When studying the relationship between nutrition and disease, researchers are interested in evaluating the role of the quantita- tive aspect of the diet (total energy intake) separately from its qualitative aspect (nutrient composition). The use and interpreta- tion 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. Compositional data describe parts of a whole and, conse- quently, 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 Com- positional 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.7–10 Although such measurements can be found in various elds of science, the mathematical dif culties 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 propor- tional nature, the only meaningful functions of a composition consist of ratios of its parts. We have previously proposed a compositional data approach to analyse dietary data and discussed its potential advantages over the usual analytical methods.11 Here, we expand the discussion by exemplifying the use of sequential binary partition (SBP) and demonstrating its suitability for investigating the relationships between dietary macronutrient balances and diseases.
A compositional data perspective on studying the associations between macronutrient balances and diseases
Prinelli F.
2017
Abstract
When studying the relationship between nutrition and disease, researchers are interested in evaluating the role of the quantita- tive aspect of the diet (total energy intake) separately from its qualitative aspect (nutrient composition). The use and interpreta- tion 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. Compositional data describe parts of a whole and, conse- quently, 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 Com- positional 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.7–10 Although such measurements can be found in various elds of science, the mathematical dif culties 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 propor- tional nature, the only meaningful functions of a composition consist of ratios of its parts. We have previously proposed a compositional data approach to analyse dietary data and discussed its potential advantages over the usual analytical methods.11 Here, we expand the discussion by exemplifying the use of sequential binary partition (SBP) and demonstrating its suitability for investigating the relationships between dietary macronutrient balances and diseases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
