用神经微分方程建模儿童糖尿病血糖分布随时间变化，更灵敏捕捉治疗效果。
Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes
- 用高斯混合模型结合神经微分方程，动态建模血糖分布演变
- 在26周试验中检测到传统方法忽略的细微治疗改善
- 适合关注慢性病动态监测与数字疗法评估的研究者
理解生物标志物分布随时间的变化是数字健康和慢性病监测的核心挑战。在糖尿病中，血糖测量分布的变化可揭示疾病进展与治疗反应模式，而这些常被传统统计指标遗漏。基于一项为期26周的临床试验，比较t:slim X2闭环胰岛素系统与标准疗法在1型糖尿病儿童中的效果，我们提出一种概率框架，利用每5分钟采集的连续葡萄糖监测（CGM）数据，建模时间索引分布的连续时间演化。将血糖分布表示为高斯混合模型，其时变混合权重由神经微分方程控制。通过基于最大均值差异（MMD）的分布匹配准则估计模型参数。该框架具有可解释性、计算高效，并对细微的时间分布变化敏感。应用于CGM试验数据时，方法成功检测到传统分析难以捕捉的治疗相关血糖动力学改善。
原文摘要 · Abstract (English)
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.
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