Nonparametric zero-inflated measurement error models and their applications

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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.