Bioequivalence and Bioavailability Forum

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.

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?

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 \(\small{\frac{\textsf{evidence}}{\textsf{justification}}}\).

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 AUC_0–t (or AUC_0–72?). Contaminate the data with missings at the end (mimicking BLQs). Calculate serial partial AUCs starting from t_max to the end (say, pAUC_0–2, pAUC_0–3, …, pAUC_0–72). 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 t_½ 1 – 656 h); sampling up to 1,848 (‼) hours ( hy­droxy­chloro­quine) and concluded

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

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?
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 \(\small{\frac{\textsf{should}}{\textsf{will}}}\) drop the additional AUC_0–∞.

❝ ❝ ...71 h → AUC_0–71...

❝

❝ 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 AUC_0–t. We write the SAPs accordingly. Before the study starts, agency A allows AUC_0–72. 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 T_1/2 equals to 18 hours. 4*T_1/2=72 so we can leave 72 hours as the last sampling point. Which of the two parameters AUC_last or AUC₇₂ should be used to choose the best strategy to confirm BE in this case?

Since this is an IR formulation, AUC_0–72. 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 AUC_partial to calculate AUC₇₂, so for 72 hours it would be equal to AUC_all but not AUC_last! For some subjects the last sample could be below LLOQ, for them AUC_all>AUC_last with an area of triangle.

AUC_all is \(\small{\frac{\textsf{Pharsight’s}}{\textsf{Certara’s}}}\) 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.]