Modeling energy expenditure in children and adolescents using quantile regression.

Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in energy expenditure (EE). Study objective is to apply quantile regression (QR) to predict EE and determine quantile-dependent variation in covariate effects in nonobese and obese children. First, QR models will be developed to predict minute-by-minute awake EE at different quantile levels based on heart rate (HR) and physical activity (PA) accelerometry counts, and child characteristics of age, sex, weight, and height. Second, the QR models will be used to evaluate the covariate effects of weight, PA, and HR across the conditional EE distribution. QR and ordinary least squares (OLS) regressions are estimated in 109 children, aged 5-18 yr. QR modeling of EE outperformed OLS regression for both nonobese and obese populations. Average prediction errors for QR compared with OLS were not only smaller at the median τ = 0.5 (18.6 vs. 21.4%), but also substantially smaller at the tails of the distribution (10.2 vs. 39.2% at τ = 0.1 and 8.7 vs. 19.8% at τ = 0.9). Covariate effects of weight, PA, and HR on EE for the nonobese and obese children differed across quantiles (P < 0.05). The associations (linear and quadratic) between PA and HR with EE were stronger for the obese than nonobese population (P < 0.05). In conclusion, QR provided more accurate predictions of EE compared with conventional OLS regression, especially at the tails of the distribution, and revealed substantially different covariate effects of weight, PA, and HR on EE in nonobese and obese children.

Cross-sectional time series and multivariate adaptive regression splines models using accelerometry and heart rate predict energy expenditure of preschoolers.

Prediction equations of energy expenditure (EE) using accelerometers and miniaturized heart rate (HR) monitors have been developed in older children and adults but not in preschool-aged children. Because the relationships between accelerometer counts (ACs), HR, and EE are confounded by growth and maturation, age-specific EE prediction equations are required. We used advanced technology (fast-response room calorimetry, Actiheart and Actigraph accelerometers, and miniaturized HR monitors) and sophisticated mathematical modeling [cross-sectional time series (CSTS) and multivariate adaptive regression splines (MARS)] to develop models for the prediction of minute-by-minute EE in 69 preschool-aged children. CSTS and MARS models were developed by using participant characteristics (gender, age, weight, height), Actiheart (HR+AC_x) or ActiGraph parameters (AC_x, AC_y, AC_z, steps, posture) [x, y, and z represent the directional axes of the accelerometers], and their significant 1- and 2-min lag and lead values, and significant interactions. Relative to EE measured by calorimetry, mean percentage errors predicting awake EE (-1.1 ± 8.7%, 0.3 ± 6.9%, and -0.2 ± 6.9%) with CSTS models were slightly higher than with MARS models (-0.7 ± 6.0%, 0.3 ± 4.8%, and -0.6 ± 4.6%) for Actiheart, ActiGraph, and ActiGraph+HR devices, respectively. Predicted awake EE values were within ±10% for 81-87% of individuals for CSTS models and for 91-98% of individuals for MARS models. Concordance correlation coefficients were 0.936, 0.931, and 0.943 for CSTS EE models and 0.946, 0.948, and 0.940 for MARS EE models for Actiheart, ActiGraph, and ActiGraph+HR devices, respectively. CSTS and MARS models should prove useful in capturing the complex dynamics of EE and movement that are characteristic of preschool-aged children.

Validation of uniaxial and triaxial accelerometers for the assessment of physical activity in preschool children.

PURPOSE: Given the unique physical activity (PA) patterns of preschoolers, wearable electronic devices for quantitative assessment of physical activity require validation in this population. Study objective was to validate uniaxial and triaxial accelerometers in preschoolers. METHODS: Room calorimetry was performed over 3 hours in 64 preschoolers, wearing Actical, Actiheart, and RT3 accelerometers during play, slow, moderate, and fast translocation. Based on activity energy expenditure (AEE) and accelerometer counts, optimal thresholds for PA levels were determined by piecewise linear regression and discrimination boundary analysis. RESULTS: Established HR cutoffs in preschoolers for sedentary/light, light/moderate and moderate/vigorous levels were used to define AEE (0.015, 0.054, 0.076 kcal·kg-1·min-1) and PA ratio (PAR; 1.6, 2.9, 3.6) thresholds, and accelerometer thresholds. True positive predictive rates were 77%, 75%, and 76% for sedentary; 63%, 61%, and 65% for light; 34%, 52%, and 49% for moderate; 46%, 46%, and 49% for vigorous levels. Due to low positive predictive rates, we combined moderate and vigorous PA. Classification accuracy was improved overall and for the combined moderate-to-vigorous PA level (69%, 82%, 79%) for Actical, Actiheart, and RT3, respectively. CONCLUSION: Uniaxial and triaxial accelerometers are acceptable devices with similar classification accuracy for sedentary, light, and moderate-to-vigorous levels of PA in preschoolers.

Validation of cross-sectional time series and multivariate adaptive regression splines models for the prediction of energy expenditure in children and adolescents using doubly labeled water.

Accurate, nonintrusive, and inexpensive techniques are needed to measure energy expenditure (EE) in free-living populations. Our primary aim in this study was to validate cross-sectional time series (CSTS) and multivariate adaptive regression splines (MARS) models based on observable participant characteristics, heart rate (HR), and accelerometer counts (AC) for prediction of minute-by-minute EE, and hence 24-h total EE (TEE), against a 7-d doubly labeled water (DLW) method in children and adolescents. Our secondary aim was to demonstrate the utility of CSTS and MARS to predict awake EE, sleep EE, and activity EE (AEE) from 7-d HR and AC records, because these shorter periods are not verifiable by DLW, which provides an estimate of the individual's mean TEE over a 7-d interval. CSTS and MARS models were validated in 60 normal-weight and overweight participants (ages 5-18 y). The Actiheart monitor was used to simultaneously measure HR and AC. For prediction of TEE, mean absolute errors were 10.7 +/- 307 kcal/d and 18.7 +/- 252 kcal/d for CSTS and MARS models, respectively, relative to DLW. Corresponding root mean square error values were 305 and 251 kcal/d for CSTS and MARS models, respectively. Bland-Altman plots indicated that the predicted values were in good agreement with the DLW-derived TEE values. Validation of CSTS and MARS models based on participant characteristics, HR monitoring, and accelerometry for the prediction of minute-by-minute EE, and hence 24-h TEE, against the DLW method indicated no systematic bias and acceptable limits of agreement for pediatric groups and individuals under free-living conditions.

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.

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, HR(2), and PA and 1- and 2-min lagged values of PA, PA(2), age, age(2), sex, weight, height, minimum HR, sitting HR, HR x height, HR x weight, HR x age, PA x weight, and PA x 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.

Body size, body composition, and metabolic profile explain higher energy expenditure in overweight children.

Lower relative rates of energy expenditure (EE), increased energetic efficiency, and altered fuel utilization purportedly associated with obesity have not been demonstrated indisputably in overweight children. We hypothesized that differences in energy metabolism between nonoverweight and overweight children are attributable to differences in body size and composition, circulating thyroid hormones, sympathetic nervous system, and adrenomedullary activity. A total of 836 Hispanic children, 5-19 y old, participated in 24-h calorimetry, anthropometric, and dual-energy X-ray absorptiometry measurements. Biochemistries were determined by standard techniques. Absolute total EE (TEE) and its components (sleep EE, basal EE, sedentary EE, cycling EE, walking EE, activity EE, nonexercising activity thermogenesis) were higher in overweight children (P = 0.001). Net mechanical energetic efficiency of cycling was lower in overweight children (P = 0.001). Adjusting for body size and composition accounted for differences in TEE, its components, and energetic efficiency. Net carbohydrate and fat utilization did not differ between groups. TEE was independently influenced by sex, Tanner stage, fat free mass, fat mass (FM), fasting serum nonesterified fatty acids (NEFA), leptin, free thyroxine, triiodothyronine, and 24-h urinary norepinephrine and epinephrine. Fat utilization was independently associated with age2, sex, FM, fasting serum NEFA, triacylglycerol, adiponectin, leptin, total thyroxine, and free triiodothyronine. Higher EE in overweight children was largely explained by differences in body size and composition, with minor contributions of thyroid and sympathoadrenal systems. Alterations in EE, energetic efficiency, and substrate utilization were not evident in the overweight children.

Normalization of energy expenditure data for differences in body mass or composition in children and adolescents.

The most appropriate model for normalization of energy expenditure (EE) data for body mass or composition in growing children and adolescents has not been studied extensively. In this study, we investigated allometric modeling for the normalization of EE data for body mass or composition in a large cohort of children (n = 833), ages 5-19 y for a wide range of physical activities. Anthropometry was performed by standard techniques, and total body fat-free mass (FFM) and fat mass (FM) were determined by dual-energy X-ray absorptiometry (DXA). Weight status was defined as nonoverweight or overweight based on the 95th percentile for BMI. Total energy expenditure (TEE), basal energy expenditure (BEE), sleeping energy expenditure (SEE), and cycling EE were measured during 24-h room respiration calorimetry. Walking and maximal EE (MaxEE) were measured according to a treadmill protocol. Allometric or power function models were used to identify appropriate scaling parameters for EE. For BEE and lower levels of EE, weight scaled to 0.5. For cycling and treadmill walking/running, the weight exponent approached 0.7. Scaling EE for FFM resulted in exponents of 0.6 for lower rates of EE and 0.8-1.0 for higher rates of EE. Appropriate scaling of EE for body weight and composition of children and adolescents varied primarily as a function of the level of EE. In some instances, the exponents for scaling EE by body weight or composition were influenced by gender and weight status, but not by age.

Prediction of activity energy expenditure using accelerometers in children.

PURPOSE: To validate two accelerometer-based activity monitors as measures of children's physical activity using energy expenditure as the criterion measure. METHODS: Actiwatch (AW) and Actical (AC) activity monitors were validated against continuous 4-h measurements of energy expenditure (EE) in a respiratory room calorimeter and 1-h measurements in an exercise laboratory using a portable calorimeter and treadmill in 32 children, ages 7-18 yr. The children performed structured activities including basal metabolic rate (BMR), playing Nintendo, using a computer, cleaning, aerobic exercise, ball toss, treadmill walking, and running. Equations were developed to predict activity energy expenditure (AEE = EE - BMR), and physical activity ratio (PAR = EE/BMR) from a power function of AW or AC, and age, sex, weight, and height. Thresholds were determined to categorize sedentary, light, moderate, and vigorous levels of physical activity. RESULTS: Activity counts accounted for the majority of the variability in AEE and PAR, with small contributions of age, sex, weight, and height. Overall, AW equations accounted for 76-79% and AC equations accounted for 81% of the variability in AEE and PAR. Relatively wide 95% prediction intervals suggest the accelerometers are best applied to groups rather than individuals. Sensitivities were higher for the vigorous threshold (97%) than the other thresholds (86-92%). Specificities were on the order of 66-73%. The positive predictive values for sedentary, light, moderate, and vigorous categories were 80, 66, 69, and 74% for AW, respectively, and 81, 68, 72, 74% for AC, respectively. CONCLUSION: Both accelerometer-based activity monitors provided valid measures of children's AEE and PAR, and can be used to discriminate sedentary, light, moderate, and vigorous levels of physical activity but require further development to accurately predict AEE and PAR of individuals.