Nonparametric zero-inflated measurement error models and their applications

饮食评估是生命科学各个领域（包括营养、公共卫生和流行病学）众多研究的核心。在这些评估中，研究人员通常感兴趣的是获取个人饮食成分的长期平均摄入量，通常称为通常摄入量；确定消费模式及其与健康结果的关系。在这种情况下，通常使用自我报告工具来评估饮食摄入量，该工具仅允许捕获一天的食物和营养摄入量。由于这种快照不能准确地反映长期平均摄入量，因此人们早就认识到，这种观察结果是受测量误差污染的通常摄入量的版本。当一种食物/营养素每天被消耗，并且可以用一个连续变量来表示时，关于测量误差的大量文献显示了如何抓住个人通常摄入量的分布或其与健康结果的关系。然而，人们对偶尔摄入的食物或营养物质更感兴趣，比如酒精、鱼、牛奶等。由于这些食物或营养素不是每天都消耗，因此出现的一个复杂情况是，报告的摄入量中有不可忽略的比例等于零。这种特殊性通常被称为一个多余的零。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物，测量文献中开发的任何标准现有技术都不能成功地应用于分析此类数据。最近，文献中提出了一些专门用于零膨胀饮食数据的技术，但这些方法基于参数假设，难以在实践中证明。本建议通过设计新的统计方法来解决这个问题，这些方法尽可能放松现有文献中所做的许多强参数假设。因此，本研究项目的主要关注点是方法论，旨在开发灵活的非参数估计程序，用于涉及观察的各种模型，例如饮食评估中出现的模型，即零通胀和测量误差。重点将指向从业者在现实生活中遇到的设置。因此，所提出的方法还将通过揭示数据集中隐藏在参数模型约束下的特征，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生活的决定的核心。因此，这项建议的结果必须也将会得到广泛的关注，包括从事饮食评估等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.