Bioequivalence and Bioavailability Forum

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     CVintra
Clast      86.16  63.67 116.58   51.6
Ctrough   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.

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• 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%.

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Ceterum censeo parameter C_fin malus est.