Distributed lag and spline modeling for predicting energy expenditure from accelerometry in youth

Abstract

Movement sensing using accelerometers is commonly used for the measurement of physical activity (PA) and estimating energy expenditure (EE) under free-living conditions. The major limitation of this approach is lack of accuracy and precision in estimating EE, especially in low-intensity activities. Thus the objective of this study was to investigate benefits of a distributed lag spline (DLS) modeling approach for the prediction of total daily EE (TEE) and EE in sedentary (1.0-1.5 metabolic equivalents; MET), light (1.5-3.0 MET), and moderate/vigorous (> or = 3.0 MET) intensity activities in 10- to 17-year-old youth (n = 76). We also explored feasibility of the DLS modeling approach to predict physical activity EE (PAEE) and METs. Movement was measured by Actigraph accelerometers placed on the hip, wrist, and ankle. With whole-room indirect calorimeter as the reference standard, prediction models (Hip, Wrist, Ankle, Hip+Wrist, Hip+Wrist+Ankle) for TEE, PAEE, and MET were developed and validated using the fivefold cross-validation method. The TEE predictions by these DLS models were not significantly different from the room calorimeter measurements (all P > 0.05). The Hip+Wrist+Ankle predicted TEE better than other models and reduced prediction errors in moderate/vigorous PA for TEE, MET, and PAEE (all P < 0.001). The Hip+Wrist reduced prediction errors for the PAEE and MET at sedentary PA (P = 0.020 and 0.021) compared with the Hip. Models that included Wrist correctly classified time spent at light PA better than other models. The means and standard deviations of the prediction errors for the Hip+Wrist+Ankle and Hip were 0.4 +/- 144.0 and 1.5 +/- 164.7 kcal for the TEE, 0.0 +/- 84.2 and 1.3 +/- 104.7 kcal for the PAEE, and -1.1 +/- 97.6 and -0.1 +/- 108.6 MET min for the MET models. We conclude that the DLS approach for accelerometer data improves detailed EE prediction in youth.

Fig. 1.

Normalized overlaid plot for a representative participant (10-year-old boy, weight = 76.5 kg, height = 155 cm) obtained during first 600 min of the ∼24-h stay in the whole-room indirect calorimeter. A: energy expenditure (EE) measured by room calorimetry (gray lines) and the raw physical activity (PA) counts (dark lines) obtained at hip, wrist, and ankle. B: EE measured by room calorimetry (gray lines) and the distributed lag PA counts (dark lines). The distributed lag PA counts were generated by taking the weighted average of the raw PA counts from lag −1 to lag 2.

Fig. 2.

The means of predicted EE (kcal/min) per PA raw count worn at hip, wrist, and ankle against lag and time (min). The predicted means are for lags 9 to −2 from the current measurement (lag 0 or time t), and time (min) is from past (−9 min) to future (+2 min).

Fig. 3.

The distributions of the square root of the mean of squared errors (MSE; kcal/min) for prediction of TEE from the distributed lag and spline (DLS) models calculated for each participant. The horizontal bars represent the means. *P < 0.001 vs. Hip+Wrist+Ankle model; †P < 0.001 vs. Hip+Wrist model; ^§P < 0.001 vs. Hip model.

Fig. 4.

Bland-Altman agreement plots between total energy expenditure (TEE, kcal/day) measured during ∼24-h stay in the whole-room indirect calorimeter, and TEE predicted from the DLS models using PA measurements (counts) obtained from Actigraph accelerometers. The horizontal dashed line represents the mean difference between the TEE measured by the room calorimeter and predicted by the DLS models, and the upper and lower dotted lines are 95% limits of agreement calculated as mean difference ± 2 SDs. Values above and below the middle horizontal zero line are underestimation and overestimation of TEE, respectively. ● and ○, boys and girls, respectively.

Fig. 5.

Bland-Altman agreement plots between PAEE (kcal) during waking (nonsleeping) period measured during ∼24-h stay in the whole-room indirect calorimeter and PAEE predicted from the DLS models using PA measurements (counts) obtained from Actigraph accelerometers. The horizontal dashed line represents the mean difference between the PAEE measured by the room calorimeter and predicted by the DLS models and the upper and lower dotted lines are 95% limits of agreement calculated as mean difference ± 2 SDs. Values above and below the middle horizontal zero line are underestimation and overestimation of PAEE, respectively. ● and ○, boys and girls, respectively.

Fig. 6.

Bland-Altman agreement plots between measured metabolic equivalents (MET) in the whole-room indirect calorimeter calculated as a ratio of EE during waking period and sleeping EE and predicted from models. The METs were summed over waking period (MET min). The METs were predicted from the DLS MET models developed to predict MET during waking period and 2 previously published models, the linear model for children (Freedson child model) (11, 30) and the 2-component regression model (Crouter model) (8). The horizontal dashed line represents the mean difference between the methods, and the upper and lower dotted lines are 95% limits of agreement calculated as mean difference ± 2 SDs. Values above and below the middle horizontal zero line are underestimation and overestimation of METs, respectively. ● and ○, boys and girls, respectively.

Fig. 7.

Box plots of differences (measured − predicted) in EE (kcal) between measurements obtained from the whole-room indirect calorimeter and predicted from the DLS TEE models during waking period in sedentary (1.0–1.5 MET), light (1.5–3.0 MET), and moderate/vigorous (≥3.0 MET) PA intensity levels. ●, individual TEE differences.