Abstract
Nutritional exposures are often measured with considerable error in commonly used surrogate instruments such as the food frequency questionnaire (FFQ) (denoted by Q(i) for the ith subject). The error can be both systematic and random. The diet record (DR) denoted by R(i) for the ith subject is considered an alloyed gold standard. However, some authors have reported both systematic and random errors with this instrument as well.One goal in measurement error research is to estimate the regression coefficient of T(i) (true intake for the ith subject) on Q(i) denoted by lambda(TQ). If the systematic errors in Q(i) and R(i) (denoted by q(i) and r(i)) are uncorrelated, then one can obtain an unbiased estimate of lambda(TQ) by lambda(RQ) obtained by regressing R(i) on Q(i). However, if Corr(q(i), r(i))>0, then lambda(RQ)>lambda(TQ).In this paper, we propose a method for indirectly estimating lambda(TQ) even in the presence of correlated systematic error based on a longitudinal design where Q(i) (surrogate measure of dietary intake), R(i) (a reference measure of dietary intake), and M(i) (a biomarker) are available on the same subjects at 2 time points. In addition, between-person variation in mean levels of M(i) among people with the same dietary intake is also accounted for. The methodology is illustrated for dietary vitamin C intake based on longitudinal data from 323 subjects in the European Prospective Investigation of Cancer (EPIC)-Norfolk study who provided two measures of dietary vitamin C intake from the FFQ (Q(i)) and a 7-day DR (R(i)) and plasma vitamin C (M(i)) 4 years apart.