Bioequivalence and Bioavailability Forum

Dear Hsin-ya & Yung-ji!

❝ I just like to know if it is reasonable to estimate lambda_z when doing data analysis of a multiple-dosed steady-state (SS) BE/BA study.

Good question!

❝ It is because we just collect the plasma/blood sample within one dosing interval (Tau) at steady-state in a multiple-dosed BE/BA study.

Most people would do so – although I’ve seen others who took samples after τ.

❝ It looks like there is no such terminal phase at all in multiple-dosed BE/BA study.

We should be cautious in using ‘terminal phase’ – especially in NCA. Personally I prefer ‘apparent elimination’ or the like to express that I’m not dealing with a particular PK model.

❝ If it is not reasonable,…

In steady state within τ you may get a value similar to SD, but with noisy data – and if more than one compartment is needed to describe the PK – most likely not. Think about a two-compartment model with accumulation due to the ‘deep’ compartment. In SD you would only catch the first one (you think it’s elimination, but in ‘reality’ it’s only distribution). In steady state the second one becomes visible.

❝ … is there any way to estimate the elimination rate constant (k_el), half-life, V_ss or the accumulation index?

Tricky.

• I would not try to play around with elimination from steady state within τ.
  
• Accumulation index is easy – and actually the most interesting metric if we compare SD with MD. I only use
  \(R=\frac{AUC_{0-\tau}}{AUC_{0-\infty}}\; \begin{matrix}
  \text{(steady state)}\\
  \text{(single dose)}
  \end{matrix}\)
  In a linear PK system \(R=1\). With a reasonably sensitive analytical method you should not be hit by a second phase appearing from the 'underground' too much. When I plan a steady state study I try to ‘guesstimate’ (based on the relationship of the LLOQ of the method and the AUC observed after a SD) how much % of the AUC would possibly account for a deep compartment. As a rule of thumb I assume a 10times slower half life. Doing so avoids surprises by not beeing in steady state with the planned dose regimen. If I get an accumulation index in the MD study more or less different from 1 I try to give additional information, whether the drug shows true nonlinear PK, or only a small shift due to the second compartment.
  
• V_ss is a strange metric. It sounds so easy to divide the amount in the body at steady by the average steady state concentration, but there are different methods used in computation. Wagner, Benet & Galeazzi, Rowland & Tozer, Gibaldi & Perrier use the term – but don’t necessarily mean the same thing… IMHO, without PK modeling it does not make much sense at all (if ever possible I simply avoid it). BTW, I also don’t like V/F for extravascular data since what does it mean? We refer to a volume divided by an (unknown!) fraction absorbed – so what?

❝ In WinNonlin v5.x, lambda_z still needs to be estimated first for further calculations of other NCA parameters.

That’s rubbish. WinNonlin uses

\(\small{R=}\frac{1}{\left| 1-\text{e}^{-\lambda_z\cdot \tau} \right|}\)

which needs

• λ_z,
  
• a constant τ (what about a dose regimen of 6/6/12 or actual sampling times?), and
  
• is only valid for a one-compartmental model (the most serious drawback).

At least Phoenix/WinNonlin 6 is more flexible in dealing with irregular dose regimens and sampling times, but still uses the same method for the calculation of R. In my studies I compare AUCs from SD to MD only.