Application of cross-sectional time series modeling for the prediction of energy expenditure from heart rate and accelerometry

Accurate estimation of energy expenditure (EE) in children and adolescents is required for a better understanding of physiological, behavioral, and environmental factors affecting energy balance. Cross-sectional time series (CSTS) models, which account for correlation structure of repeated observations on the same individual, may be advantageous for prediction of EE. CSTS models for prediction of minute-by-minute EE and, hence, total EE (TEE) from heart rate (HR), physical activity (PA) measured by accelerometry, and observable subject variables were developed in 109 children and adolescents by use of Actiheart and 24-h room respiration calorimetry. CSTS models based on HR, PA, time-invariant covariates, and interactions were developed. These dynamic models involve lagged and lead values of HR and lagged values of PA for better description of the series of minute-by-minute EE. CSTS models with random intercepts and random slopes were investigated. For comparison, likelihood ratio tests were used. Log likelihood increased substantially when random slopes for HR and PA were added. The population-specific model uses HR and 1- and 2-min lagged and lead values of HR, HR2, and PA and 1- and 2-min lagged values of PA, PA2, age, age2, sex, weight, height, minimum HR, sitting HR, HR × height, HR × weight, HR × age, PA × weight, and PA × sex interactions (P < 0.001). Prediction error for TEE was 0.9 ± 10.3% (mean ± SD). Errors were not correlated with age, weight, height, or body mass index. CSTS modeling provides a useful predictive model for EE and, hence, TEE in children and adolescents on the basis of HR and PA and other observable explanatory subject characteristics of age, sex, weight, and height