## Science vs. (EMA) GL aka PK primer [Regulatives / Guidelines]

replying myself to clarify things. Starter: Scheerans

*et al.*(2008).

^{1}t

_{max}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 t_{inpt}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

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

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

AUC in the interval [0, a] is given as the definite integral of ƒ(x) by\(\small{A \left ( (e^{k_a \cdot a}-1)/k_a - (e^{k_{el}\cdot a}-1)/k_{el} \right )}\)

_{a}1.3863 (t

_{½a}0.5), k

_{el}0.6931 (t

_{½el}1). Although Scheerans

*et al.*recommended their procedure for k

_{a}≥ 3k

_{el}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.

At t

_{max}75% are absorbed (AUC

_{t}/AUC

_{∞}25%) and at t

_{inpt}already 93.75% (AUC

_{t}/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 t

_{inpt}equals four absorption half-lives (alternative method for the calculation of % absorbed: 100 – 100/2

^{4·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.

`t`

_{last} % abs % AUC_{∞}

1.0 = t_{max } 75.00 25.00

2.0 = t_{inpt} 93.75 56.25

2.161 _{ } 95.00 60.28

2.5 = 5×t_{½a } 96.88 67.77

3.244 _{ } 98.89 80.00

3.322 _{ } 99.00 81.00

_{inpt}is a reasonable starting point for the estimation of

*λ*

_{z}(forget max. R²

_{adj}including earlier time points since elimination is contaminated by absorption), it should be possible to have ≥3 data points in the interval [t

_{inpt}, t

_{last}]. We can expect to get a reliable estimate of

*λ*

_{z}. But what’s the use of it? The EMA’s metric for extent of absorption is AUC

_{t}. We could reliably estimate it with an earlier cut-off as well!

^{2,3}Are we comparing

*λ*

_{z}of test and reference? No. On the contrary – we assume identical inter-occasion clearances (or V + k

_{el}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 k

_{el},

^{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 AUC

_{t}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).

- 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.

- 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.

- 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.

- Abdallah HY.
*An Area Correction Method To Reduce Intrasubject Variability In Bioequivalence Studies.*J Pharm Pharmaceut Sci. 1998;1(2):60–5. free resource.

- Note that the FDA – although
*both*AUC_{t}and AUC_{∞}are required – doesn’t have such a cut-off.

*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

### Complete thread:

- AUCt not covering at least 80% of AUCinf ratnakar1811 2013-03-05 08:30 [Regulatives / Guidelines]
- AUCt not covering at least 80% of AUCinf d_labes 2013-03-05 11:12
- AUCt not covering at least 80% of AUCinf ratnakar1811 2013-03-06 08:50
- AUCt not covering at least 80% of AUCinf ElMaestro 2013-03-06 11:10
- Science vs. regulations Helmut 2013-03-06 14:30
- Science vs. regulations cakhatri 2013-03-10 08:59
- ratio = difference of logs! Helmut 2013-03-11 01:17

- Science vs. (EMA) GL aka PK primerHelmut 2013-03-11 03:17
- Science vs. regulations qualityassurance 2020-04-23 14:11
- Science vs. regulations Helmut 2020-04-23 17:32
- Science vs. regulations Achievwin 2020-05-07 22:59
- Science vs. regulations Helmut 2020-05-07 23:54

- Science vs. regulations Achievwin 2020-05-07 22:59

- Science vs. regulations Helmut 2020-04-23 17:32

- Science vs. regulations cakhatri 2013-03-10 08:59
- AUCt not covering at least 80% of AUCinf Brus 2018-11-20 13:01
- AUCt not covering at least 80% of AUCinf Astea 2020-06-05 19:05
- So what? Helmut 2020-06-06 12:02
- Carrot and whip Astea 2020-06-06 21:11
- Gedankenexperiment Helmut 2020-06-07 12:41
- Dead dogs mittyri 2020-06-07 20:32
- Aber meine Herren das ist keine physik Astea 2020-06-08 00:08
- Aber meine Dame, das ist alles Unsinn! Helmut 2020-06-08 01:04
- Bizarre paper Helmut 2020-06-08 12:43
- Bizarre paper ElMaestro 2020-06-08 15:33
- OT: Bias of AUCt, AUCall, pAUC Helmut 2020-06-08 15:53
- OT: Bias of AUCt, AUCall, pAUC ElMaestro 2020-06-09 08:45
- OT: Bias of AUCs; example Helmut 2020-06-09 14:07

- OT: Bias of AUCt, AUCall, pAUC ElMaestro 2020-06-09 08:45

- OT: Bias of AUCt, AUCall, pAUC Helmut 2020-06-08 15:53
- Maxwell's demon Astea 2020-06-12 14:15

- Bizarre paper ElMaestro 2020-06-08 15:33

- Dead dogs Helmut 2020-06-08 10:40

- Aber meine Herren das ist keine physik Astea 2020-06-08 00:08

- Dead dogs mittyri 2020-06-07 20:32

- Gedankenexperiment Helmut 2020-06-07 12:41

- Carrot and whip Astea 2020-06-06 21:11

- So what? Helmut 2020-06-06 12:02

- AUCt not covering at least 80% of AUCinf Astea 2020-06-05 19:05

- AUCt not covering at least 80% of AUCinf ratnakar1811 2013-03-06 08:50

- AUCt not covering at least 80% of AUCinf d_labes 2013-03-05 11:12