Nonlinear mixed effect model

Gist

between-subject variability
- Intersubject variability
- Between-individual variability
  - EXAMPLE: Statistical-mathematical expression relating subject-specific PK or PD model parameter values to random variables describing population variability:
    $$CL_i = CL_{pop} + \eta_i$$where CL_i is the indiivdualized value of drug clearance, $C L_{p o p}$ is the population level clearance, and $η$ is the random effect usually drawn from a Normal Distribution
Between occasion variability
- Interoccasion variability
  -Statistical-mathematical expression relating subject-specific PK or PD model parameter values to random variables describing their variation between different study sessions:
$C L_{i} = [C L_{p o p} + κ_{k}] + η_{i} $ $ w h e r e C L_{i} i s t h e i n d i i v d u a l i z e d v a l u e o f d r u g c l e a r a n c e, $ C L_{p o p} $ i s t h e p o p u l a t i o n l e v e l c l e a r a n c e, a n d $ η $ i s t h e r a n d o m e f f e c t u s u a l l y d r a w n f r o m a [[N o r m a l D i s t r i b u t i o n$
- Statistical-mathematical expression relating PK/PD or disease model predictions tot he actual trial measurement

Y(time) = F(time) + \epsilon(time)$$where CL_i is the indiivdualized value of drug clearance, $CL_{pop}$ is the population level clearance, and $\eta$ is the random effect usually drawn from aNormal Distribution## Parameter distributions 1) Variability in physically processes: constrained normal or log-normal distributions as negative values are not possible for such processes 2) Thus even if a parameter is log normal, its natural log is more approximately normal ## Covariate - To identify sub-groups of patients that may be at potential risk of toxciity or sub-therapeutic effect - Confirm absence of important influence from covariate - Increase the mechanistic interpretability of the mdoel - Understand trial characteristics - Hypothesis generation - Increase the predictive performance of the model - Increase the understanding ofa. studied system ### Steps in covariate model building 1) Include all covairate parameters of interest 2) Funnel it down to scientific plausibility 3) Funnel it down to statistical signifiance 4) Funnel it down to clinical relevance 5) Final covariate-parameter relationships ## In R [^1]: (Video) Population pharmacokinetics with Dr. Robert R. Bies