Compositional data analysis as an alternative paradigm for nutritional studies

Methods: The analyses of data from an Italian population study of 673 non-diabetic women aged 40-74 years were based on isometric log-ratio (ilr) transformation applied to three dietary compositions: seven-part macronutrients, nine-part vitamins and six-part minerals. The ilr transformation produces new variables that represent specific contrasts (balances) between the compositional parts. Different sequential binary partitions have been described and used as a means of flexibly defining balances on the basis of a researcher's interest, and the new variables (that are suitable for undergoing standard statistical procedures) have been included as covariates in linear regression models in order to examine the isocaloric associations between specific dietary balances and waist circumference (WC).

Background & aim: Although the compositional nature of dietary data is well recognized, little attention has been given to the methods specifically developed for the statistical analysis of compositional data. The use of standard statistical procedures that ignore the relative nature of compositional elements can lead to spurious results when applied to crude data. This note proposes using a compositional data approach for the statistical analysis of nutritional data.