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MEANING: Models for random variables
CONTEXT: Abbreviated code
DISCUSSION:
The following are examples of commonly used models using random vari-
ables.
Models for CL in terms of TVCL ("typical value of clearance") and ETA
are examples of models expressing population inter-individual vari-
ability.
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 sin-
gle-subject data, in which case ERR stands for EPS or ETA, respec-
tively.
Additive models
CL=TVCL+ETA(1)
Y=F+ERR(1)
Proportional (CCV; Constant Coefficient of Variation) models
CL=TVCL*(1+ETA(1))
Y=F*(1+ERR(1))
An equivalent way of coding the proportional model is:
CL=TVCL+TVCL*ETA(1)
Y=F+F*ERR(1)
Exponential models
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., NON-
MEM cannot distinguish between them.
During estimation by a conditional estimation method, the expo-
nential 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
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 (slope-intercept model)
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.
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
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