Simulating long-term human weight-loss dynamics in response to calorie restriction

Abstract

Background: Mathematical models have been developed to predict body weight (BW) and composition changes in response to lifestyle interventions, but these models have not been adequately validated over the long term.

Objective: We compared mathematical models of human BW dynamics underlying 2 popular web-based weight-loss prediction tools, the National Institutes of Health Body Weight Planner (NIH BWP) and the Pennington Biomedical Research Center Weight Loss Predictor (PBRC WLP), with data from the 2-year Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy (CALERIE) study.

Design: Mathematical models were initialized using baseline CALERIE data, and changes in body weight (ΔBW), fat mass (ΔFM), and energy expenditure (ΔEE) were simulated in response to time-varying changes in energy intake (ΔEI) objectively measured using the intake-balance method. No model parameters were adjusted from their previously published values.

Results: The PBRC WLP model simulated an exaggerated early decrease in EE in response to calorie restriction, resulting in substantial underestimation of the observed mean (95% CI) BW losses by 3.8 (3.5, 4.2) kg. The NIH WLP simulations were much closer to the data, with an overall mean ΔBW bias of -0.47 (-0.92, -0.015) kg. Linearized model analysis revealed that the main reason for the PBRC WLP model bias was a parameter value defining how spontaneous physical activity expenditure decreased with caloric restriction. Both models exhibited substantial variability in their ability to simulate individual results in response to calorie restriction. Monte Carlo simulations demonstrated that ΔEI measurement uncertainties were a major contributor to the individual variability in NIH BWP model simulations.

Conclusions: The NIH BWP outperformed the PBRC WLP and accurately simulated average weight-loss and energy balance dynamics in response to long-term calorie restriction. However, the substantial variability in the NIH BWP model predictions at the individual level suggests cautious interpretation of individual-level simulations. This trial was registered at clinicaltrials.gov as NCT00427193.

Figures

FIGURE 1

Mean data from female (n = 78, left column) and male (n = 35, right column) participants in the CALERIE study who had complete data (•) on (A) energy intake, (B) body weight, (C) fat mass, and (D) energy expenditure changes following 2 years of calorie restriction. The NIH BWP model (solid black curves) and PBRC WLP model (dashed black curves) simulations are depicted in response to time-varying mean energy intake measurements described by the best-fit exponential time course and its 95% CI (solid black curves and dashed gray curves in panel A, respectively). The simulated ranges for body weight, fat mass, and energy expenditure changes for the NIH BWP model are bounded by the solid gray curves, and the corresponding simulated PBRC model ranges are bounded by the gray dotted curves. Error bars are ±95% CI. CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; NIH BWP, National Institutes of Health Body Weight Planner; PBRC WLP, Pennington Biomedical Research Center Weight Loss Predictor; Δ, change from baseline.

FIGURE 2

Individual female (n = 78, left column) and male (n = 35, right column) subjects in the CALERIE study were simulated using the NIH BWP model (open bars) and PBRC WLP model (gray bars) and compared to the data (black bars) for (A) ΔBW, (B) ΔFM, and (C) ΔEE for given ΔEI measured using the intake-balance method. Different letters indicate significant differences between models and data at each time point as determined by paired, 2-sided t tests. Error bars are ±95% CI. ΔBW, change in body weight; CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; ΔEE, change in energy expenditure; ΔFM, change in fat mass; NIH BWP, National Institutes of Health Body Weight Planner; PBRC WLP, Pennington Biomedical Research Center Weight Loss Predictor.

FIGURE 3

Residuals between CALERIE study data in 78 women for individual NIH BWP model (left column) and PBRC WLP model (right column) simulations of (A) ΔBW, (B) ΔFM, and (C) ΔEE for given ΔEI measured over each 6-month period using the intake-balance method. The dashed horizontal line is the mean model residual bias, and the dotted horizontal lines indicate the limits of agreement (±1.96 × SD of the residuals). The solid line is the best fit linear regression line. The mean bias of the simulated ΔBW was –0.5 kg for the NIH BWP and 3.5 kg for the PBRC WLP. The mean bias of the simulated ΔFM was 0.82 kg for the NIH BWP and 2.9 kg for the PBRC WLP. The mean bias of the simulated ΔEE was –12 kcal/d for the NIH BWP and –41 kcal/d for the PBRC WLP. ΔBW, change in body weight; CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; ΔEE, change in energy expenditure; ΔFM, change in fat mass; NIH BWP, National Institutes of Health Body Weight Planner; PBRC WLP, Pennington Biomedical Research Center Weight Loss Predictor.

FIGURE 4

Residuals between CALERIE study data in 35 males for individual NIH BWP model (left column) and PBRC WLP model (right column) simulations of (A) ΔBW, (B) ΔFM, and (C) ΔEE for given ΔEI measured over each 6-month period using the intake-balance method. The dashed horizontal line is the mean model residual bias, and the dotted horizontal lines indicate the limits of agreement (±1.96 × SD of the residuals). The solid line is the best fit linear regression line. The mean bias of the simulated ΔBW was –0.4 kg for the NIH BWP and 4.7 kg for the PBRC WLP. The mean bias of the simulated ΔFM was 0.7 kg for the NIH BWP and 3.3 kg for the PBRC WLP. The mean bias of the simulated ΔEE was –19 kcal/d for the NIH BWP and –54 kcal/d for the PBRC WLP. ΔBW, change in body weight; CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; ΔEE, change in energy expenditure; ΔFM, change in fat mass; NIH BWP, National Institutes of Health Body Weight Planner; PBRC WLP, Pennington Biomedical Research Center Weight Loss Predictor.