yjlee168
★★

Kaohsiung, Taiwan,
2009-07-14 14:16

Posting: # 3954
Views: 12,915

## half-life in multiple-dosed steady-state BE/BA study? [NCA / SHAM]

Dear All,

I just like to know if it is reasonable to estimate lambdaz when doing data analysis of a multiple-dosed steady-state (SS) BE/BA study. 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. It looks like there is no such terminal phase at all in multiple-dosed BE/BA study. If it is not reasonable, is there any way to estimate the elimination rate constant (kel), half-life, Vss or the accumulation index? In WinNonlin v5.x, lambdaz still needs to be estimated first for further calculations of other NCA parameters. Thanks in advanced.

All the best,
-- Yung-jin Lee
bear v2.8.8:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear
Helmut
★★★

Vienna, Austria,
2009-07-15 15:09

@ yjlee168
Posting: # 3955
Views: 10,957

## half-life in steady state; WinNonlin

Dear Hsin-ya & Yung-ji!

» I just like to know if it is reasonable to estimate lambdaz 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 (kel), half-life, Vss 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.
• Vss 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, lambdaz 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
• λz,
• 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.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yjlee168
★★

Kaohsiung, Taiwan,
2009-07-16 11:53
(edited by yjlee168 on 2009-07-16 12:06)

@ Helmut
Posting: # 3957
Views: 10,675

## no lambda(z), no NCA?

Dear Helmut,

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

For what purpose to take blood sample after tau? Is it worth to do so?

» We should be cautious in using ‘terminal phase’ – especially in NCA. Personally I prefer ‘apparent elimination’ [...]

Absolutely agree.

» 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 [...]

So, it looks like that no lambdaz, no NCA...

» Tricky. I would not try to play around with elimination from steady state within τ.

It is inevitable for us in Taiwan or in China to conduct a multiple-dose BE/BA study when the target product is modified release dosage form.

» Accumulation index is easy – and actually the most interesting metric if we compare SD with MD. I only use
$$R=\frac{AUC_{0-\tau}}{AUC_{0-\infty}}\; \begin{matrix} \text{(steady state)}\\ \text{(single dose)} \end{matrix}$$

The formula is only for when conducting both a SD and a MD BE/BA studies simultaneously. If we just have a MD BE study, we still need a lambdaz.

» Vss is a strange metric. It sounds so easy to divide [...]

Indeed. We calculate Vss just because WinNonlin does so. Not a necessary procedure in a BE study.

» That’s rubbish. WinNonlin uses
$$\small{R=}\frac{1}{\left| 1-\text{e}^{-\lambda_z\cdot \tau} \right|}$$
» which needs λz, 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). [...]

Good point!
Since we're about to release next version (v2.3.3) of bear, we added data analysis for MD BE/BA since this release. I used to estimate lambdaz of MD study with the same method that we did in SD study. However, I was not very comfortable to do so for a long time.

All the best,
-- Yung-jin Lee
bear v2.8.8:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear
Helmut
★★★

Vienna, Austria,
2009-07-16 14:06

@ yjlee168
Posting: # 3959
Views: 11,576

## NCA without lambda(z)

Dear Hsin-ya & Yung-jin,

» For what purpose to take blood sample after tau? Is it worth to do so?

I only said that I have seen people doing so. IMHO, it does not make any sense.

» » 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 [...]

» So, it looks like that no lambdaz, no NCA...

Why? According to my knowledge no guideline specific for MD-studies calls for λz.

» » I would not try to play around with elimination from steady state within τ.

An example for different λz-estimates obtained from SD and MD for a two-compartment model (similar to this post, but τ=24h, 4 doses): Running WinNonlin’s PK model 11 (extravascular, first order absorption, 2 compartments, no lag-time, micro-constants parametrization, w=1/y2) we get
 V1_F  76.41   L K01    2.422  /hr  (t½ 0.2862 hr) K10    0.1410 /hr  (t½ 4.916  hr) K12    1.383  /hr  (t½ 0.5014 hr) K21    0.9421 /hr  (t½ 0.7357 hr)
NCA-estimation of λz from the last three points (12/14/24hr) gives 0.1233/hr (t½ 5.624hr). If we use the predicted concentrations we would get 0.1030/hr (t½ 6.732hr). Running a simulation of the dosage regimen and estimating λz from data in the last interval (84/86/96hr) we get 0.1397/hr (t½ 4.963) – which is faster than the SD-estimate. Metaphorically speaking in log-scale in any given dosage interval we place another ‘triangle’ on top of the remaining profile – it’s clear that the descending slope gets steeper. If one is really interested in λz and has no SD-phase in the study, sampling should continue until concentrations from previous doses are washed out – I would expect any estimate within the MD-profile to be biased towards faster elimination.

» It is inevitable for us in Taiwan or in China to conduct a multiple-dose BE/BA study when the target product is modified release dosage form.

OK, same in the EU.

» The formula is only for when conducting both a SD and a MD BE/BA studies simultaneously. If we just have a MD BE study, we still need a lambdaz.

Do Chinese guidelines call for λz, accumulation index, ?

» » Vss is a strange metric.
» Indeed. We calculate Vss just because WinNonlin does so.

That’s not a good reason.
WinNonlin carries some really outdated legacy from previous versions. I talked to Simon last week, and it seems that Pharsight is reluctant in removing anything in order to keep backwards-compatibility. BTW, who needs an 80% confidence interval or – even worse – Westlake’s confidence intervals? Does anybody understand how WinNonlin calculates the ridiculous a posteriori power?

» Since we're about to release next version (v2.3.3) of bear, we added data analysis for MD BE/BA since this release.

Great!

» I used to estimate lambdaz of MD study with the same method that we did in SD study. However, I was not very comfortable to do so for a long time.

Given my comments from above I’m not convinced whether it is really needed and makes sense at all.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
yjlee168
★★

Kaohsiung, Taiwan,
2009-07-16 22:17
(edited by yjlee168 on 2009-07-16 22:34)

@ Helmut
Posting: # 3960
Views: 10,892

## No rule is the rule - lambda(z) of MD BE

Dear Helmut,

» I only said that I have seen people doing so. IMHO it does not make any sense.

I see.

» » So, it looks like that no lambdaz, no NCA...
»
» Why? According to my knowledge no guideline specific for MD-studies calls for λz.

» » » I would not try to play around with elimination from steady state within τ.

In Taiwan, we have to provide three Cmins before starting sampling for Css(n) at the steady-state (SS) for one dosing interval to prove that we do have Cmax(ss) and AUCtau(ss). For example, if the tau is fixed at 24 hr, then we start dosing volunteers for 5 consecutive days. And on the 3rd, 4th and 5th day, we need get each blood sample before next dose as Cmin. So we will have 3 Cmins and a serial C(n)ss within one tau at SS on the 6th day as the attached plot. Unfortunately, sometimes these three Cmins data before SS can be quite noisy. It can be difficult to tell the SS has been reached. In this situation, we can provide half-life (T1/2) at the same time to prove that the SS has been reached during the time period that we collect blood samples for one tau. For instance, If estimated T1/2 is 18 hr, then we do collect blood samples at SS since it has been 120 hr which is more than 5*T1/2 (90 hr). That's why we have to play with elimination from SS within tau.

» [..] washed out - I would expect any estimate within the MD-profile to be biased towards faster elimination.

Nice example. I did that once. I used nonlinear regression to fit conc-time data obtained from a MD BE study. Of course, I tried 1-, 2- and 3-compartment PK models and then used AIC to pick the final model. From fitting results of the final model, I got T1/2 indirectly with further calculation. That helped me to explain "Hey! I really did sampling at SS." The approach was accepted with that case.

» Do Chinese guidelines call for λz, accumulation index, ?

No. Not even FDA, EMEA or Japan for MD BE study, as far as I remember. So no rule is the rule.

» » » Vss is a strange metric.
» » Indeed. We calculate Vss just because WinNonlin does so.
»
» That’s not a good reason.

I know. Just because people or regulators have been getting used to WinNonlin.

» WinNonlin carries some really outdated legacy from previous versions. I talked to Simon last week, and it seems at Pharsight is reluctant in removing anything in order to keep backwards-compatibility. BTW, who needs a 80% confidence interval or – even worse – Westlake's confidence intervals? Does anybody understand how WinNonlin calculates the ridiculous a posteriori power?

, only can be heard exclusively at this Forum.

» [...] added data analysis for MD BE/BA since this release.
»
» Great!

We will still use ARS, TTT, or AIC or the combination methods as we do with SD BE study to estimate lambdaz without including Cmax(ss) in bear. Options are up to user.

» Given my comments from above I’m not convinced whether it is really needed and makes sense at all.

explained as above. Many thanks.

All the best,
-- Yung-jin Lee
bear v2.8.8:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear
oksanachlebko
☆

Ukraine,
2018-01-05 00:10

@ Helmut
Posting: # 18146
Views: 5,386

## Distinguish accumulation

Dear Helmut!
I kindly ask you to help me with the following question!

» 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.

is it possible to distinguish true nonlinear PK and shift due to other compartments?
What if the dose proportionality is proven but accumulation index is more than 1.4?

All the Best!
Oksana