Complex covariates

A DeepPumas take on covariate modelling

Niklas Korsbo

2025-10-12

Covariates … ?

• A measurable characteristic of an individual that explains part of the variability in model parameters across a population.

Between-subject variability … ?

• Differences in outcomes between individuals that cannot be explained by the model structure and random noise alone

• Typically handled by introducing individual-specific parameters

• Random effects can characterize this variability as a posterior distribution of patient features

Augment workflow

• Green: observed quantities
• Blue: Fixed effects
• Red: Random effects

Covariate-free model

• So far, our models have been covariate-free
• They cannot exploit known heterogeneity in the patients to give better predictions

Can we predict the values of the random effect from the covariates?

Supervised learning

Augmented model

To make it harder…

• We could use EBEs directly - in DeepPumas, we don’t
• We can use transformed EBEs - that we do
  • orthogonalized MvNormals
  • standardized to similar absolute values
  • unconstrained values
  • invertible
  • We can weight with sensitivity of the loglikelihood
• We could use the “full” posterior distribution

What we’re really after

\[ \eta_i \sim p(\eta | \text{covariates}) \]

A rich description of how covariate information affects the prior distribution of the random effects.

To be presented at ACoP in two weeks