Скачать или смотреть Compositional Data in Nutritional Epidemiology

This article, titled "Applying compositional data methodology to nutritional epidemiology" by Maria Léa Corrêa Leite, presents a novel and formally appropriate statistical approach for analyzing dietary data in nutritional epidemiology. Published in Statistical Methods in Medical Research, this work addresses a critical challenge in the field: investigating the effects of specific dietary components independently of total energy intake.

The core issue lies in the compositional nature of dietary data, where measurements represent parts of a whole (e.g., percentages or proportions of macronutrients contributing to total energy). Such data are constrained to a constant sum and convey only relative information, leading to a negatively biased covariance structure and occupying a restricted space known as a D-part simplex. Consequently, standard statistical methods designed for unconstrained variables are inappropriate for analyzing raw compositional data, as they are based on Euclidean space variances and covariances, not those suitable for the simplex. Traditional multivariate analyses struggle to disentangle the specific effects of individual macronutrients from the generic effect of total energy on disease risk due to this inherent compositional constraint.

To overcome these limitations, the article advocates for a compositional data perspective, building upon the foundational work of Aitchison. This approach is centered on log-ratio transformations, which convert compositional data from the restricted simplex space to an unconstrained real space, thereby enabling the use of standard multivariate statistical techniques. While additive log-ratio (alr) and centered log-ratio (clr) transformations exist, the paper focuses on the isometric log-ratio (ilr) transformation. The ilr transformation is particularly advantageous because it preserves all simplicial metric properties by transforming compositions into real orthogonal coordinates, allowing for systematic application of usual statistical methods. A specific form of ilr coordinates, known as balances, offers a straightforward interpretation by representing the relative variation and relationships between groups of parts within the composition.

Reference:

Leite, M. L. C. (2016). Applying compositional data methodology to nutritional epidemiology. Statistical Methods in Medical Research, 25(6), 3057–3065. https://doi.org/10.1177/0962280214560047