Estimating the Distribution of Dietary Consumption Patterns

TL;DR

This paper presents a Bayesian method using MCMC to estimate the distribution of dietary quality scores in children, addressing measurement error and complex data modeling challenges.

Contribution

It introduces a novel Bayesian zero-inflated multivariate model for dietary data, enabling distribution estimation where traditional methods fail.

Findings

Successfully estimated the HEI-2005 score distribution in children

Demonstrated the effectiveness of Bayesian MCMC for complex survey data

Provided standard errors using survey-sampling techniques

Abstract

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. We were interested in 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, using a national survey and incorporating survey weights. We developed a highly nonlinear, multivariate zero-inflated data model with measurement error to address this question. Standard nonlinear mixed model software such as SAS NLMIXED cannot handle this problem. We found that taking a Bayesian approach, and using MCMC, resolved the computational issues and doing so enabled us to provide a realistic distribution estimate for the HEI-2005 total score. While our computation and thinking in solving this problem was Bayesian, we relied on the well-known close relationship between Bayesian posterior means and maximum likelihood, the latter not computationally feasible, and thus were able to develop standard errors using balanced repeated replication, a survey-sampling approach.