ABSTRACT

Many nutritional studies focus on the relationship between individuals' diets and resulting health outcomes. 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. In this work, we focus on situations where the association between intake and health outcomes is nonlinear. Since we can only obtain noisy measurements of intake, 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. Properties of the estimators are explored for a model where we assume that the unobservable usual intake is normally distributed. We then propose an extended model where we no longer assume that the distribution for the unobservable predictor is 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.

摘要

许多营养研究侧重于个人饮食与由此产生的健康结果之间的关系。在检查这些关系时，研究人员通常对个人长期的平均营养摄入量感兴趣。但是，通常只收集 1-2 天的数据。如果在没有考虑估计通常摄入量的错误的情况下进行分析，估计就会有偏差。在这项工作中，我们关注摄入量与健康结果之间的关联是非线性的情况。由于我们只能获得摄入量的噪声测量值，因此我们建议实施一个非线性测量误差模型，该模型在估计长期平均摄入量时解释了令人讨厌的日常方差。使用最大似然执行模型的估计。为模型探索估计量的属性，在该模型中，我们假设不可观察的通常摄入量是正态分布的。然后，我们提出了一个扩展模型，我们不再假设不可观察预测变量的分布是正态的，而是离散分布的有限混合。最后，我们使用 2015-2016 年全国健康和营养检查调查 (NHANES) 的数据完成了一项应用程序，在该调查中我们检查了钾摄入量与收缩压之间的关系。