Structured measurement error in nutritional epidemiology: applications in the Pregnancy, Infection, and Nutrition (PIN) Study.

Preterm birth, defined as delivery before 37 completed weeks' gestation, is a leading cause of infant morbidity and mortality. Identifying factors related to preterm delivery is an important goal of public health professionals who wish to identify etiologic pathways to target for prevention. Validation studies are often conducted in nutritional epidemiology in order to study measurement error in instruments that are generally less invasive or less expensive than "gold standard" instruments. Data from such studies are then used in adjusting estimates based on the full study sample. However, measurement error in nutritional epidemiology has recently been shown to be complicated by correlated error structures in the study-wide and validation instruments. Investigators of a study of preterm birth and dietary intake designed a validation study to assess measurement error in a food frequency questionnaire (FFQ) administered during pregnancy and with the secondary goal of assessing whether a single administration of the FFQ could be used to describe intake over the relatively short pregnancy period, in which energy intake typically increases. Here, we describe a likelihood-based method via Markov Chain Monte Carlo to estimate the regression coefficients in a generalized linear model relating preterm birth to covariates, where one of the covariates is measured with error and the multivariate measurement error model has correlated errors among contemporaneous instruments (i.e. FFQs, 24-hour recalls, and/or biomarkers). Because of constraints on the covariance parameters in our likelihood, identifiability for all the variance and covariance parameters is not guaranteed and, therefore, we derive the necessary and suficient conditions to identify the variance and covariance parameters under our measurement error model and assumptions. We investigate the sensitivity of our likelihood-based model to distributional assumptions placed on the true folate intake by employing semi-parametric Bayesian methods through the mixture of Dirichlet process priors framework. We exemplify our methods in a recent prospective cohort study of risk factors for preterm birth. We use long-term folate as our error-prone predictor of interest, the food-frequency questionnaire (FFQ) and 24-hour recall as two biased instruments, and serum folate biomarker as the unbiased instrument. We found that folate intake, as measured by the FFQ, led to a conservative estimate of the estimated odds ratio of preterm birth (0.76) when compared to the odds ratio estimate from our likelihood-based approach, which adjusts for the measurement error (0.63). We found that our parametric model led to similar conclusions to the semi-parametric Bayesian model.