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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