Compositional data analysis as an alternative paradigm for nutritional studies

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.

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).

Regardless of the dietary compositions, total energy was positively and fibre intake was negatively associated with WC. Net of these effects and keeping constant the proportional relationships between the other dietary components, WC was negatively associated with the relative increase in starches, and positively associated with the relative niacin content. Vitamin C was negatively associated with WC, whereas folate content was positively related.

The proposed approach allows a clear interpretation of the relative roles of different dietary components within a holistic overview of a diet. The analyses involving WC provide some useful insights.