Abstract

Continuous glucose monitors (CGMs) are small, wearable devices that frequently measure interstitial glucose levels, typically every five minutes. CGMs are increasingly utilized in both diabetes management and research studies. Despite the richness of the temporal data provided by CGMs, current analyses often rely on crude summaries, such as the mean and standard deviation. Moreover, CGM data collected under free-living conditions present challenges for applying functional data analysis methods due to time misalignments in meal intake and observation periods. Distributional learning improves upon traditional summaries by leveraging the entire distribution function of glucose measurements as the response while avoiding time alignment issues. However, the widespread adoption of a distributional regression framework for CGM data analysis remains limited due to several challenges, such as capturing local glucose temporal variability, lack of uncertainty quantification with a large number of covariates, and prohibitively high computational costs. Motivated by these challenges, we enhance the model capacity and develop new, fast algorithms for distributional regression, making subsampling-based inference computationally feasible. We demonstrate our approach by analyzing CGM data from patients with type 2 diabetes and obstructive sleep apnea.