Bioequivalence and Bioavailability Forum

Dear Luvblooms,

I guess you're talking about time-dependent clearance here.

❝ But, even the tissue where it has been distributed keeps on proliferating or growing thus increasing the number of cells available for metabolism or in other term with increase in the number of cell, the metabolic capability increases thus that may lead to increase metabolism of the drug in that specific region or tissue.

❝

❝ My question is that

❝ 1. Is there will be any effect on the PD out come because of the increased metabolism/ increased metabolic activity of the tissue where the drug is distributed or it is simply controlled by the systemic clearance?

Yes and no. It depends on the changes of clearance (Cl). However, you may need to know when Cl is going to change (its starting time and stopping time) first. Of course, you can have as many as Cls you want, only if you need to know each Cl's starting time and stopping time to switch to different Cl. That's the difficult part. However, you figure it out from your data by plotting all data with 'Conc. vs. Time' first; and make your guess. It may take you some time to get good guess (trial-and-error).

❝ 2. Is there any PK PD model is available for the same?

Not totally the same but should have a lot of similar PK/PD models. You can look for Pubmed with keyword "time-dependent clearance" or google it.

❝ 3. If no PK PD model available, what approaches one should try for to generate one.

❝

❝ I hope someone at the forum will help me out with this as I am stuck and not finding any way out.

I think you may need to create this model yourself to fit your data (needs). I would suggest that you can try ADAPT v5 (a fortran compiler required, freeware), Boomer (no compiler required, freeware), or Winnonlin (commercial), SAAM-II (commercial). Hope this can help.

Dear Luvblooms!

First I agree with Yung-jin’s post.

I’m afraid you have to give us more information. Normally the half-life of drugs is too short to be influenced by an increasing number of cells (are you thinking about a tumor?). Exceptions are drugs with very long half-lives (let’s say, more than a week), or the patient is in true steady-state (again, I’m talking about weeks).
What we see in time-dependent clearances Yung-jin mentioned are mainly following types:

• AUC_τ (steady state) > AUC_∞ (single dose): Capacity limited and/or Auto-inhibition
  
• AUC_τ (steady state) < AUC_∞ (single dose): Auto-induction

If other drugs are administered simultaneously, PK interactions (mainly competitive inhibition) may occur as well.

Some general remarks about modeling:

• Get some books. Read them. Take a vacation. Read them again.
  
• Consider getting some training.
  
• Yung-jin called it trial-and-error. Carl Metzler (the author of NONLIN in the mid-1960s) once published a paper “Curve-Fitting: Art or Science?”… Be prepared, it will take you some time. The worst I know was a population PK/PD model, where an experienced group (!) of pharmaco­kineticists worked almost one year (!!) on two datasets (SD, MD)…
  
• If you really notice a change in clearance (e.g., in a multiple dose study trough values increase to a pseudo-equilibrium and subsequently decrease to the final steady state), try the following methods to model the changing clearance:
  • Add a lag-time.
    
  • Try a catenary model (additional hypothetical compartment before the central).
    
  • Try a sigmoidal model.
• Classical PK/PD modeling may work well for some subjects, but fail terribly for others. Or you may end up with a one-compartment model for subjects with low concentrations and a two-compartment model for others. Population PK/PD is a much better choice, but the learning curve is even more steep… If you have sparse data (not a ‘rich dataset’ of well-defined profiles), only Pop-PK/PD will work.
  
• Try to get as much data as possible. If you have urine data, simultaneous fitting may improve your model. If you have data of a metabolite, fine.
  
• Start with an unweighted model. If one of the variants of the Gauss-Newton algorithm fails, try a grid-search (Simplex). Use these estimates as new starting values for Gauss-Newton. If still not stable (high standard errors), tweak the constraints (parameters’ boundaries). Try different weighting schemes next. Look at the residuals: Evenly spread around zero? Any trend? Funnel pattern? Base the model selection on the minimum AIC.
  
• The error distribution of the parts of the dataset may differ. Sometimes 1/y² is best for plasma and 1/y for urine. If PD-data cover only a limited range, unweighted may be the best.
  
• Once you have a Pop-PK/PD model of acceptable quality, start adding covariates (e.g., body weight/surface, sex, creatine clearance, disease state,…) until you get no further improvement.
  
• Pop-PK/PD models must be validated (Search the Guidelines for ‘Population’).
  • Internal validation: Randomly select a group of subjects from the dataset, estimate model parameters, and check the agreement of the remaining group of subjects with predicted data.
    
  • External validation (preferred): Check the prediction from the model with observed values of another study.

Good luck!

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Suggestions:

J Gabrielsson and D Weiner
Pharmacokinetic an Pharmacodynamic Data Analysis: Concepts and Applications
Swedish Pharmaceutical Press, Stockholm (4^th edition 2007)
  Good starting point, many examples, code for WinNonlin.
P Bonate
Pharmacokinetic-Pharmacodynamic Modeling and Simulation
Springer, New York (2006)
  Nothing to read in the subway. Good examples on model-identifiability and -discrimination.
M Rowland and T Tozer
Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications
Lippincott Williams & Wilkins, Baltimore (4^th edition 2010)
  The classic one.