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


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. 


Alex’s notes: Math, it’s all fun in games until you hit calculus. If you do manage to make it past that level, you have the change of doing things like the present study, which used a mathematical model of energy balance dynamics to address the reason for the commonly seen weight-loss plateau occurring around six months after the start of a dieting program. The researchers addressed whether the timing of the weight plateau primarily results from suppressed energy expenditure (EE; the metabolic slow-down) or simply a loss of diet adherence.

The reason I want to briefly discuss the findings of this study is that it is now widely recognized that self-reported energy and food intake is highly unreliable. It is estimated that the average rate of under-reporting energy intake is 28% with food frequency questionnaires, and 15% with 24-hour recalls. This isn’t surprising by any means; those people who have the weight problems to begin with typically don’t consider that cookie or sugar in their coffee as significant, but that stuff adds up. Not to mention portion sizes… but I digress. The point is that we have all heard of people who claim to not be able to lose weight despite eating “nothing” or that the metabolic down-regulation that does occur with dieting has gone so unrealistically low that not even starvation will have them lose weight. It’s bullsh*t, and this study proves it.

The current study created two experiments to answer two questions:

  1. 1.How does a reduction in EEs beyond those accounted for by weight affect the length of time for weight to plateau?
  2. 2.How does an intermittent lack of adherence to dietary prescriptions translate to changes in the weight plateau?

With regard to the first question, the researchers adjusted a model parameter that controlled the suppression of energy expenditure during weight loss, and found that variations in this parameter only affected the magnitude of weight change but not the timing of the weight plateau. Specifically, they had a used a normal metabolic slow-down condition and compared it to two conditions where metabolic slow-down was 5% & 10% greater than what should be expected. Although these other conditions resulted in less weight loss (because they assumed greater metabolic slow-down), the plateau consistently occurred between 1-2 years, suggesting that even unrealistic levels of metabolic adaptation to dieting do not affect the timing of plateaus.

Things change gears when looking at the second question. To answer this one, the researchers allowed for random fluctuations in energy intake (EI) to simulate intermittent loss of dietary adherence. By month, women on average were calculated as 80% adherent in month 1, 60% adherent in month 2, 50% adherent in month 3, and 40% adherent after month 3. Similarly, men were calculated to be 80% adherent from months 1 to 5 and 70% adherent thereafter. Importantly, falling off the band-wagon didn’t mean that EI was necessarily greater, as the model assumed EI on non-adherent days to be over or under prescribed intakes by a back-calculated amount. Not surprisingly, compared to the model assuming 100% dietary adherence in which weight-loss continued past the six month mark, the seemingly innocuous intermittent loss of dietary adherence results in weight-loss plateaus for both men and women at the six month mark.

So the next time someone complains about a stall, tell them to write down everything they put in their mouth – everything. I bet they will be surprised. Also, as a final point regarding the whole “metabolic damage” crap that people seem to think they have from years of yo-yo dieting or whatever, it’s also bullsh*t. Studies consistently show that there is no correlation between a suppressed resting metabolic rate and later weight gain, and there is also no evidence for a change in suppressed EE even after maintaining weight-loss for 1 year. When you lose weight, you have less mass and your metabolism decreases accordingly. Even in the Minnesota starvation experiment, 25% of the 40% metabolic reduction was because of weight loss, with the other 15% being metabolic down-regulation.

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