Background Four modelling approaches are commonly used to adjust for overall energy intake when seeking to estimate the causal effect of an individual 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’ examines the exposure as a proportion of total energy, and (4) the ‘residual model’ indirectly adjusts for total energy by using the residual from regressing the exposure nutrient on total energy intake. Unfortunately, it remains underappreciated that each approach evaluates a different causal effect estimand and only partially accounts for confounding by common causes of dietary intake and composition.
Methods Semi-parametric directed acyclic graphs and Monte Carlo simulations were used to identify the estimand implied by each approach and the correct interpretation of the model results. The performance of each model for estimating the corresponding target estimand was explored both in the absence and presence of confounding that acts through diet. An alternative approach based on the energy partition model that simultaneously adjusts for all competing dietary components, termed the ‘all-components model’, was also explored and compared with the four traditional approaches. This model involves using the weighted coefficients of different dietary components to estimate any desired causal effect estimand.
Results The ‘standard model’ and the mathematically identical ‘residual model’ both estimate the average relative causal effect (i.e. a ‘substitution’ effect) but provide biased estimates even in the absence of any confounding. The ‘energy partition model’, that adjusts for remaining energy intake, estimates the total causal effect (i.e. an ‘additive’ effect) but only provides unbiased estimates in the absence of confounding or when all individual nutrients have equal effects on the outcome. The ‘nutrient density model’ does not target a causally meaningful estimand but can provide extremely biased estimates of the average relative causal effect of the exposure rescaled as a percentage of total energy intake. Accurate estimates of both the total and average relative causal effects were obtained with the ‘all-components model’.
Conclusion Only the ‘all-components model’ produces unbiased estimates of different causal effects. Lack of awareness of the estimand differences and accuracy of the different modelling approaches may explain some of the apparent heterogeneity among existing nutritional studies. Serious questions may be raised regarding the validity of meta-analyses where different strategies returning different estimands have been inappropriately pooled.
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