Correlations between estimated and true dietary intakes: using two instrumental variables

We describe a new application of the method of triads that allows an estimate of the correlation between a dietary questionnaire measure (Q) and true intake (T).

Three surrogate variables Q, M, and P are observed where M and P are both instrumental (often biological) variables. A reference dietary method (R) is not required. The variables M and P may be concentration rather than recovery biomarkers. Estimating equations produce Corr(Q,T), Corr(M,T), Corr(P,T), conditional on assumptions about error correlations. Correlations between errors in both Q and a reference dietary measure can also be estimated if R is available. A small validation study of California Seventh-day Adventists provided food frequency, repeated 24-hour dietary recalls (R), and biological data (blood, overnight urines, and subcutaneous fat).

Values of Corr(Q,T) ranged between 0.40 and 0.66. Values of Corr(R,T) were higher, between 0.48 and 0.83. Estimated correlations between errors in R and Q were all positive.

When carefully chosen, M and P, rather than M and R, should better satisfy assumptions about error correlations. Food frequency data and repeated 24-hour recalls both provide estimates of T, but the latter has greater validity. Standard errors suggest that for good precision Corr(Q,T) requires large validation studies (2000-3000 subjects).