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 |                            RANDOM MODELS                        |
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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 varia-
 bility.

 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, 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
      exponential  and  proportional models for inter-individual varia-
      bility 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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