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

Abstract

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.

FIGURE 1

y-axis: individual PAL (TEE/BMR) values for 7 d predicted from the MARS model in nonoverweight (n = 36) and overweight (n = 24) children and adolescents enrolled in the validation study shown as a function of age (x-axis).

FIGURE 2

Bland-Altman plot of the differences in TEE predicted by the CSTS and DLW methods versus the mean of the 2 methods in 60 children and adolescents enrolled in the validation study. Horizontal lines indicate mean differences, mean ± 1 SD and mean ± 2 SD intervals (1 kcal = 4.184 kJ).

FIGURE 3

Bland-Altman plot of the differences in TEE predicted by the MARS and DLW methods versus the mean of the 2 methods in 60 children and adolescents enrolled in the validation study. Horizontal lines indicate mean differences, mean ± 1 SD and mean ± 2 SD intervals (1 kcal = 4.184 kJ).

FIGURE 4

Concordance plot between TEE predicted by the CSTS and MARS methods in 60 children and adolescents enrolled in the validation study (CCC = 0.951, P = 0.001, SE = 0.013, 95% = CI 0.926–0.975) (1 kcal = 4.184 kJ).

FIGURE 5

Bland-Altman plot of the differences in TEE predicted by the CSTS and MARS methods versus the mean of the 2 methods in 60 children and adolescents enrolled in the validation study. Horizontal lines indicate mean differences, mean ± 1 SD and mean ± 2 SD intervals (1 kcal = 4.184 kJ).