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

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