Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression and treatment response that conventional summary measures miss. Motivated by a 26-week clinical trial comparing the closed-loop insulin delivery system t:slim X2 with standard therapy in children with type 1 diabetes, we propose a probabilistic framework to model the continuous-time evolution of time-indexed distributions using continuous glucose monitoring data (CGM) collected every five minutes. We represent the glucose distribution as a Gaussian mixture, with time-varying mixture weights governed by a neural ODE. We estimate the model parameter using a distribution-matching criterion based on the maximum mean discrepancy. The resulting framework is interpretable, computationally efficient, and sensitive to subtle temporal distributional changes. Applied to CGM trial data, the method detects treatment-related improvements in glucose dynamics that are difficult to capture with traditional analytical approaches.

Blood glucose simulation allows the effectiveness of type 1 diabetes (T1D) management strategies to be evaluated without patient harm. Deep learning algorithms provide a promising avenue for extending simulator capabilities; however, these algorithms are limited in that they do not necessarily learn physiologically correct glucose dynamics and can learn incorrect and potentially dangerous relationships from confounders in training data. This is likely to be more important in real-world scenarios, as data is not collected under strict research protocol. This work explores the implications of using deep learning algorithms trained on real-world data to model glucose dynamics. Free-living data was processed from the OpenAPS Data Commons and supplemented with patient-reported tags of challenging diabetes events, constituting one of the most detailed real-world T1D datasets. This dataset was used to train and evaluate state-of-the-art glucose simulators, comparing their prediction error across safety critical scenarios and assessing the physiological appropriateness of the learned dynamics using Shapley Additive Explanations (SHAP). While deep learning prediction accuracy surpassed the widely-used mathematical simulator approach, the model deteriorated in safety critical scenarios and struggled to leverage self-reported meal and exercise information. SHAP value analysis also indicated the model had fundamentally confused the roles of insulin and carbohydrates, which is one of the most basic T1D management principles. This work highlights the importance of considering physiological appropriateness when using deep learning to model real-world systems in T1D and healthcare more broadly, and provides recommendations for building models that are robust to real-world data constraints.