Misdefined energy flux and increased fatness

Dear Editor:

The recent article by Hume et al. (1) investigates energy metabolism in adolescence and early adulthood and how differences therein may predict subsequent excess fat gain. Unfortunately, there were errors in the definition of terms and flaws in the statistical approach that resulted in fatally flawed conclusions.

The authors incorrectly refer to the term “energy intake” as habitual energy intake. Habitual energy intake is defined as the energy consumed to maintain stable body energy stores or, in the case of children, normal growth of those stores. What they calculated was the short-term energy intake for the 2-wk period of doubly labeled water measurement. The result was a faulty conclusion that long-term habitual energy surfeit predicts future fat gain, when, in fact, it was the 2-wk energy surfeit that was tested.

The authors also misdefined energy flux as the sum of energy intake and energy expenditure. This definition is wrong. Flux is the magnitude and direction of flow through a system. Energy intake is the influx of energy into the body, and energy expenditure is the efflux of energy from the body. The 2 are equal at energy balance, and the difference between the 2 is energy imbalance. Summing ignores directionality of the flow, and the sum has no numerical or physiologic definition. Only influx and efflux, or their difference, have physiologic meaning.

Contrary to the statements of the authors, the misdefined “high flux” values they reported could still have resulted from high short-term energy intake or a high total energy expenditure (TEE), either of which could have been traced to a high resting metabolic rate (RMR), a high physical activity expenditure, or a large body size. The exclusion of those with a difference of >33% is arbitrary and does not solve the problem of having the same “flux” but for different reasons. Moreover, as indicated in the authors’ Figure 3, 70% of the increase in the “high flux” group was actually due to high 2-wk calculated energy intake and was not traced to high physical activity. Thus, they should have concluded that the best predictor of a lower percentage of body fat was a 2-wk period of 700 kcal excessive energy intake/d. This conclusion is counterintuitive, suggesting there are other flaws in the analysis, but it is what their data analysis actually implies. It is interesting to note that some of these authors previously used another statistical model for the analysis of excess weight gain, and the authors reported that excessive weight gain during the first 2 y of follow-up in these studies was due to high energy intake (2). That model also did not include any adjustment for differences in body size; thus, those conflicting findings were also flawed.

In this current analysis, the authors do attempt an adjustment for metabolic body size, but that adjustment introduces bias. They expressed the energy terms (either “energy flux” or RMR) per kilogram of fat-free mass (FFM). Although both TEE and RMR are linearly related to FFM, the regression lines do not have a zero intercept and thus the use of the ratio is contraindicated (3). The use of the ratio introduces artifacts that create apparent deficiencies in energy expenditure among those subjects who are larger than the cohort average. The appropriate adjustment for FFM is to use FFM as a covariant for energy expenditure (3).

The authors’ Figure 1 indicates that these correlations, flawed as they are, are also highly influenced by a few data points at the extremes. This is particularly true for study 2, for which a single data point at the right-most extreme has an excessive influence on the correlation.

The authors failed to account for the complexity of normal weight and fatness changes during adolescence. It is not clear why this was not done because some of the authors did include such considerations in a previous analysis of this data (4).

The correlation between the authors’ “energy flux” and RMR is a trivial association. RMR is the largest component of TEE and TEE is the largest component of “energy flux.” Thus, correlation is expected because of interdependence of the variables. To test the hypothesis that RMR is influenced by either energy intake imbalance of high levels of physical activity, either TEE − energy intake or TEE − RMR should be used as the dependent variable.

The calculated energy balances as presented in this article are, as indicated above, the short-term energy balance during the 2-wk doubly labeled water period and not the inferred long-term energy balances and would not be sustained without large changes in weight. It is likely that the absolute imbalances have been overestimated because of the limiting precision of the body-composition measurement. Air-displacement plethysmography has a lower reproducibility than many other methods. Precisions are on the order of 1% fat, or up to 1.4% for the difference between serial measures as used in this article (5). This uncertainty for the change in percentage of fat over 2 wk in a 60-kg individual introduces a 1-SD random error of ≤570 kcal/d on energy intake. Thus, many of their conclusions were based on small effect sizes.

The conclusions drawn by Hume et al. in their recent article (1) are flawed. This is due to their incorrect and inconsistent use of the term “energy flux,” which, at points in the article, is defined as the energy sum of the components of energy expenditure, to the sum of intake and expenditure, to an absolute level of energy balance, and to levels of physical activity. They further compound this lack of consistency by erroneously stating that their estimate of 2-wk energy intake is a measure of habitual energy intake and by using an adjustment for body size that is known to bias the resulting relations. It is not clear why they selected these flawed approaches instead of appropriately adjusted, correctly defined flux measures that are available to them.