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LETTERS TO THE EDITOR
doi: 10.3945/ajcn.2009.29042.
Estimating the quantitative relation between food energy intake and changes in body weight Dear Sir: We read with great interest the recent pair of articles by Swinburn et al (1, 2) that address the important relation between changes in food energy intake and body weight. We recently proposed a mathematical model of adult human energy expenditure that quantitatively relates body weight to changes in food energy intake as well as in physical activity (3, 4). We were surprised to find that the predictions of the adult power law equation proposed by Swinburn et al differed significantly from our model—a result that was particularly perplexing because our results closely agree with the 94 kJ kg21 d21 regression line slope depicted in Figure 2 of Swinburn et al (2). A plot of both the regression line and the power law relation reported by Swinburn et al, which were derived from the same doubly labeled water data, is shown in Figure 1. Clearly, the slope of the power law relation is much greater at the mean body weight where the curves intersect and will thereby result in an underestimate of weight change for a given increment of food intake. We believe that this difference resulted from the choice of regressing the logarithm of the body weight compared with the logarithm of the energy expenditure rather than vice versa. It is well known that regression curves can be different when the coordinates of the data are exchanged because the regression procedure minimizes the square of the ordinate distance between the curve and the data. Placing the body-weight measurement on the abscissa is more appropriate because it has a much smaller uncertainty than the energy expenditure measurement. Transforming the data into logarithmic coordinates also amplifies any uncertainty because the slope of the regressed line in logarithmic coordinates is the power law exponent in linear coordinates. Thus, we believe that the power law equation proposed by Swinburn et al (2) predicts a steady state increment of body weight that is too small for a given change in food energy intake. Our model predictions, which agree with Swinburn et al’s linear regression curve but not the power law, have been validated in cases
FIGURE 1. Power law and linear regression curves fit to the same doubly labeled water data as reported by Swinburn et al (2).
of underfeeding and overfeeding and in longitudinal changes of 24-h energy expenditure in adults (3, 4). Our results fully agree with the main conclusion of Swinburn et al that the rise of the food energy supply is more than sufficient to account for the adult obesity epidemic and that suggests that there has been a progressive increase of food waste in America that has been underestimated by traditional food waste methods (3). This research was supported by the Intramural Research Program of the NIH/NIDDK. Neither author declared a conflict of interest.
Kevin D Hall Carson C Chow Laboratory of Biological Modeling National Institute of Diabetes and Digestive and Kidney Diseases Bethesda, MD 20892 E-mail:
[email protected]
REFERENCES 1. Swinburn B, Sacks G, Ravussin E. Increased food energy supply is more than sufficient to explain the US epidemic of obesity. Am J Clin Nutr 2009;90:1453–6. 2. Swinburn BA, Sacks G, Lo SK, et al. Estimating the changes in energy flux that characterize the rise in obesity prevalence. Am J Clin Nutr 2009;89:1723–8. 3. Hall KD, Guo J, Dore M, Chow CC. The progressive increase of food waste in America and its environmental impact. PLoS One 2009;4:e7940. 4. Hall KD, Jordan PN. Modeling weight-loss maintenance to help prevent body weight regain. Am J Clin Nutr 2009;88:1495–503. doi: 10.3945/ajcn.2009.28922.
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