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. 2012 Jul 6;39(4):393–414. doi: 10.1007/s10928-012-9258-0

Table 4.

Covariate, inter-individual variability, and residual error relationships considered during model building

Mathematical function Compounds tested
Covariate relationshipa
 Continuous covariate
  No relationship Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
  Additive Inline graphic Citalopram, DMAG, Olanzapine, Perphenazine
  Proportional Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine
  Exponential Inline graphic Citalopram, DMAG, Escitalopram, Perphenazine, Risperidone, Olanzapine, Ziprasidone
  Power-law Inline graphic Citalopram, Escitalopram, Olanzapine, Perphenazine
  Michaelis–Menten Inline graphic DMAG
 Discrete
  No relationship Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
  Additive Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Ziprasidone
  Proportional Inline graphic Perphenazine
  Exponential Inline graphic Risperidone, Perphenazine
 Type of inter-individual variabilityb
  No relationship Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
  Exponential Inline graphic Citalopram, DMAG,Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
 Type of residual variabilityc
  Additive Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
  Proportional Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone
  Combined additive and proportional Inline graphic Citalopram, DMAG, Escitalopram, Olanzapine, Perphenazine, Risperidone, Ziprasidone

aModification of a typical value for the example of clearance of the ith individual by the jth covariate or where x i,j is the value of the jth covariate for the ith patient, Inline graphic is the median value of the jth covariate, Inline graphic is the category (counting) number of the jth covariate for the ith patient, and Inline graphic is a parameter for functional form n that describe the relationship of the jth covariate

bInter-individual function forms considered for the example of the clearance of the ith individual. The Inline graphic takes a standard normal distribution with standard deviation Inline graphic

cResidual variability function forms considered. The variable Y i,j is the jth observation for the ith patient, F i,j is the corresponding model prediction, and Inline graphic and Inline graphic take standard normal distributions with variances Inline graphic and Inline graphic, respectively