Bioequivalence and Bioavailability Forum • Cmin (story continued)

Helmut
★★★

Vienna, Austria,
2011-06-22 19:03
(5064 d 17:52 ago)

Posting: # 7160
Views: 10,352

Cmin (story continued) [NCA / SHAM]

Dear all,

I want to share with you some experiences with C_min. Introduction here, some more stuff there. From our simulations we expected CVs of AUC_τ ≈7%, C_max ≈15%, C_min ≈75%. The study was BE in the first stage; we got CVs of 4.23% (AUC_τ), 8.54% (C_max), and 51.6% (C_last).
The IR GL states:

In multiple-dose studies, the pre-dose sample should be taken immediately before (within 5 minutes) dosing and the last sample is recommended to be taken within 10 minutes of the nominal time for the dosage interval to ensure an accurate determination of AUC_(0-τ).

What is written in the GL about time deviations is even more crucial if C_min is concerned. We took pre-dose samples 5 minutes prior to administration – which meant also in steady state (OAD) at 23:55 hours post dose instead of 24 hours. We improved the analytical method to a calibration range of 1:510, but this a clearly the end taking the detector response into account. We could go further down with LLOQ by a factor of 10 (to 5 pg/mL), but then we wouldn’t be able to run all samples of a subject in a single batch (see draft GL):

It is advised to analyse all samples of one subject together in one analytical run to reduce the variability in outcome.

In the protocol we stated to correct for time deviations in the following way: The concentration at t=0 was linear interpolated between t=-5 min and the first measured concentration (30 min). We calculated C_min,τ = C_trough = C_last·e^{-λ_z(τ–t_last)} (EMA: „By C_min,ss we mean the concentration at the end of the dosage interval, i.e. C_trough.”). Note that if t_last = τ no correction is done, since τ–t_last = 0 and e⁰ = 1; therefore C_min,τ = C_last.
Now for the more interesting part: Although we didn’t expect that, in 9% of cases at τ the concentration was below the LLOQ. By using C_last in these subjects we are actually comparing C₁₆ to C₂₄ – which due to the short half life of 2–3 hours is a nightmare (see above for the CV). If we use the estimated C_trough, the CV decreases substantially. To give you an idea:

metric PE 90% CI CV_intra C_last 86.16 63.67 116.58 51.6 C_trough 101.42 86.06 119.53 26.8

Note especially the biased PE which is due to the imbalanced occurrence of C_last<LLOQ (in 6% of subjects after reference and in 12% after test). A classical example of ‘apples-and-oranges’ statistics. Almost all (!) other PK metrics* showed T/R-ratios of ±3% (!!) from 100%. I would strongly argue for using the estimated C_trough – not only if samples <LLOQ are concerned, but to be protected against missing samples at τ as well. The GL states:

Unbiased assessment of results from randomised studies requires that all subjects are observed and treated according to the same rules. These rules should be independent from treatment or outcome.

The protocol was approved by the BfArM (we mentioned both metrics and argued for not assessing C_min for bioequivalence due to ethical reasons). According to current (!) thinking of EMA, multiple dose studies of MR product will not be required any more if no accumulation occurs (single dose AUC_t/AUC_∞ >80%), but the issue with missing samples applies to steady state studies after substantial accumulation – though to a lesser degree – as well.

AUC_τ, C_max, AUC_0-4, AUC_4-24, C_max,0-4, C_max,4-24, %PTF, MRT_τ; HVD and t_75% within ±7%.

Ceterum censeo parameter C_fin malus est.

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Marcel ★ 2011-09-15 12:21 (4980 d 00:35 ago) @ Helmut Posting: # 7353 Views: 8,360	Cmin (story continued) Post reply
	Hi HS, Another nightmare experience with Cmin. How did you explain that Cmin is not a good metric to look at in your case? Cheers, Marcel

Helmut
★★★

Vienna, Austria,
2011-09-15 16:37
(4979 d 20:19 ago)

@ Marcel
Posting: # 7354
Views: 8,297

Cmin (story continued)

Post reply

Γεια σου, Μαρσέλ!

❝ Another nightmare experience with Cmin.

As expected.

❝ How did you explain that Cmin is not a good metric to look at in your case?

Most importantly we gave a justification already in the protocol (which was accepted by the IEC and the German BfArM):

unethical; sample size 12 ⇒ 194 (see here),
no accumulation expected (simulated from the SD study to be 0.7%; see here),
in line with recent regulatory point of view (MD expected to be no more required if residual area in SD <20% of AUC_∞ and BE of C_last demonstrated; see here),
C_last considered unreliable (time deviations, missing samples); planned to use estimated C_min,τ instead, and
evaluation only exploratory.

BTW our simulation of accumulation from SD dose data turned out to be correct; we found 0.9% (test) and 1.0% (reference).
I will report here how the regulator(s) will like the study…

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Marcel
★

2011-09-16 10:01
(4979 d 02:54 ago)

@ Helmut
Posting: # 7355
Views: 8,333

Cmin (story continued)

Post reply

Geia sou, Helmut!

Thanks for the feedback. I think a lot of people are having problem with Cmin because of some of the reasons you mention and because some/most people don't power their studies to Cmin, but to Cmax and occasionally AUC.

At what point do you think the increase in sample size becomes unethical?

Do you have a good reference article that shows that Clast is considered unreliable? By Clast, you mean the sample taken ~5 minutes prior to dosing, right?

Problems will continue to arise with steady state studies until this new draft guideline is released.

Take care,
Marcel

Helmut
★★★

Vienna, Austria,
2011-09-16 15:26
(4978 d 21:30 ago)

@ Marcel
Posting: # 7361
Views: 8,412

Cmin (cave: lengthy post)

Post reply

Dear Marcel!

❝ At what point do you think the increase in sample size becomes unethical?

Good question, next question. Gut feeling:^* n>40 (T/R 0.95, power 0.80, CV_intra just slightly >30%). That’s actually the sample size for HVDs/HVDPs.

❝ Do you have a good reference article that shows that Clast is considered unreliable?

No. I would not say it’s unreliable. Only:

C_last is likely to be the worst metric when it comes to variability. Variability was the reason why EMA and WHO are asking in single dose studies for AUC_t – not AUC_∞ – as the metric for extent of absorption.
Missing samples are a nightmare. A similar case can be made for truncated AUC₇₂ or AUC_t in general. Any missing last sample(s) will bias the estimated T/R ratio of the particular subject(s) away from 100% – that’s probably the reason why regulators don’t care about this issue. But what if the ‘true’ ratio of the formulations is 105% and in one subject after test the last scheduled sample is missing? This subject will pull the study’s ratio towards 100% (shifting the CI downwards, increasing the chance of BE, and thus increasing patient’s risk). In my studies I pragmatically use AUC_t if the LOQ is low enough so that my residual AUCs are quite small – crossing fingers that everything means out. Haven’t performed a study with AUC₇₂ yet, but most likely I will try to make an argument for an estimated Ĉ₇₂ (since residual AUC will be much higher and the effect on the overall estimate larger).
Given the problems above for AUC, C_last (as a single point metric) is much more difficult to handle. If your drug accumulates, fine – but still the variability is expected to be the highest of all metrics. If not – very bad. The concept paper (Section 3.1) states:

The newly revised Note for Guidance on the Investigation of Bioequivalence (EWP/QWP/1401/98 rev1), the emergence of science as well as applications on new types of formulations require thorough discussions on: […]
• possibility of widening (and narrowing) of acceptance ranges
In the presentations given here this statement was mentioned in the introduction but not further explored. No idea whether the PK group is considering it. A multiple dose study in a replicate design is no fun – lots of samples.

❝ By Clast, you mean the sample taken ~5 minutes prior to dosing, right?

Yes. In the actual study we sampled 5 minutes prior to the 2^nd dosing (1^st period: 23:55) and at 24:00 post dose in the last profile (2^nd period) in order to get values as close as possible to τ. We could reliably estimate λ_z. Since the study was balanced we had to estimate C₂₄ from C_23:55 in 50% of cases – we also used the estimated AUC_τ. Another option would be to sample in all profiles at 23:55 (consistent with the IR GL, Section 4.1.4):

Why ≤-5 min (pre dose) and ≤±10 min at τ?
I prefer to get »an accurate determination of AUC_(0-τ)« by sampling at the intended τ if possible and use an estimate otherwise.

❝ Problems will continue to arise with steady state studies until this new draft guideline is released.

Right. Problems with the current NfG arise from its ambiguities:

4.1.1. Rate and extent of absorption, fluctuation
The pharmacokinetic parameters of interest are AUC, C_max and C_min or other means reflecting fluctuation.
5.1 Prolonged release formulations
Assessment of bioequivalence will be based on AUC_τ, C_max and C_min applying similar statistical procedures as for the immediate release formulations.
(my emphases; note ‘and vs. or’)

Sorry for the lenghty post.

I try not to think with my gut. If I’m serious about understanding the world,
thinking with anything besides my brain, as tempting as that might be,
is likely to get me into trouble. Carl Sagan

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

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Marcel
★

2011-09-20 10:33
(4975 d 02:23 ago)

@ Helmut
Posting: # 7376
Views: 8,279

Cmin (cave: lengthy post)

Post reply

Howdy Helmut,

Thanks for the information. It's quite detailed and well thought out. I hadn't made the connection with the ethical nature of the sample size estimate. That's useful information to keep stored for a rainy day...but how long is that going to be? As happened when the draft guideline for immediately release preparations first came out, I think as soon as the first draft of the new sustain release guideline is out, the authorities won't ask for them anymore. But for now, they are treating steady state studies as the be-all-end-all of establishing bioequivalence.

Anyway, Cmin has been giving me nightmares lately, and the experiences you share are quite helpful in stressing that all considerations with Cmin need to be thouroughly analysed beforehand (prospectively). Seems like the authorities are more willing to bend the rules when that's the case.

Take care,
Marcel

Helmut
★★★

Vienna, Austria,
2011-09-20 12:08
(4975 d 00:47 ago)

@ Marcel
Posting: # 7378
Views: 8,307

Cmin no more?

Post reply

Dear Marcel!

I’m not so sure whether C_min will vanish once the MR draft is out. I’m currently at a BE conference at Brussels; another presentation about the current thinking of the PK group will be given by Christoph Baumgärtel (AGES PharmMed, Austria) tomorrow. I will keep you updated.

Edit 2011-09-21: Christoph Baumgärtel was ill and could not attend. So nothing to report… [Helmut]

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

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ElMaestro
★★★

Denmark,
2011-09-20 12:01
(4975 d 00:55 ago)

@ Helmut
Posting: # 7377
Views: 8,235

perspective from the PD world

Post reply

Hi HS,

very good post and very well illustrated C_last isn't easy to work with.
Here is a perspective from the world of pharmacodynamics for inhaled products.
In some cases therapeutic equivalence is evaluated by giving patients a puff of the medicines and then measuring and comparing the lung function (often an endpoint called FEV1) over time. In certain cases clients of mine have been suggested to include FEV1 at the last sampling point in the comparison as one of the primaries.
This is every bit as bad as the story with C_last. I can certainly see why a regulator might want 'something like that' but I think we are getting away from proper science to semi-thought-through-solutions that sound intuitively correct but by closer scrutiny aren't really practical, feasible and valid for the reasons you already gave. For inhaled products FEV1_max may have an intraCV of around 20% on a good day whereas the intraCV for FEV1_last can exceed 80% when the same product (same brand, same batch) is dosed. That's pretty showstopping.
Solution: Treat guidelines as variable constants and confront regulators in an sc. advice application - is there any acceptable design that does not require evaluation of C_last (or FEV1_last)? In one case I know of they caved in and accepted an alternative. Just unfortunate that this adds 3-4 months to the project plan.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2011-09-20 12:20
(4975 d 00:36 ago)

@ ElMaestro
Posting: # 7379
Views: 8,180

perspective from the PD world

Post reply

Dear ElMaestro!

THX for sharing your excursion into the minefields of PD.

❝ […] Treat guidelines as variable constants. [sic!]

Wonderful. Reminds me on Lagrange’s method to solve inhomogeneous linear ordinary differential equations. BTW:

Rose
is a rose
is a rose
is a rose. Gertrude Stein (1913)

Guidelines
are guidelines
are guidelines. Henrike Potthast, BfArM (ca. 2004)

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

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