Effect of dietary adherence on the body weight plateau: a mathematical model incorporating intermittent compliance with energy intake prescription

Abstract

Background: Clinical weight loss in individuals typically stabilizes at 6 mo. However, validated models of dynamic energy balance have consistently shown weight plateaus between 1 and 2 y. The cause for this discrepancy is unclear.

Objective: We developed 2 mathematical models on the basis of the first law of thermodynamics to investigate plausible explanations for reaching an early weight plateau at 6 mo.

Design: The first model was an energy-expenditure adaptation model and was applied to determine the degree of metabolic adaptation required to generate this plateau. The second model was an intermittent lack-of-adherence model formulated by using a randomly fluctuating energy intake term accounting for intermittent noncompliance in dietary intake to reach this plateau. To set model variables, validate models, and compare free-living weight-loss patterns to in-residence supervised programs, we applied the following 4 different studies: The US NHANES 1999-2004, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy (CALERIE) weight-loss study, the Bouchard Twin overfeeding study, and the Minnesota Starvation Experiment.

Results: The metabolic adaptation model increased final weight but did not affect the predicted plateau time point. The intermittent lack-of-adherence model generated oscillating weight graphs that have been frequently observed in weight-loss studies. The model showed that a 6-mo weight-loss plateau can be attained despite what can be considered as high diet adherence. The model was programmed as a downloadable application.

Conclusions: An intermittent lack of diet adherence, not metabolic adaptation, is a major contributor to the frequently observed early weight-loss plateau. The new weight-loss prediction software, which incorporates an intermittent lack of adherence, can be used to guide and inform patients on realistic levels of adherence on the basis of patient lifestyle.

Trial registration: ClinicalTrials.gov NCT00099151.

© 2014 American Society for Nutrition.

Figures

FIGURE 1.

A–D: Level of agreement between dynamic model predictions of weight and measured weight at 84 and 168 d in the 23 CALERIE study participants who were undergoing weight loss through calorie restriction (9). E and F: Agreement between dynamic model predictions with measured weight from the Bouchard Twin study (11). A, C, and E: Dynamic model–predicted final weight against actual final weight. B, D, and F: Bland-Altman analyses of model predictions. The validation against the CALERIE study at 3 mo yielded good agreement [R2 = 0.99, , bias = 0.4 kg (95% CI: −2.4, 3.2 kg); 6 mo: R2 = 0.96, , bias = 2.2 kg (95% CI: −2.4, 6.8 kg)]. There was a trend in the error at 3 mo (R2 = 0.22, y = 0.06x + 5.1, P = 0.02), but it was NS at 6 mo (R2 = 0.05, , P = −0.32). The overfeeding validation (11) yielded better agreement than the calorie restriction validation [correlation: R2 = 0.93, , bias = 0.9 kg (95% CI: −3.7, 5.5 kg)], again with no significant trend in error (R2 = 0.01, , P = 0.6). CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy.

FIGURE 2.

Simulations of the effect of reduced EE on body weight over time beyond those accounted for in the dynamic model (7) for men (left) and women (right). Dotted curves represent a 10% decrease in EE beyond the expected, dashed curves represent a 5% decrease in EE beyond the expected, and solid curves represent no change in EE from original model predictions. Although a decreasing EE generated a value at which weight plateaued, the time at which the weight loss plateau was achieved did not change. EE, energy expenditure.

FIGURE 3.

Depicted are actual weight graphs (solid), dynamic model simulations (7) with assumption of 100% compliance to the prescribed calorie restriction (dashed), and simulations of the adherence model matched to actual weight graphs (dotted) from the participants in the 25%-below-baseline-energy-requirements cohort in the Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy study (9). A and B: Simulations for women and men, respectively. C and D: Extension of simulations of dynamic and adherence models to 1 y. The percentage of adherence after 6 mo was set as 6-mo calculated values from matching the model to the data. In both groups, a weight plateau was generated at 24 wk by the adherence model. In contrast, the dynamic model, which assumed 100% compliance, continued to decrease and deviate from adherence model predictions.

FIGURE 4.

Weight compared with study week during prescribed restriction of energy intake in the MN Starvation Experiment (10) (A) and 25% CR participants from the CALERIE study (9) (B). Weight graphs from the MN Starvation Experiment were monotonically decreasing, whereas weight graphs from the free-living CALERIE study oscillated with intermittent periods of weight gain. CALERIE, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; MN, Minnesota; 25% CR, calorie reduction 25% below baseline energy requirements.