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. 2022 Jan 11;115(1):189-198.
doi: 10.1093/ajcn/nqab266.

Adjustment for energy intake in nutritional research: a causal inference perspective

Affiliations

Adjustment for energy intake in nutritional research: a causal inference perspective

Georgia D Tomova et al. Am J Clin Nutr. .

Abstract

Background: Four models are commonly used to adjust for energy intake when estimating the causal effect of a dietary component on an outcome: 1) the "standard model" adjusts for total energy intake, 2) the "energy partition model" adjusts for remaining energy intake, 3) the "nutrient density model" rescales the exposure as a proportion of total energy, and 4) the "residual model" indirectly adjusts for total energy by using a residual. It remains underappreciated that each approach evaluates a different estimand and only partially accounts for confounding by common dietary causes.

Objectives: We aimed to clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding.

Methods: Semiparametric directed acyclic graphs and Monte Carlo simulations were used to identify the estimands and interpretations implied by each model and explore their performance in the absence or presence of dietary confounding.

Results: The "standard model" and the mathematically identical "residual model" estimate the average relative causal effect (i.e., a "substitution" effect) but provide biased estimates even in the absence of confounding. The "energy partition model" estimates the total causal effect but only provides unbiased estimates in the absence of confounding or when all other nutrients have equal effects on the outcome. The "nutrient density model" has an obscure interpretation but attempts to estimate the average relative causal effect rescaled as a proportion of total energy. Accurate estimates of both the total and average relative causal effects may instead be derived by simultaneously adjusting for all dietary components, an approach we term the "all-components model."

Conclusions: Lack of awareness of the estimand differences and accuracy of the 4 modeling approaches may explain some of the apparent heterogeneity among existing nutritional studies. This raises serious questions regarding the validity of meta-analyses where different estimands have been inappropriately pooled.

Keywords: causal inference; compositional data; directed acyclic graphs; estimand; nutritional epidemiology.

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Figures

FIGURE 1
FIGURE 1
Directed acyclic graph showing the compositional nature of nutritional data. TE (the “whole,” purple) is fully determined by energy intake from 7 constituent macronutrients (the “parts,” blue and red). The nutrient exposure (nonmilk extrinsic sugars, blue) and 6 competing energy sources (red) all cause the outcome (GLUC concentration, gray) and are themselves caused by all unobserved determinants of dietary intake and composition (gray). The absence of an arc from energy intake to GLUC reflects the lack of an independent causal effect, conditional on all components of energy intake, i.e., any observed effect is the average combined causal effect of all nutrients on GLUC concentration.
FIGURE 2
FIGURE 2
Directed acyclic graphs showing how confounding by common determinants of dietary intake and composition can be reduced when estimating the total causal effect (blue arc) of a nutritional exposure (e.g., nonmilk extrinsic sugars, blue) on an outcome (e.g., fasting plasma glucoseconcentration). Confounding by common determinants of dietary intake and composition will exist if ≥1 of the competing nutritional components (red) also cause the outcome (red arcs). This can be reduced (A) by conditioning on the remaining energy intake or (B) by conditioning on each of the competing nutritional components directly. For key see Figure 1.
FIGURE 3
FIGURE 3
Directed acyclic graphs showing the consequences of adjusting for total energy when estimating the causal effect of a nutrient exposure (e.g., nonmilk extrinsic sugars, blue) on an outcome (e.g., GLUC concentration, gray). Total energy is completely determined by the exposure nutrient (nonmilk extrinsic sugars, blue) and all competing energy sources (red). Adjusting for TE (purple) opens conditional dependencies between the exposure and all competing energy sources (purple dashed arcs), so that the total causal effect (blue arc) is now in competition with the (average) effect of all competing energy sources (red arcs). The average relative causal effect thus represents the difference between the total causal effect of the exposure and the weighted average effect of all other energy sources. For key, see Figure 1.

Comment in

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