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Abstract:
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Many nutritional studies focus on the relationship between individuals' diets and resulting health outcomes. In this work, we focus on situations where the association is nonlinear. When examining these relationships, researchers are generally interested in individuals' long-term, average intake of nutrients; however, typically only 1-2 days of data are collected. If analyses are performed without accounting for the error in estimating usual intake, estimates will be biased. We propose implementing a nonlinear measurement error model which accounts for the nuisance day-to-day variance when estimating long-term average intake. Estimation of the model is performed using maximum likelihood. We further propose an extended model where the distribution for the unobservable predictor is not restricted to be assumed normal, but is instead a finite mixture of discrete distributions. We finish with an application using data from the 2015-2016 National Health and Nutrition Examination Survey (NHANES) where we examine the association between potassium intake and systolic blood pressure.
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