Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology

TL;DR

This paper introduces a Bayesian copula-based semiparametric method for estimating the densities of long-term dietary intakes from zero-inflated, error-prone 24-hour recall data in nutritional epidemiology, improving upon existing approaches.

Contribution

It develops a novel hierarchical latent variable framework combined with copula modeling to accurately estimate densities of episodically consumed dietary components.

Findings

The method outperforms existing approaches in simulation studies.

It provides more realistic estimates of dietary intake patterns.

Efficient MCMC algorithms enable practical application.

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-hour 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.