The goal of precision medicine--tailoring patients' treatments to account for heterogeneity in a way that is data-driven and reproducible--is particularly relevant in diseases that manifest in continuous-time systems with a high degree of variability between patients. Consider a system of several continuous-time processes, one of which is the process of interest, the rest of which are history variables that impact the rate of change of the process of interest in an unknown way. In such settings, knowledge of an individual patient's system dynamics could provide crucial information for treatment assignment. While precision medicine methods to estimate the history variables' contribution to the mean of the process of interest exist, current methods do not take into account that the process of interest's variability may also be influenced by history variables. Using a form of Itô's equation, we present a novel method for estimating both mean- and variance-level system dynamics. We demonstrate this method with a real-world example from type I diabetes.