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

PURPOSE: 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). METHODS: 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). RESULTS: 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. CONCLUSIONS: 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).