Abstract

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hr recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

摘要

估计不同膳食成分的长期平均摄入量的边际和联合密度是营养流行病学中的一个重要问题。由于这些变量无法直接测量，数据通常以 24 小时摄入量召回的形式收集，这显示了条件异方差的显着模式。使挑战更加复杂的是，对偶尔食用的饮食成分的召回还包括精确的零。从他们观察到的测量误差污染的代理估计潜在长期摄入的密度的问题是密度与零膨胀数据的反卷积问题。我们提出了该问题的贝叶斯半参数解决方案，建立在一种新颖的分层潜在变量框架上，该框架将问题转化为仅涉及连续代理的问题。对于适应问题的重要方面至关重要，然后我们设计了一种基于 copula 的方法来对所涉及的联合分布进行建模，对不同饮食成分的边缘采用不同的建模策略。我们为后验推理设计了高效的马尔可夫链蒙特卡罗算法，并通过仿真实验说明了所提出方法的有效性。应用于我们的激励营养流行病学问题，与其他方法相比，我们的方法提供了对偶尔消耗的饮食成分的消费模式的更现实的估计。本文的补充材料，