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A compositional data perspective on studying the associations between macronutrient balances and diseases

European Journal of Clinical Nutrition volume 71, pages 1365–1369 (2017)Cite this article

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When studying the relationship between nutrition and disease, researchers are interested in evaluating the role of the quantitative aspect of the diet (total energy intake) separately from its qualitative aspect (nutrient composition). The use and interpretation of energy-adjustment regression models in nutritional epidemiology was much debated, particularly in the 1990s,1, 2, 3, 4, 5 but the critical point is the fact that it is not possible to disentangle the generic effect of total energy from that of the separate components of energy (proteins, fats and carbohydrates) that make up the total by means of multivariate analysis. The mathematics underlying regression analysis will fail if there is perfect collinearity amongst the independent variables, and this occurs when they are exact linear functions of each other. In energy-adjusted models, perfect collinearity exists since each macronutrient component of energy can be expressed as a combination of the total energy and the other sources, such as energy from proteins=total energy−energy from fats−energy from carbohydrates. Despite having four variables in this case, we only have three degrees of freedom and unless one of the four terms is removed from the regression model, mathematical calculation cannot be made because the information as a whole is overlapped. Essentially, the heart of the matter lies in the compositional nature of the dietary data.

Compositional data describe parts of a whole and, consequently, convey only relative information. They are usually recorded in a closed form (proportions or percentages), and their particular numerical properties hamper the use of standard statistical methods designed for unconstrained variables.6 Compositional data occupy a restricted space known as the simplex whose peculiar geometry has been developed over the last 30 years mainly on the basis of the contributions of Aitchison.7, 8, 9, 10 Although such measurements can be found in various fields of science, the mathematical difficulties in applying analytical tools based on the so-called Aitchison geometry have probably prevented their wider use in research communities. Fortunately, simple methodologies based on logarithms of ratios have been proposed as a convenient means of transforming compositional data, allowing the use of standard statistical procedures. The basic idea of the log-ratio transformations is that, given their proportional nature, the only meaningful functions of a composition consist of ratios of its parts.

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  1. National Research Council, Institute of Biomedical Technologies, Milan, Italy

    M L C Leite & F Prinelli

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  1. M L C Leite
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Correspondence to M L C Leite.

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Leite, M., Prinelli, F. A compositional data perspective on studying the associations between macronutrient balances and diseases. Eur J Clin Nutr 71, 1365–1369 (2017). https://doi.org/10.1038/ejcn.2017.126

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