On the formation and use of calibration equations in nutritional epidemiology – Discussion of the Paper by R. L. Prentice and Y. Huang

Prentice and Huang (2018) provide an interesting review of the current and future challenges facing the field of nutritional epidemiology. We fully concur with their stress on the importance of statistical concepts and methods in meeting these challenges. We welcome the opportunity here to expand in two directions on the approaches suggested in their review: first, to show that in implementing their approach extra statistical steps may be required; and second to highlight some dangers of misuse of the estimator, x̃(t), of true dietary intake that is central to their approach. In their development, the authors postulate the availability in their cohort study of the following information: a self-report assessment of the dietary intake of interest, q(t); personal characteristics, v(t), relevant to the self-reported dietary intake and the disease outcome, and in a sub-sample biomarker measurements, w(t), that measure the dietary intake in an unbiased manner with independent errors. From these elements, they construct a variable x̃(t) that measures x(t) with Berkson error, and that may consequently be used to relate dietary intake to disease outcome in a Cox regression model. The question we raise is ‘what is the nature of the biomarker measurements w(t)? ’. One may consider three classes of such biomarkers. The first class contains the recovery biomarkers, biological products that derive from a relatively simple metabolic process that leads to a direct and very close correspondence to the dietary intake. There are only a few such biomarkers available and these measure energy, protein, potassium, and sodium intakes, but their use in Prentice and Huang’s approach is straightforward. The second class contains the biomarkers (e.g., metabolites) that are developed from human feeding studies, in which volunteers are fed specified diets over a period of several weeks, and markers, denoted by vectorm, measured in biological samples from the volunteers, are then determined. These markers are then related to the known intakes of specific foods or nutrients in an equation x = f (m)+ e, where x is the known intake of the food or nutrient of interest, f is some mathematical function of the vector m and e is error independent of f (m). The new problem that now arises is that f (m) does not have the desirable statistical property enjoyed by Prentice and Huang’s w(t), namely that w(t) = x(t)+ e(t), where e(t) is independent of x(t). Therefore, a further statistical step is required to find a function of m that indeed has this property. If x and f (m) were joint normally distributed, this step would be achieved by the simple device of inverting the regression to be of the form f (m) = a0 + a1x + e∗, where e* is error independent of x, and then using g(m) = f (m) − a0/a1 as the biomarker measure for x. In practice, one may need to work with mathematically transformed values of x to approximate the joint normality assumption. See Tasevska et al. (2011) for a similar approach to creating a biomarker measure with the desired statistical properties. A third class of biomarkers is the creation of a biomarker signature for a specific dietary pattern. A metabolite profile is one such example of this type of biomarker. Biomarkers of dietary patterns offer unique statistical challenges (Carroll, 2014) and very little methodologic work has yet been done in this area. Guasch-Ferré, Bhupathiraju, and Hu (2018) review efforts to develop such signatures from metabolomics profile data for vegetarian, Western, Mediterranean, and Nordic dietary patterns among others. Prentice and Huang rightfully acknowledge both the promise of such approaches and the need for innovations in statistical methodology to better handle the complex measurement properties of these data. The challenges of intraand inter-person variability of these markers (Ala-Korpela, 2018; Guasch-Ferré et al., 2018; Johnson & Gonzalez, 2012), the many host and environmental factors, including age, genetic factors, disease, drugs, diet, lifestyle, and environment factors (Guasch-Ferré et al., 2018; Johnson & Gonzalez, 2012)