DeepNLME for pharmacometrics

Authors:
Mohamed Tarek, Niklas Korsbo

DeepNLME for pharmacometrics

Summary

DeepNLME

Population-level parameters: \(\theta\), \(\Omega\), \(c\), \(\sigma\)

Covariates: \(\text{Age}_i\), \(\text{Weight}_i\),

Random effects: \(\eta_i \sim \mathcal{N}(0, \Omega)\)

Individual derived parameters: \[ \begin{aligned} \text{Ka}_i & = \theta_1 \cdot e^{\eta_{i,1}} + c_1 \cdot \text{Age}_i + \\ \text{CL}_i & = \theta_2 \cdot e^{\eta_{i,2}} \\ \text{V}_i & = \theta_3 \cdot e^{\eta_{i,3}} + c_2 \cdot \text{Weight}_i^{c_3} + \end{aligned} \]

Dynamics: \[ \begin{aligned} \frac{d[\text{Depot}_i]}{dt} & = - \text{Ka}_i \cdot [\text{Depot}_i] \\ \frac{d[\text{Central}_i]}{dt} & = \text{Ka}_i \cdot [\text{Depot}_i] \, - \end{aligned} \]

Error model: \[ \text{Outcome}_i \sim \mathcal{N}(\text{Central}_i, \text{Central}_i \cdot \sigma) \]

Exercise: DeepNLME for pharmacometrics

Flexible local information processing

Baseline covariate identification

Classical NLME model

Covariate-free model

  • The NLME UDE models we have seen are covariate free!
  • They cannot exploit covariates to give better predictions!
  • In absence of observed response data, their best prediction is independent of the individual under consideration.
  • This is far from ideal.
  • However, if we could find a function mapping the covariates to the random effects of the UDE model, we could give better predictions even in absence of observed data.

Supervised machine learning

Augmenting the model

Summary

  1. Fit an NLME model to describe individual time courses using random effects
  2. Extract an approximation of the posterior distribution of the random effects for each subject in the training data.
  3. Fit a machine learning model to use the covariates to predict these posterior distributions.
  4. Augment the original NLME model with the machine learning prediction of the random effect value.