Validation of an inexpensive and accurate mathematical method to measure long-term changes in free-living energy intake

Abstract

Background: Accurate measurement of free-living energy intake (EI) over long periods is imperative for understanding obesity and its treatment. Unfortunately, traditional methods rely on self-report and are notoriously inaccurate. Although EI can be indirectly estimated by the intake-balance method, this technique is prohibitively labor-intensive and expensive, requiring repeated measures of energy expenditure via doubly labeled water (DLW) along with multiple dual-energy X-ray absorptiometry (DXA) scans to measure changes in body energy stores.

Objective: Our objective was to validate a mathematical method to measure long-term changes in free-living energy intake.

Design: We measured body weight and EI changes (ΔEI) over 4 time intervals by using the intake-balance method in 140 individuals who underwent 2 y of caloric restriction as part of the Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy study. We compared the ΔEI values calculated by using DLW/DXA with those obtained by using a mathematical model of human metabolism whose only inputs were the initial demographic information and repeated body weight data.

Results: The mean ΔEI values calculated by the model were within 40 kcal/d of the DLW/DXA method throughout the 2-y study. For individual subjects, the overall root mean square deviation between the model and DLW/DXA method was 215 kcal/d, and most of the model-calculated ΔEI values were within 132 kcal/d of the DLW/DXA method.

Conclusions: Accurate and inexpensive estimates of ΔEI that are comparable to the DLW/DXA method can be obtained by using a mathematical model and repeated body weight measurements.

Trial registration: ClinicalTrials.gov NCT00427193.

Keywords: caloric restriction; dietary assessment; energy balance; energy intake; mathematical modeling; weight loss.

FIGURE 1

Individual results for a 66-kg, 45-y-old woman on a 2-y calorie-restricted diet as part of the CALERIE study. (A) Body weight measurements (boxes) were used as inputs to the NIDDK mathematical model to calculate ΔEI. (B) Comparison of ΔEI and its estimated 95% CI as calculated by the NIDDK model (black dots with gray shading) and the ΔEI calculated by the DLW/DXA method (horizontal solid black line). The dashed horizontal lines indicate the estimated 95% CIs of the DLW/DXA method. CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; DLW, doubly labeled water; DXA, dual-energy X-ray absorptiometry; ΔEI, energy intake change from baseline; NIDDK, National Institute of Diabetes and Digestive and Kidney Diseases.

FIGURE 2

(A) Mean body weight time course (boxes, means ± SEMs) for the 112 subjects with complete data for the entire 2-y CALERIE study. (B) Comparison of the mean (95% CI) ΔEI calculated by the NIDDK model and the DLW/DXA method. Results from the 2 methods were not significantly different during any of the 4 time segments. CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; DLW, doubly labeled water; DXA, dual-energy X-ray absorptiometry; ΔEI, energy intake change from baseline; NIDDK, National Institute of Diabetes and Digestive and Kidney Diseases.

FIGURE 3

(A) Distributions of the frequency (black bars) and cumulative percentage (dotted curve) of RMS deviations between the model and DLW/DXA method for individual ΔEI values at all time intervals. (B) Distributions of the frequency (black bars) and cumulative percentage (dotted curve) of RMS deviations between the model and DLW/DXA method for ΔEI values averaged over all time intervals for each subject. DLW, doubly labeled water; DXA, dual-energy X-ray absorptiometry; ΔEI, energy intake change from baseline; RMS, root mean square.