Neural Controlled Differential Equation and Its Application in Pharmacokinetics and Pharmacodynamics

With the recent advances in machine learning (ML) and artificial intelligence (AI), data-driven modeling approaches for pharmacokinetics (PK) and pharmacodynamics (PD) have gained popularity due to their versatility in diverse settings and reduced reliance on prior assumptions. However, most of the ML methods ignore the hidden dynamics behind the data, lacking interpretability. This study investigated the applicability of neural controlled differential equation (NCDE), a novel ML method that is suitable for data-driven modeling of PK and PD profiles, especially in the setting of multiple dosing. We demonstrated that NCDE was capable of combining differential-equation-based dynamics with data-driven characteristics, flexibly incorporating various types of inputs, and embedding discontinuous dynamics. Moreover, a direct correspondence was identified between the learned dynamics of NCDE and the dynamics behind the data, which highlights the intrinsic interpretability of NCDE. Additionally, the influence of important hyperparameters was systematically investigated, and it was found that L1 regularization and the AdaMax optimizer were useful for stabilizing the training process and leading to a generalizable NCDE model. Together, these findings demonstrate the accuracy, generalizability, and interpretability of NCDE, indicating that NCDE is a reliable method for further application. In the future, NCDE may further facilitate PK and PD prediction in general.