Tamara van Donge

Chapter 7 144 Supporting information Supporting Information 1 Non-linear mixed effect modeling description The population analysis was performed by applying non-linear mixed effect modelling approaches. These models take into account both explained and unexplained variability at inter- and intra-individual levels. Non-linear mixed effect models are characterized in terms of: (i) Fixed effects: this is the population average of the model parameters θ. These parameters are susceptible to various factors, such as physiological characteristics (gestational age, body weight, etc), genetic characteristics, or drug-drug interactions. These last factors are the fixed effect covariates, z i . (ii) Random effects: this is the part of the variability that is not explained by the above fixed effect and allows quantification of: • The inter-individual variability (also called the between subject variability), which is the variability between two different individuals. It is expressed by ω 2 , which is the variance of the fixed effect parameter θ. For an individual i, • ! = ∙ exp( ! ) , , with ! ~ (0, ω " ) • The intra-individual variability (also called the residual unexplained variability), which is the variability within the same individual over time i.e. between two given moments. It is expressed by σ 2 . For an observation j, the corresponding prediction ŷ for an individual is !,# = ŷ + !,# , with !,# ~ (0, $ ) Thus, the general mixed effects model is written: !,# = # !# , ϕ $ ' × !,# And the parameter model: ϕ ! = g ( " , θ) + η " Where !" !" ϕ # !" ! $ Ω . is the j th observation in an individual i, !" !" ϕ # !" ! $ Ω . are the design variables for an individual i, !" !" ϕ # !" ! $ Ω . is the vector of model parameters for an individual i, and !" !" ϕ # !" ! $ Ω . represents the residual error; g is a structural model which is function of fixed effects covariates z i , and fixed effects parameters θ; finally, !" !" ϕ # !" ! $ Ω . represents the structural model. In this general model, residual error !" !" ϕ # !" ! $ Ω . is proportional and is assumed to follow a log-normal distribution with mean 0 and a unit variance σ 2 .