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

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