A New Class of Measurement Error Models, with Applications to Dietary Data

Measurement error modeling occurs when one cannot observe a covariate, but instead has possibly replicated surrogate versions of this covariate measured with error. The vast majority of the literature in measurement error modeling assumes (typically with good reason) that given the value of the true but unobserved (latent) covariate, the replicated surrogates are unbiased for latent covariate and conditionally independent. In the area of nutritional epidemiology, there is some evidence from biomarker studies that this simple conditional independence model may break down due to two causes: (a) systematic biases depending on a person's body mass index; and (b) an additional random component of bias, so that the error structure is the same as a one{way random e ects model. We investigate this problem, in the context of (1) the estimation of the distribution of usual nutrient intake; (2) estimating the correlation between a nutrient instrument and usual nutrient intake; and (3) estimating the true relative risk from an estimated relative risk using the error{prone covariate. While systematic bias due to body mass index appears to have little e ect, the additional random e ect in the variance structure is shown to have a potentially important impact on overall results, both on corrections for relative risk estimates and in estimating the distribution of usual nutrient intake. However, the impact of dietary measurement error on both factors is shown via examples to depend strongly on the data set being used. Indeed, one of our data sets suggests that dietary measurement error may be masking a strong risk of fat on breast cancer, while a second data set suggests this may be unlikely. Until further understanding of dietary measurement is available, measurement error corrections must be done on a study{speci c basis.