#610: Rock, Paper, Salmon – Errors in Interpreting Food Substitution Models

Useful Terminology

• Food substitution model: A statistical approach used to estimate the association of consuming one food, nutrient, or dietary component instead of another.
• Comparator: The food, nutrient, or background dietary mixture that an exposure is being compared against.
• Isocaloric principle: The principle that total energy intake should be held constant when estimating the health association of a specific dietary component. This is routine in feeding trials and is often approximated in epidemiology by adjusting for total energy intake.
• Energy adjustment: Statistical adjustment for total energy intake or related energy variables. Energy adjustment can reduce confounding from body size, appetite, and overall food intake, but different adjustment methods target different causal questions and can produce different interpretations.
• Total causal effect: The estimated effect of increasing one dietary component while holding all other dietary components constant. Tomova et al. describe this as an additive-type question. In practice, this is often less relevant to foods because people rarely add food without compensating elsewhere.
• Average relative causal effect: The estimated effect of increasing one dietary component while decreasing other energy-providing components to keep total energy constant. This is the substitution-type question most closely linked to total energy adjustment.
• Non-specified substitution: A model in which energy is adjusted for, but the replacement food is not explicitly named. The comparator is therefore the weighted average of other foods in the population’s background diet, or the remaining diet after other covariates are included.
• Specified substitution: A model that explicitly defines the replacement, such as replacing one serving of processed meat with one serving of fish, or replacing 100 g/d of conventional fruits and vegetables with 100 g/d of organic fruits and vegetables.
• Residual confounding: Remaining distortion in an association after statistical adjustment. In food substitution models, residual confounding can arise because food choices are linked to overall diet quality, health consciousness, socioeconomic position, physical activity, smoking, medical screening, and other factors.
• Mixed-unit model: A model that combines food variables in one unit, such as grams, with energy adjustment in another unit, such as calories. Ibsen and Dahm emphasise that mixed units can produce obscure interpretations and, in simulations and reanalyses, can even reverse coefficient direction.

Interpreted in Isolation

Our episode was built around a seemingly simple question: when we say one food is associated with better or worse health, what is it being compared with? Nutrition research is inherently comparative because diets are finite. Eating more of one thing usually means eating less of another, increasing total energy intake, or changing the broader dietary pattern.

The comparator determines the meaning of the result.

• A food may appear beneficial, neutral, or harmful depending on what it replaces.
• Eggs compared with processed meat and butter can look different from eggs compared with a typical background diet.
• Dairy compared with refined starch and processed meat can look different from dairy compared with nuts, legumes, or olive oil.
• Fish compared with legumes may look different from fish compared with processed meat or refined carbohydrates.

The “compared to what?” question is obvious in trials but often hidden in observational analyses.

• • In a controlled feeding trial, the intervention and control diets must both be defined.
  • If a trial increases egg intake, the control group must eat something instead of eggs.