NCA software (like Phoenix) uses AUCpartial to calculate AUC72, so for 72 hours it would be equal to AUCall but not AUClast! For some subjects the last sample could be below LLOQ, for them AUCall>AUClast with an area of triangle.

AUCall is \(\small{\frac{\textrm{Pharsight’s}}{\textrm{Certara’s}}}\) invention. If you find it in a single textbook about PK, let me now. IMHO, it should go into the waste bin.
An example in PHX8.1: Two compartments, half lives: absorption 30 minutes, distribution one hour, elimination 18 hours, lin-up/log-down trapezoidal.

 t        C1     pAUC1    C2     pAUC2
──────────────────────────────────────
 0.000    0.0    0.000    0.0    0.000
 0.167   29.8    2.488   29.8    2.488
 0.333   52.1    9.286   52.1    9.286
 0.667   81.1    31.53   81.1    31.53
 1.00    96.2    61.05   96.2    61.05
 1.25   102.0    85.83  102.0    85.83
 1.50   104.7   111.7   104.7   111.7
 2.00   105.1   164.1   105.1   164.1
 2.50   102.2   215.9   102.2   215.9
 3.00    98.5   266.0    98.5   266.0
 4.00    91.2   360.9    91.2   360.9
 6.00    80.9   532.8    80.9   532.8
 9.00    70.9   760.2    70.9   760.2
12.00    63.0   960.8    63.0   960.8
16.00    54.0  1194      54.0  1194
24.00    39.7  1566      39.7  1566
36.00    25.0  1948      25.0  1948
48.00    15.7  2188      15.7  2188
72.00     6.3  2435      BQL
──────────────────────────────────────
AUClast        2435            2188
AUCall         2435            2188
AUC72          2435            2433

Which version of Phoenix are you using? The last triangle is not added in the second data set (containing the 72 h time point and BQL). You would only get AUCall 2376 if you set the last concentration to zero. IMHO, not a good idea.
The value of the last triangle depends on the time interval between the time point of the last measured concentration and the next one with C=0. [Thoughtless comment removed by the author.]

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mittyri
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Russia,
2020-06-07 20:32
(224 d 13:49 ago)

@ Helmut
Posting: # 21505
Views: 5,383
 

 Dead dogs

Hi Helmut,

» If you have a lot of time and nothing better to do, perform simulations. On my to-do list for ages. Currently in the “dead dogs” folder of my machine.

I had in mind more simplistic approach: shiny app to give points, parameters of 2cpt model and to see what parameters will give ratio less than 80%.
I like 'dead dogs', will rename it :-)

» … должно быть ≈ should be or must be? :-D
» In guidelines commonly “should be” is used. What’s your interpretation of the Russian original? Does it smell of a recommendation or rather a requirement?

That's a matter of expert's taste and mood :cool:
see later:
Однако если AUC(0–t) не перекрывает 80 процентов AUC(0–∞) в более чем 20 процентах случаев, следует усомниться в результатах такого исследования.
Are you good enough to extinguish doubts from expert's mind? You never know!

» Which version of Phoenix are you using?

That rule is not changed for decades in Winnonlin.

» The value of the last triangle depends on the time interval between the time point of the last measured concentration and the next one with C=0. You would only get a meaningful result if (1) you use the lin-up/log-down trapezoidal and (2) the interval equals t½. Since (2) is never fulfilled for all profiles, forget it.

Regarding (1): lin-up/log-down is overriden by linear rule if the end point is non-positive.

Kind regards,
Mittyri
Astea
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2020-06-08 00:08
(224 d 10:13 ago)

@ mittyri
Posting: # 21506
Views: 5,391
 

 Aber meine Herren das ist keine physik

Dear Helmut and Mittyri!

» Scientifically there is no point on measuring that long (IR only, of course) and the regulatory “≥80%-rule” is made out of thin air.

Do you know a legend about Ehrenfest's parrot? I wish I have that parrot to say: "Aber meine Herren das ist keine Wissenschaft!" every time I get the request to use 80% rule :-D

» If you have a lot of time and nothing better to do, perform simulations.

"Spare time" are the two very funny words, I wish I knew their meaning. Nevertherless thank you for the point, may be I will investigate it one day. Let all dogs be alive!
By the way is not it similar to one used in 1997 by Endrenyi L. et al1?

» In guidelines commonly “should be” is used. What’s your interpretation of the Russian original? Does it smell of a recommendation or rather a requirement?

As far as I know the war almost starts when russian experts try to translate this word properly. For me "должно быть" sounds like an order. We use "следует" to slightly soften the meaning and "рекомендуется" for the recommendation.
("Marain was a synthetic language, designed to be phonetically and philosophically as expressive as the pan-human speech apparatus and the pan-human brain would allow")

» Let’s heighten the absurdity. We want to submit to two agencies, A and B, where B accepts a study with a foreign reference product. Both agencies have GLs asking for AUC0–t. We write the SAPs accordingly. Before the study starts, agency A allows AUC0–72. We write an amendment for agency A. Study performed. We have one (!) data set and will have no problems with agency A but likely receive a deficiency letter from agency B.

This situation is not that absurd. I often deal with protocols where the definition of AUC is ambiguously: in the one part of the protocol they are talking about AUC0–72 and in the other - about AUC0–t (AUClast). Noone understands how it can differ if t=72 hours. About AUC0–t (AUCall) see also Oishi M. et al.2

» Which version of Phoenix are you using? The last triangle is not added in the second data set (containing the 72 h time point and BQL). You would only get AUCall 2376 if you set the last concentration to zero. IMHO, not a good idea.

Yes, you guessed, that was a stupid case of zero as LLOQ. I use 8.2. As Mittyri pointed out upper, the calculation doesn't depend from the version. Anyway one may note that AUC0-72 and AUC0-t when t=72 are not always equal (especially considering the cases with deviations in sampling time).


  1. Endrenyi L, Csizmadia F, Tothfalusi L, Balch AH, Chen ML. The duration of measuring partial AUCs for the assessment of bioequivalence. Pharm Res. 1998;15(3):399‐404. doi:10.1023/A:1011916113082.
  2. Oishi M, Chiba K, Fukushima T, Tomono Y, Suwa T. Different truncation methods of AUC between Japan and the EU for bioequivalence assessment: influence on the regulatory judgment. Drug Metab Pharmacokinet. 2012;27(6):658‐662. doi:10.2133/dmpk.DMPK-12-RG-033.

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2020-06-08 01:04
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@ Astea
Posting: # 21507
Views: 5,359
 

 Aber meine Dame, das ist alles Unsinn!

Hi Nastia,

» Do you know a legend about Ehrenfest's parrot?

Yes. Do you know Wigner’s friend?

» I wish I have that parrot to say: "Aber meine Herren das ist keine Wissenschaft!" every time I get the request to use 80% rule :-D

:lol3:

» By the way is not it similar to one used in 1997 by Endrenyi L. et al*?

Yes and no. There are many papers about partial AUCs but most of them deal with early exposure. That’s not what I’m interested in. BTW, a plot of Mei-Ling’s paper1 shows also that the CV decreases with time. OK, little bit unfair. Not with time itself but with median tmax, where pAUC0–ref,tmax.

[image]


A small case study2 shows also the high variability of pAUC0–ref,tmax.

» As far as I know the war almost starts when russian experts try to translate this word properly. For me "должно быть" sounds like an order.

Shall I say I expected that?

» ("Marain was a synthetic language, designed to be phonetically and philosophically as expressive as the pan-human speech apparatus and the pan-human brain would allow")

Great! Do you know Volapük?

» I often deal with protocols where the definition of AUC is ambiguously: in the one part of the protocol they are talking about AUC0–72 and in the other - about AUC0–t (AUClast).

Shit. That’s why I give in my protocols even a plot to show how I deal with cut-off times…

» About AUC0–t (AUCall) see also Oishi M. et al.

Funny abstract. Can you send me a copy?


  1. Chen M-L, Davit B, Lionberger R, Wahba Z, Ahn H-Y, Yu LX. Using Partial Area for Evaluation of Bioavailability and Bioequivalence. Parm Res. 2011;28(8):1939–47. doi:10.1007/s11095-011-0421-x.
  2. Najib NM, Salem I, Hasan R, Idkaidek NM. Effect of Truncated AUC Method on Drug Bioequivalence in Humans. J Bioequiv Bioavail. 2009;1(4):112–4. doi:10.4172/jbb.1000017. [image] Open access.

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2020-06-08 12:43
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@ Astea
Posting: # 21510
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 Bizarre paper

Hi Nastia,

THX for the paper! 1
Regrettably the authors got many things wrong. The FDA does not require AUC0–t or AUC0–∞ but both. Reading educates.
The infamous AUCall is nowhere recommended in the Japanese Guideline 2 (AUCt as everywhere else). Given, the “80% rule” is mentioned as well. The Q&A 3 is more specific and states in A-28:

AUC is calculated by a trapezoidal rule as the area under the straight lines connecting the measured points.

(my emphasis)
OK, the bloody linear trapezoidal but can we measure zero? Nope.

Hence this one

[image]


as the base of all simulations is already wrong and IMHO, the article missed the point.
BTW, this figure is extremely funny cause AUCall is >100% of AUCinf. Rule fulfilled → tick the box → mission accomplished. :crying: LLOQ 17% of Cmax, fantastic bioanalytics.
This example demonstrates that setting the first value after tlast to zero is nonsense. I have seen splendid rules like “set first one after tlast to LLOQ/2 and keep subsequent ones as BQL”. Here also >100% of AUCinf. Forget it.


  1. Oishi M, Chiba K, Fukushima T, Tomono Y, Suwa T. Different truncation methods of AUC between Japan and the EU for bioequivalence assessment: influence on the regulatory judgment. Drug Metab Pharmacokinet. 2012;27(6):658‐662. doi:10.2133/dmpk.DMPK-12-RG-033.
  2. PMDA. Guideline for Bioequivalence Studies of Generic Products. Feb 29, 2012.
  3. PMDA. Q&A. Feb 29, 2012.

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ElMaestro
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Denmark,
2020-06-08 15:33
(223 d 18:48 ago)

@ Helmut
Posting: # 21511
Views: 5,241
 

 Bizarre paper

Hi all,

possibly a little off topic but even with AUCall in all its ugliness and over-estimation, it will not necessarily imply a bias on the BE conclusion unless someone can prove that E(ln(AUCall,T - ln(AUCall,R)) does not equal E(ln(AUCT) - ln(AUCR)), regardless of whether the latter is expressed as AUCinf or AUCt.

This isn't about imagining scenarios where the equality does not hold (that would be easy enough) but a consideration of the general (expected) case. For the general case I think we're ok.

Pass or fail!
ElMaestro
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2020-06-08 15:53
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@ ElMaestro
Posting: # 21512
Views: 5,247
 

 OT: Bias of AUCt, AUCall, pAUC

Hi ElMaestro,

» […] it will not necessarily imply a bias on the BE conclusion unless someone can prove that E(ln(AUCall,T - ln(AUCall,R)) does not equal E(ln(AUCT) - ln(AUCR)), regardless of whether the latter is expressed as AUCinf or AUCt.

There will always be a bias in any AUC-approach if BQLs come into play and the true T/R-ratio is not  exactly  sufficiently close to unity. Exceptions: Comparison of (reliably) estimated AUC0–∞ or AUC0–t(common).

Since the bias will point away from unity, the T/R-ratio will get worse and regulators don’t care (wrong but conservative).

Example: I used the C1-column of this post as the reference (complete data). Then I generate three others (T) as R/2. Lin-up/log-down trapezoidal AUCs. The T/R-ratio should be 0.5.
  1. Complete data
    PK metric    T      R   T/R     %RE
    AUClast   1217.3 2434.6 0.500  ±0.00
    AUCall    1217.3 2434.6 0.500  ±0.00
    AUCcommon 1093.8 2187.5 0.500  ±0.00
    AUC72     1217.3 2434.6 0.500  ±0.00
    AUCinf    1298.4 2596.9 0.500  ±0.00

  2. C72 of T missing
    PK metric    T      R   T/R     %RE
    AUClast   1093.8 2434.6 0.449 –10.20
    AUCall    1093.8 2434.6 0.449 –10.20
    AUCcommon 1093.8 2187.5 0.500  ±0.00
    AUC72     1216.6 2434.6 0.500  ±0.00
    AUCinf    1297.2 2596.9 0.500  ±0.00

  3. C72 of T set to zero
    PK metric    T      R   T/R     %RE
    AUClast   1093.8 2434.6 0.449 –10.20
    AUCall    1188.0 2434.6 0.488  –2.40
    AUCcommon 1093.8 2187.5 0.500  ±0.00
    AUC72     1188.0 2434.6 0.488  –2.40
    AUCinf    1297.2 2596.9 0.500  ±0.00
As I wrote above, if we have missing(s) only AUC0–∞ and AUC0–t(common) are unbiased regardless the chosen method.

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ElMaestro
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2020-06-09 08:45
(223 d 01:36 ago)

@ Helmut
Posting: # 21514
Views: 5,127
 

 OT: Bias of AUCt, AUCall, pAUC

Hi again Helmut,

there is no doubt that AUC calculation can be biased. Whether the ln difference or ratio is biased, generally, is another matter and this is where I meant to draw the attention - this is the BE outcome. If one could make a case for saying that this bias affects T more often or to a larger extent than it affects R, generally, then that is where the use of this approach would be not just ugly but even worse also clearly biased.
I am not aware this would or should be the case.

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2020-06-09 14:07
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@ ElMaestro
Posting: # 21519
Views: 5,132
 

 OT: Bias of AUCs; example

Massa,
I dunno understand wat ya sayin’. :confused:

» there is no doubt that AUC calculation can be biased.

OK.

» Whether the ln difference or ratio is biased, generally, is another matter and this is where I meant to draw the attention - this is the BE outcome. If one could make a case for saying that this bias affects T more often or to a larger extent than it affects R, generally, then that is where the use of this approach would be not just ugly but even worse also clearly biased.

If we can measure all concentrations, any of the methods is unbiased as is the T/R estimate (yep, even by the linear trapezoidal and the bloody AUCall). I’m only talking about cases where we deal with BQLs.

If T = R (and for nitpickers: we have balanced sequences / equal group sizes) both treatments will be affected to the same extent, the bias of the AUC will mean out and the estimate will tell used T ≈ R.
If T < R, T will be more often affected than R. If T > R, R will be more often affected than T. In the first case the T/R estimate will have a negative bias (since we have more cases where T is underestimated) and in the second a positive one (since we have more cases where R is underestimated).

Example: One-compartment, D 100, V 1, t½a 1 h, t½e 4 h, FR 1, FT 0.8–1, t 0, 1, 2, 2.5, 3, 3.5, 4, 4.5, 6, 9, 12, 16, 24; λz estimated from the last two measurable concentrations. LLOQ 3% of theoretical Cref,max (62.996). Lin-up / log-down trapezoidal method for AUC0–t, AUC0–∞, and AUC0–t(common).

[image]


[image]As long as we can measure all concentrations of both T and R, the PE of AUC0–t is unbiased. Once we drop below the LLOQ, the PE will be negatively biased because we are comparing AUC0–16 of T with AUC0–24 of R. Here it happens below a true f of 0.9071 where Clast of T with 1.8898 will be below the LLOQ of 1.8899.
The PEs of AUC0–∞ and AUC0–t(common) are always unbiased.*


  • Fisher D, Kramer W, Burmeister Getz E. Evaluation of a Scenario in Which Estimates of Bioequivalence Are Biased and a Proposed Solution: tlast (Common). J Clin Pharm. 2016; 56(7): 794–800. doi:10.1002/jcph.663. [image] Open access.

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Astea
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Russia,
2020-06-12 14:15
(219 d 20:06 ago)

@ Helmut
Posting: # 21532
Views: 4,402
 

 Maxwell's demon

Dear Helmut!

» Regrettably the authors got many things wrong.

Oh, I suspected something like that.
Thank you for your valuable comments! I shall start a new entry to discuss some features of PK parameters that were raised here.

"Being in minority, even a minority of one, did not make you mad"
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2020-06-08 10:40
(223 d 23:41 ago)

@ mittyri
Posting: # 21509
Views: 5,284
 

 Dead dogs

Hi mittyri,

» I had in mind more simplistic approach: shiny app to give points, parameters of 2cpt model and to see what parameters will give ratio less than 80%.

Yep but that’s for a particular study where you have some ideas about the PK model. I had a more general approach in mind.

» » … должно быть ≈ should be or must be? :-D
» » In guidelines commonly “should be” is used. […] Does it smell of a recommendation or rather a requirement?
»
» That's a matter of expert's taste and mood :cool:
» see later:
» Однако если AUC(0–t) не перекрывает 80 процентов AUC(0–∞) в более чем 20 процентах случаев, следует усомниться в результатах такого исследования.
» Are you good enough to extinguish doubts from expert's mind? You never know!

следует усомниться ≈ should doubt.
As Nastia wrote:
» We use "следует" to slightly soften the meaning…
But you are right; to dispel doubts can be difficult.

» » The value of the last triangle depends on the time interval between the time point of the last measured concentration and the next one with C=0. You would only get a meaningful result if (1) you use the lin-up/log-down trapezoidal and (2) the interval equals t½. Since (2) is never fulfilled for all profiles, forget it.
»
» Regarding (1): lin-up/log-down is overriden by linear rule if the end point is non-positive.

I should have RTFM. While you replied I deleted this part from my OP, since esp. (2) is nonsense.

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