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.

We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data analysis approach produces more accurate 1- to 20-step-ahead point and interval forecasts than Lee–Carter method, Hyndman–Ullah method and two naïve random walk methods. The improved forecast accuracy of period life-table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities. Although we focus on temporary annuity prices, we consider long-term contracts that make the annuity almost lifetime, in particular when the age at entry is sufficiently high.