Parametric and Nonparametric Population Modeling: a brief Summary

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Parametric and Nonparametric Population Modeling
a brief Summary

• Roger Jelliffe, M.D.
• USC Lab of Applied Pharmacokinetics

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InTER-Individual Variability

• The variability between subjects in a
  population.
• Usually a single number (SD, CV) in parametric
  population models
• But there may be specific subpopulation groups
• eg, fast, slow metabolizers, etc.
• How describe all this with one number?
• What will you DO with it?

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InTRA-Individual Variability

• The variability within an individual subject.
• Assay error pattern, plus
• Errors in Recording times of samples
• Errors in Dosage Amounts given
• Errors in Recording Dosage times
• Structural Model Mis-specification
• Unrecognized changes in parameter values during
  data analysis.
• How describe all this with one number?
• How describe interoccasional variability
  only with one number?
• What will you DO with these numbers?

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Bottom line for researchor for TDM

• Dont wait for steady state
• Dont wait for distribution after the dose
• Start TDM with 1st dose
• Use D-opt principles

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Parametric Population Models IT2B, NONMEM, etc

• Assume shape (normal, lognormal) of param
  distribs. (Describe params parametrically)
• Get the param param values param means, SDs,
  covariances, etc.
• Get F from intermixed IVPO dosage
• Get SEMs, some confidence limits, signif tests.
• Separate Inter - from Intra - Individual
  from assay Variability
• But, usually get only summary single values for
  parameter distributions.
• And also, they are not consistent.

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SummaryParametric Population Models

• Single point parameter estimates only.
• Only one (1) model.
• Cannot discover unsuspected subpopulations
• Cannot predict precision of goal achievement
• Most currently available ones not consistent.
• Can estimate Parameter ranges

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A Parametric Population Model Joint Density
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800 Normally distributed (K,V) points,
correlation 0.6
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A Population Model, made by Breugel
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What is the IDEAL Pop Model?

• The correct structural PK/PD Model.
• The collection of each subjects exactly known
  parameter values for that model.
• Therefore, multiple individual models, one for
  each subject.
• Usual statistical summaries can also be obtained,
  but usually will lose info.
• How best approach this ideal? NP!

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An NPML Population Model, made by Mallet
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800 normal points give 70 NPAG support points
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Nonparametric Population Models (1)

• Get the entire ML distribution, a DiscreteJoint
  Density one param set per subject, its prob.
• Shape of distribution not determined by some
  equation, only by the data itself.
• Multiple indiv models, up to one per subject.
• Can discover, locate, unsuspected subpopulations.
• Get F from intermixed IVPO dosage.

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Nonparametric Population Models (2)

• The multiple models permit multiple
  predictions.
• Can predict precision of goal achievement by a
  dosage regimen.
• Behavior is consistent.
• Use IIV /or assay SD, stated ranges.

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