Stochastic structure

The following are examples of commonly used models using stochastic structures, aka "random models".

Models for CL in terms of TVCL ("typical value of clearance") and ETA are examples of models expressing population inter-individual variability.

Models for Y involving F ("prediction based on the pharmacokinetic parameters") and ERR are examples of models for intra-individual ("residual") variability. They are used with both population or single-subject data, in which case ERR stands for EPS or ETA, respectively.

Additive models

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      CL=TVCL+ETA(1)
      Y=F+ERR(1)

Proportional

Also known as CCV; Constant Coefficient of Variation models

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      CL=TVCL*(1+ETA(1))
      Y=F*(1+ERR(1))

An equivalent way of coding the proportional model is:

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      CL=TVCL+TVCL*ETA(1)
      Y=F+F*ERR(1)

Exponential

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      CL=TVCL*EXP(ETA(1))
      Y=F*EXP(ERR(1))

During estimation by the first-order method, the exponential model and proportional models give identical results, i.e., NONMEM cannot distinguish between them.

During estimation by a conditional estimation method, the exponential and proportional models for inter-individual variability give different results. During simulation, the two models give different results, in both the inter- and intra-individual cases.

Power Function model

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      Y=F+F**P*ERR(1)

The Power Function model has both the additive and the CCV error models as special cases, and smoothly interpolates between them in other cases.

Combined Additive and Proportional model

Also known as slope-intercept model.

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      Y =F*(1+ERR(1))+ERR(2)

Here is an alternative parameterization for the same model when there is no covariance between ERR(1) and ERR(2). Any THETA may be used.

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      W=(1+THETA(5)*THETA(5)*F*F)**.5
      Y=F+W*ERR(1)

REFERENCES: Guide V, section 3 , 4.1 , 7.5 , 8.3

REFERENCES: Guide V, section 8

REFERENCES: Guide VII, section I , III