A case study of glucose levels during sleep using fast function on scalar regression inference

TL;DR

This study compares fast univariate inference and functional additive mixed models to analyze how medications and sleep apnea influence glucose levels during sleep in diabetics, providing new methods for efficient, accurate inference in complex functional data.

Contribution

Introduces a new approach for calculating p-values in functional data analysis and offers practical guidelines to accelerate FAMM computations for large, complex datasets.

Findings

Biguanide medication significantly reduces glucose levels during sleep.

Sleep apnea severity is associated with higher glucose trajectories.

Effects of medications and sleep apnea are time-invariant during sleep.

Abstract

Continuous glucose monitors (CGMs) are increasingly used to measure blood glucose levels and provide information about the treatment and management of diabetes. Our motivating study contains CGM data during sleep for 174 study participants with type II diabetes mellitus measured at a 5-minute frequency for an average of 10 nights. We aim to quantify the effects of diabetes medications and sleep apnea severity on glucose levels. Statistically, this is an inference question about the association between scalar covariates and functional responses. However, many characteristics of the data make analyses difficult, including (1) non-stationary within-day patterns; (2) substantial between-day heterogeneity, non-Gaussianity, and outliers; 3) large dimensionality due to the number of study participants, sleep periods, and time points. We evaluate and compare two methods: fast univariate inference (FUI) and functional additive mixed models (FAMM). We introduce a new approach for calculating p-values for testing a global null effect of covariates using FUI, and provide practical guidelines for speeding up FAMM computations, making it feasible for our data. While FUI and FAMM are philosophically different, they lead to similar point estimators in our study. In contrast to FAMM, FUI is fast, accounts for within-day correlations, and enables the construction of joint confidence intervals. Our analyses reveal that: (1) biguanide medication and sleep apnea severity significantly affect glucose trajectories during sleep, and (2) the estimated effects are time-invariant.