Addressing model discrepancy in a clinical model of the oxygen dissociation curve

Many mathematical models suffer from model discrepancy, posing a significant challenge to their use in clinical decision-making. In this article, we consider methods for addressing this issue. In the first approach, a mathematical model is treated as a black box system, and model discrepancy is defined as an independent and additive term that accounts for the difference between the physical phenomena and the model representation. A Gaussian Process (GP) is commonly used to capture the model discrepancy. An alternative approach is to construct a hybrid grey box model by filling in the incomplete parts of the mathematical model with a neural network. The neural network is used to learn the missing processes by comparing the observations with the model output. To enhance interpretability, the outputs of this non-parametric model can then be regressed into a symbolic form to obtain the learned model. We compare and discuss the effectiveness of these approaches in handling model discrepancy using clinical data from the ICU and the Siggaard-Andersen oxygen status algorithm.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.