Bioequivalence and Bioavailability Forum

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.