Orthonormal balances as a means of characterizing dietary exposure

Evaluating the effect of nutritional components on health outcomes is hampered by technical difficulties that are closely related to the compositional nature of dietary data. Compositional data consist of parts of a whole and, on the basis of the assumption that any relevant information they provide is contained in the ratios between them, procedures based on log-ratio transformations have been proposed for their analysis. It has been previously suggested that nutrient compositions can be analyzed using isometric log-ratio transformations which allow the compositions to be represented by a system of orthogonal coordinates corresponding to the log-contrasts between the compositional parts. One particular expression of these contrasts is called balances, and the aim of this note is to provide a step-by-step description of how to construct orthonormal balances and show how they can be applied to dietary data by means of an example based on data coming from an Italian population-based study. Nutrient balances are new variables that can be included as covariates in regression models. After fitting a linear regression model using estimates of relative fat mass as a response variable, scores indicating the obesogenic potential of foods can be defined on the basis of their nutritional contents and the estimated effect of the balances on relative fat mass. This approach to evaluating the relationship between diet and health outcomes provides insights into the roles of specific nutrient ratios and foods within a comprehensive and integrated framework that complies with the essentially compositional nature of dietary data.