martin
★★  

Austria,
2010-06-25 21:50
(5433 d 05:50 ago)

Posting: # 5563
Views: 9,180
 

 Linear kinetics - dose proportionality [PK / PD]

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Dear all!

Motivated by a recent discussion with HS I would like start a thread regarding "rather" basic principles of pharmacokinetics:
  1. On assumptions of linear kinetics, PK parameters such as half-life(s) and clearance are per definition constant for different dose levels and observed differences are simple due to variability only (correct?)
  2. Linear kinetics implies dose-proportionality but not necessarily vice versa (correct?)
  3. In practice, we are not able to "show" linear kinetics but we can assess dose-proportionality (correct?)
In the case that dose-proportionality was shown over a dose-range, is it then justified to summarize for example individual half-life(s) over all dose ranges investigated to get a "better" estimate (i.e. based on a larger sample size leading to narrower confidence intervals) ?

Best regards

Martin
 
ElMaestro
★★★

Denmark,
2010-06-26 00:27
(5433 d 03:13 ago)

@ martin
Posting: # 5564
Views: 7,851
 

 Linear kinetics - dose proportionality

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Dear Martin,

I flipped my coin a few times:
  1. Yes.
  2. Yes. But academic, isn't it? Have an example?
  3. What question are you really trying to answer? And consider the following while thinking: Can person A display 'linear kinetics' and person B not? If yes, how would this affect our thinking to all of the above?
Hint: It might not be relevant to speak of linear kinetics as a general phenomenon.

I don't have all the answers, unfortunately.

Best regards
EM.
—
Pass or fail!
ElMaestro
 
martin
★★  

Austria,
2010-06-26 10:13
(5432 d 17:27 ago)

@ ElMaestro
Posting: # 5566
Views: 7,781
 

 Linear kinetics - dose proportionality

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Dear ElMaestro!

Thank you very much for your answer and thought-provoking impulse. In my honest opinion, it is not possible to show linear kinetics (it's an assumption) in praxis but we may claim that a product exhibit sufficient dose-proportionality.

I am trying to motivate my questions with the following example:
  • Consider a parallel group design where k dose levels (IV route) are investigated
  • Extremely high variability in the predominant half-life but less variability in AUCs
  • Dose-proportionality holds evaluated based on AUCs using the power-law model
One question I am trying to answer is: How long does it take that the product is practically (i.e. 99.2% of steady state) eliminated from the body?

To answer this question, an estimate for the predominant half-life is needed as a product is practically eliminated from the body after 7 half-lifes have elapsed.

Is it justified to summarize individual predominant half-lifes over all dose levels to get a single estimate and a confidence interval for the predominant half-life to answer the question above (having in mind that dose-proportionality does not necessarily imply "linear kinetics")?

Best regards

Martin
 
ElMaestro
★★★

Denmark,
2010-06-26 13:43
(5432 d 13:57 ago)

@ martin
Posting: # 5567
Views: 7,715
 

 Linear kinetics - dose proportionality

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Dear Martin,

❝ One question I am trying to answer is: How long does it take that the

❝ product is practically (i.e. 99.2% of steady state) eliminated from the

❝ body?


"The body"...whose body? Yours? Mine? Subject number 51?
I guess this is a population question, but I could be wrong. How about bootstrapping the whole thing 8 trillion billion times and extract 8 trillion billion halflives and construct a CI on that basis?
If the sample you have reflects the distribution of the (relevant) population -whether normal or not- then I guess this approach would be difficult to reject from the regulatory side.

Best regards
EM.
—
Pass or fail!
ElMaestro
 
Ohlbe
★★★

France,
2010-06-28 00:07
(5431 d 03:33 ago)

@ martin
Posting: # 5568
Views: 7,803
 

 Linear kinetics - dose proportionality

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Dear Martin,

❝ Is it justified to summarize individual predominant half-lifes over all

❝ dose levels to get a single estimate and a confidence interval for the

❝ predominant half-life


You'll have to be aware of the limitations of the bioanalytical method you are using. If the LLOQ is not low enough you may not get a reliable estimate at the lower dose (not getting the terminal half-life but only seeing the distribution phase, or a mix of distribution and elimination).

Regards
Ohlbe
—
Regards
Ohlbe
 
Helmut
★★★
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Homepage
Vienna, Austria,
2010-06-28 14:20
(5430 d 13:21 ago)

@ martin
Posting: # 5570
Views: 7,725
 

 Linear kinetics - dose proportionality

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Dear Martin & all,

did I get you right that you
  • have established ‘linear PK’ based on NCA’s AUCs and an exponent of 1±something in the power model and
  • want a single estimate/CI of half-lives pooled across subjects and doses to predict steady state and/or complete elimination?
If you are happy with your analytical method at the lowest dose level (Ohlbe’s post), I would say you can do so in various ways. Calculate an estimate based on the harmonic mean of individual values and a jackknife (WinNonlin’s terminology: pseudo-) SD or consider a Population PK model. If you don’t want to get commercial software (NONMEM, Phoenix/NLME), MONOLIX is an alternative. A Bayesian alternative (cave: steep learning curve!) is PKBUGS/WinBUGS. I would not start to fiddle around with [image]’s nlme, because setting up the model, finding starting values and constraints may be a cumbersome task.

If you don’t want to ‘do it at home only’, see regulatory requirements for Pop-PK: FDA 1999, EMA 2007.

  1. Lam FC, Hung CT, DG Perrier DG. Estimation of Variance for Harmonic Half-Lives. J Pharm Sci. 1985;74(2):229–31.
  2. Schaaf LJ, Lam FC, DG Perrier DG. Comparison of Harmonic Mean versus Arithmetic Mean Clearance Values. J Pharm Sci. 1986;75(4):427–9.
  3. Roe DJ, MD Karol MD. Averaging Pharmacokinetic Parameter Estimates from Experimental Studies: Statistical Theory and Application.
    J Pharm Sci. 1997;86(5):621–4.
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