Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes

TL;DR

This paper introduces a continuous-time probabilistic model using neural ODEs to analyze evolving glucose distributions in children with type 1 diabetes, revealing treatment effects more effectively than traditional methods.

Contribution

The study presents a novel neural ODE-based framework for modeling time-varying biomarker distributions, specifically applied to continuous glucose monitoring data in a clinical trial setting.

Findings

Detects treatment-related improvements in glucose dynamics

Sensitive to subtle temporal distributional changes

Provides interpretable and efficient analysis

Abstract

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.