Designing and Evaluating Neural Ordinary Differential Equation Models for Pharmacokinetic and Pharmacodynamic Time Series

Abstract

PKPD modeling is the study of the effect of drugs on living organisms. It combines modeling the concentration (PK) and effect (PD) of a drug over time. This is commonly done through systems of ordinary differential equations (ODEs), although there have been increasing efforts to utilize machine learning methods in the area. In this project, discriminative neural ODE models for PKPD data were developed and compared with other common neural network models. We simulated our train and test data using an underlying PKPD model, resulting in a ground truth set to accurately test the performance of the models. The models aimed to extrapolate as well as possible to dosing regimens not seen in the training data. We found that using neural ODEs, it is possible to accurately predict concentrations and responses resulting from dose sizes that are more than twice the size of those in the training data. This vastly outperforms the other tested models. Furthermore, using the flow matching algorithm, the training time of the neural ODE model was substantially reduced. The project also investigated whether using a neural ODE as a component in a Generative PKPD model yielded any benefits. It was found that this significantly improved the quality of the samples by more closely reflecting the underlying distribution of PKPD time series. The ability of the discriminative neural ODE models to capture information about the PKPD model used to generate the model was then investigated by assessing their ability to predict uncertainty in the underlying data, as well as their capacity to identify which covariates were relevant to the underlying PKPD model. Finally, a neural ODE model was developed for modeling adverse effects, to test how well the neural ODE performed when the data was not generated using an underlying ODE. This model demonstrated excellent performance in predicting the proportion of patients who experience nausea based on the rate of dose increase over time.