Evaluating the effect of nutritional components on health outcomes is hampered by technical difficulties that are closely related to the compositional nature of dietary data. Compositional data consist of parts of a whole and, on the basis of the assumption that any relevant information they provide is contained in the ratios between them, procedures based on log-ratio transformations have been proposed for their analysis. It has been previously suggested that nutrient compositions can be analyzed using isometric log-ratio transformations which allow the compositions to be represented by a system of orthogonal coordinates corresponding to the log-contrasts between the compositional parts. One particular expression of these contrasts is called balances, and the aim of this note is to provide a step-by-step description of how to construct orthonormal balances and show how they can be applied to dietary data by means of an example based on data coming from an Italian population-based study. Nutrient balances are new variables that can be included as covariates in regression models. After fitting a linear regression model using estimates of relative fat mass as a response variable, scores indicating the obesogenic potential of foods can be defined on the basis of their nutritional contents and the estimated effect of the balances on relative fat mass. This approach to evaluating the relationship between diet and health outcomes provides insights into the roles of specific nutrient ratios and foods within a comprehensive and integrated framework that complies with the essentially compositional nature of dietary data.

中文翻译：

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正交平衡作为表征膳食暴露的一种手段

评估营养成分对健康结果的影响受到与膳食数据组成性质密切相关的技术困难的阻碍。成分数据由整体的一部分组成，并且基于它们提供的任何相关信息都包含在它们之间的比率中的假设，已经提出了基于对数比率变换的程序来进行分析。先前已经提出，可以使用等距对数比变换来分析营养成分，该变换允许由对应于组成部分之间的对数对比的正交坐标系统表示组合物。这些对比的一种特殊表现被称为平衡，本说明的目的是逐步描述如何构建标准正交平衡，并通过基于意大利人口研究数据的示例展示如何将它们应用于饮食数据。营养平衡是可以作为协变量包含在回归模型中的新变量。在使用相对脂肪量的估计值作为响应变量拟合线性回归模型后，可以根据其营养成分和平衡对相对脂肪量的估计影响来定义指示食物致肥胖潜力的分数。