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

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,1-5 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.