Multivariate adaptive regression splines models for the prediction of energy expenditure in children and adolescents

Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production or energy expenditure (EE). Multivariate adaptive regression splines (MARS) is a nonparametric method that estimates complex nonlinear relationships by a series of spline functions of the independent predictors. The specific aim of this study is to construct MARS models based on heart rate (HR) and accelerometer counts (AC) to accurately predict EE, and hence 24-h total EE (TEE), in children and adolescents. Secondarily, MARS models will be developed to predict awake EE, sleep EE, and activity EE also from HR and AC. MARS models were developed in 109 and validated in 61 normal-weight and overweight children (ages 5–18 yr) against the criterion method of 24-h room respiration calorimetry. Actiheart monitor was used to measure HR and AC. MARS models were based on linear combinations of 23–28 basis functions that use subject characteristics (age, sex, weight, height, minimal HR, and sitting HR), HR and AC, 1- and 2-min lag and lead values of HR and AC, and appropriate interaction terms. For the 24-h, awake, sleep, and activity EE models, mean percent errors were −2.5 ± 7.5, −2.6 ± 7.8, −0.3 ± 8.9, and −11.9 ± 17.9%, and root mean square error values were 168, 138, 40, and 122 kcal, respectively, in the validation cohort. Bland-Altman plots indicated that the predicted values were in good agreement with the observed TEE, and that there was no bias with increasing TEE. Prediction errors for 24-h TEE were not statistically associated with age, sex, weight, height, or body mass index. MARS models developed for the prediction of EE from HR monitoring and accelerometry were demonstrated to be valid in an independent cohort of children and adolescents, but require further validation in independent, free-living populations.