Nonparametric zero-inflated measurement error models and their applications

膳食评估是生命科学各个领域众多研究的核心，包括营养、公共卫生和流行病学。在这些评估中，研究人员往往感兴趣的是获取个人饮食成分的长期平均摄入量，通常称为正常摄入量；并确定消费模式及其与健康结果的关系。在这种情况下，经常使用自我报告工具来评估膳食摄入量，这些工具只允许记录一天的食物和营养摄入量。由于这张快照不能准确反映长期平均摄入量，人们早就认识到，这种观测是受测量误差污染的常见摄入量的版本。*当一种食物/营养素每天被消耗并且可以用一个连续变量表示时，大量关于测量误差的文献展示了如何把握个体通常摄入量的分布或其与健康结果的关系。然而，可以说，人们对偶尔摄入的食物或营养素更感兴趣，如酒精、鱼、牛奶等。由于这些食物或营养素不是每天都摄入的，因此出现的一个复杂问题是，报告摄入量中不可忽略的比例等于零。这种特殊性通常被称为过零点之一。对于这些变量，报告的摄入量是离散成分和连续成分的混合，在测量文献中开发的现有标准技术都不能用于成功分析这种数据。*最近，文献中提出了一些专门用于零膨胀饮食数据的技术，但这些方法是基于参数假设的，这在实践中很难证明其合理性。这一建议通过设计新的统计方法来解决这个问题，这些新的统计方法尽可能放宽现有文献中所做的强有力的参数假设。因此，这项研究计划的主要关注点是方法论，旨在为一系列涉及观察的模型开发灵活的非参数估计程序，例如那些在饮食评估中出现的模型，即具有零通胀和测量误差的模型。*焦点将针对从业者在现实生活中遇到的设置。因此，拟议的方法还将通过揭示数据集中隐藏在参数模型施加的限制下的特征，来加深我们对营养流行病学和饮食模式的基本机制的理解。*我们对基本模式的理解是政府政策和改变人生的决策的核心。因此，这项提案的结果必须并将惠及广大受众，其中包括从事涉及膳食评估的不同领域的统计学家和从业人员。

Dietary assessments are central to numerous investigations in various fields of life sciences, including nutrition, public health and epidemiology. In these assessments, researchers are often interested in capturing the long-term average intake, often called usual intake, of individual dietary components; and identifying consumption patterns and their connections to health outcomes. In this context, dietary intakes are often assessed using self-report instruments that allow to capture food and nutrient intake for a single day only. Because this snapshot cannot accurately reflect long-term average intake, it has long been recognized that such observations are versions of usual intakes contaminated by measurement errors. ******When a food/nutrient is consumed daily and can be represented by a continuous variable, a vast literature on measurement errors shows how to seize the distribution of the individuals' usual intake or its relationship with health outcomes. However, there is arguably a greater interest in foods or nutrients that are consumed episodically such as alcohol, fish, milk, etc. Since these foods or nutrients are not consumed everyday, a complication that arises is that a non-negligible proportion of reported intake is equal to zero. This particularity is often referred to as one of excess zeros. For those variables, the reported intake is a mixture of a discrete and a continuous component, and none of the standard existing techniques developed in the measurement literature can be applied to successfully analyse such data. ******Recently, some techniques specifically devoted to zero-inflated dietary data have been proposed in the literature, but these approaches are based on parametric assumptions, which can be hard to justify in practice. This proposal addresses this problem by targeting the design of new statistical approaches that relax as many of the strong parametric assumptions made in the existing literature as possible. As such, the primary concern of this research program is methodological, and aims to develop flexible nonparametric estimation procedures for a wide array of models involving observations such as those arising in dietary assessments, namely with zero-inflations and measurement errors. ******Focus will be directed towards settings that are encountered in real life by practitioners. Hence, the proposed methods will also allow to deepen our understanding of fundamental mechanisms in nutritional epidemiology and dietary patterns, by exposing features in datasets that are hidden otherwise under the constraints imposed by parametric models. ******Our understanding of fundamental patterns is at the heart of government policies and life-changing decisions. Consequently, the outcome of this proposal has to, and will, reach a broad audience that includes statisticians and practitioners engaged in diverse fields involving dietary assessments.