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.

翻译：理解生物标志物分布随时间演变是数字健康与慢性病监测中的核心挑战。在糖尿病领域，血糖测量值分布的变化能够揭示传统总结性指标无法捕捉的疾病进展与治疗反应模式。受一项为期26周、比较闭环胰岛素输送系统t:slim X2与标准疗法在1型糖尿病儿童中疗效的临床试验启发，我们提出一个概率框架，利用每五分钟采集的持续血糖监测数据建模时间索引分布的连续时间演化。我们将血糖分布表示为高斯混合模型，其随时间变化的混合权重由神经常微分方程控制。基于最大均值差异的分布匹配准则估计模型参数。最终框架兼具可解释性、计算高效性，并对细微的时序分布变化敏感。将该方法应用于CGM试验数据后，可检测传统分析方法难以捕捉的治疗相关血糖动力学改善。