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June 2011 A new multivariate measurement error model with zero-inflated dietary data, and its application to dietary assessment
Saijuan Zhang, Raymond J. Carroll, Douglas Midthune, Patricia M. Guenther, Susan M. Krebs-Smith, Victor Kipnis, Kevin W. Dodd, Dennis W. Buckman, Janet A. Tooze, Laurence Freedman
Ann. Appl. Stat. 5(2B): 1456-1487 (June 2011). DOI: 10.1214/10-AOAS446


In the United States the preferred method of obtaining dietary intake data is the 24-hour dietary recall, yet the measure of most interest is usual or long-term average daily intake, which is impossible to measure. Thus, usual dietary intake is assessed with considerable measurement error. Also, diet represents numerous foods, nutrients and other components, each of which have distinctive attributes. Sometimes, it is useful to examine intake of these components separately, but increasingly nutritionists are interested in exploring them collectively to capture overall dietary patterns. Consumption of these components varies widely: some are consumed daily by almost everyone on every day, while others are episodically consumed so that 24-hour recall data are zero-inflated. In addition, they are often correlated with each other. Finally, it is often preferable to analyze the amount of a dietary component relative to the amount of energy (calories) in a diet because dietary recommendations often vary with energy level. The quest to understand overall dietary patterns of usual intake has to this point reached a standstill. There are no statistical methods or models available to model such complex multivariate data with its measurement error and zero inflation. This paper proposes the first such model, and it proposes the first workable solution to fit such a model. After describing the model, we use survey-weighted MCMC computations to fit the model, with uncertainty estimation coming from balanced repeated replication. The methodology is illustrated through an application to estimating the population distribution of the Healthy Eating Index-2005 (HEI-2005), a multi-component dietary quality index involving ratios of interrelated dietary components to energy, among children aged 2–8 in the United States. We pose a number of interesting questions about the HEI-2005 and provide answers that were not previously within the realm of possibility, and we indicate ways that our approach can be used to answer other questions of importance to nutritional science and public health.


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Saijuan Zhang. Raymond J. Carroll. Douglas Midthune. Patricia M. Guenther. Susan M. Krebs-Smith. Victor Kipnis. Kevin W. Dodd. Dennis W. Buckman. Janet A. Tooze. Laurence Freedman. "A new multivariate measurement error model with zero-inflated dietary data, and its application to dietary assessment." Ann. Appl. Stat. 5 (2B) 1456 - 1487, June 2011.


Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 1223.62167
MathSciNet: MR2849782
Digital Object Identifier: 10.1214/10-AOAS446

Keywords: Bayesian methods , dietary assessment , latent variables , measurement error , mixed models , nutritional epidemiology , nutritional surveillance , zero-inflated data

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.5 • No. 2B • June 2011
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