Log-ratio transformations for dietary compositions: numerical and conceptual questions

When evaluating the impact of macronutrient intakes on health outcomes, researchers in nutritional epidemiology are mostly interested in two types of information: the relative importance of the individual macronutrients and the absolute effect of total energy intake. However, the usual substitution models do not allow these separate effects to be disentangled. Dietary data are typical examples of compositional data, which convey relative information and are, therefore, meaningfully expressed in the form of ratios. Various formulations of log-ratios have been proposed as a means of analysing compositional data, and their interrelationships when they are used as predictors in regression models have been previously reported. This note describes the application of distinct log-ratio transformations to the composition of dietary macronutrients and discusses the interpretative implications of using them as explanatory variables in regression models together with a term for the total composition (total energy intake). It also provides examples that consider serum glucose levels as the health outcome and are based on data coming from an Italian population-based study. The log-ratio transformation of dietary data has both numerical and conceptual advantages, and overcomes the drawbacks of traditional substitution models.