Functional data analysis of sleeping energy expenditure

Adequate sleep is crucial during childhood for metabolic health, and physical and cognitive development. Inadequate sleep can disrupt metabolic homeostasis and alter sleeping energy expenditure (SEE). Functional data analysis methods were applied to SEE data to elucidate the population structure of SEE and to discriminate SEE between obese and non-obese children. Minute-by-minute SEE in 109 children, ages 5–18, was measured in room respiration calorimeters. A smoothing spline method was applied to the calorimetric data to extract the true smoothing function for each subject. Functional principal component analysis was used to capture the important modes of variation of the functional data and to identify differences in SEE patterns. Combinations of functional principal component analysis and classifier algorithm were used to classify SEE. Smoothing effectively removed instrumentation noise inherent in the room calorimeter data, providing more accurate data for analysis of the dynamics of SEE. SEE exhibited declining but subtly undulating patterns throughout the night. Mean SEE was markedly higher in obese than non-obese children, as expected due to their greater body mass. SEE was higher among the obese than non-obese children (p<0.01); however, the weight-adjusted mean SEE was not statistically different (p>0.1, after post hoc testing). Functional principal component scores for the first two components explained 77.8% of the variance in SEE and also differed between groups (p = 0.037). Logistic regression, support vector machine or random forest classification methods were able to distinguish weight-adjusted SEE between obese and non-obese participants with good classification rates (62–64%). Our results implicate other factors, yet to be uncovered, that affect the weight-adjusted SEE of obese and non-obese children. Functional data analysis revealed differences in the structure of SEE between obese and non-obese children that may contribute to disruption of metabolic homeostasis.