Bioequivalence and Bioavailability Forum

Dear ElMaestro!

❝ Clearly I would use option 1b; if pre-dose is not the lowest in practice then we are looking at data that do not reflect reality but random fluctuations or mixups (unless, of course, the body is capable of synthesizing the drug or metabolite under investigation which is generally not the case for the majority of substances). And in fact Cmin,ss is to some people like me a misnomer; should be called C_trough, with trough being defined as predose.

Agree with C_trough; but I would opt for 1d, because if a lag-time comes into play, concentrations will still decrease after time of administration. In such a case C_trough ('trough' is a minimum in the English language) is not to be expected at pre-dose.

Weimann* states:

3.5 Trough value
The trough value is defined as the drug concentration measured at the end of dose interval at steady-state. […] the trough value is defined as the concentration measured immediately before the next drug-intake […]
3.6 Minimum concentration
The minimum concentration C_min is defined as the lowest concentration on a concentration-time curve at steady-state and within one dosing interval. The C_min value can – but need not necessarily – be identical to the trough value. Drugs for which C_min and trough values differ from each other are products with sustained release properties. After administration of such a formulation, the drug concentration continues to decrease until substance absorption from the administered drug product commences at the end of the lag time. […] Like C_max, the accuracy of the C_min value depends on the blood sampling pattern. This is in contrast to the trough value, which is simply determined as the predose concentration.

I leave it to you to find the contradictions.

PK-software in their default configuration (Phoenix/WinNonlin, Kinetica) come up with 1a (it needs some experience to tweak the software to come up with either one of 1b-d). IMHO 1a does not make sense, since in true steady state we would expect 50% of values at the start and end of the dosing interval due to random variability. If we look at the time point t_min we would end up with a nonsensical location of τ/2 with high variance (141% ≥ CV% ≥100%). In other words, comparing the pre-dose concentration to the concentration at the end of the dosing interval within subjects leads to some kind of ‘Apples-and-Oranges-Statistics’. The expectation of such an A&O comparison in any sample is 50% (and 25% for both pre-dose and end of dose). On the other hand, the true minimum (regardless the location) is required in the calculation of %PTF or Swing.

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• HJ Weimann
  Drug concentrations and directly derived parameters
  In: W Cawello (Ed.), Parameters for Compartment-Free Pharmacokinetics
  Shaker-Verlag, Aachen pp 31–4 (2003)

Dear D. Labes,

thanks for participating!

❝ ❝ replicate design in steady state (i.e., TTRR-RRTT)

❝                                             ^^^^ 

Something like this:
saturation phase     T       T     switch over         R       R
saturation phase     R       R     switch over         T       T
pre dose values   profile profile  pre dose values  profile profile

This is my interpretation of EMA’s MR-NfG (Section 4.1.2):

The inter-individual variability of the pharmacokinetic parameters of interest should be compared between the modified and immediate release formulation and the variability of the modified release formulation should not exceed that of the immediate release formulation. It may be valuable to assess the intra-individual variability. This could be achieved by either repeated measurements of the concentration profile at steady state or by performing a single dose study with replicate design.

(my emphasis)

Dear beman (reads BE-man?),

❝ I define the Cmin-Value in multiple dose bioequivalence studies as the 'Last concentration within the dosing interval'.

Well, that’s option 1.c and the ‘Trough concentration’ defined by Weimann and WHO (2006).

❝ If the last value in the dosing interval is <LLOQ, which value should i use ?

Hhm, this problem applies to all definitions of C_min. Nasty for a low accumulation index…

❝ - If i set the value to zero, the ratio T/R can't be calculated.

Sure. Though I’m not a fan of setting anything to LOQ/2, I used that approach in a recent study accepted by the German BfArM (low accumulation, concentrations ranging more than three orders of magnitute).

❝ - I can calculate a value <LLOQ (with the average half life time of the corresponding single dose study or the literature).

Well, why not use an estimate (from the half life of the particular subject in the multiple dose study)? We had a little discussion there.
Using the (average!) half life from another study is unacceptable IMHO. Even more from the literature.

❝ - I can use the Last concentration value >=LLOQ (for both the reference and the test formulation)

❝ - I can use the Last concentration value >=LLOQ (for only one formulation, for the other i use the last concentration value).

This problem is similar to the ‘missing 72 h value’ for truncated AUC. See this post for an example. Your first option would give an unbiased T/R (but is available in standard PK-software only for AUC_τ; see this post). You would have to set up something on your own. The second one IMHO is ‘apples-and-oranges statistics’.