A simplified approach to estimating the distribution of occasionally-consumed dietary components, applied to alcohol...

Within-person variation in dietary records can lead to biased estimates of the distribution of food intake. Quantile estimation is especially relevant in the case of skewed distributions and in the estimation of under- or over-consumption. The analysis of the intake distributions of occasionally-consumed foods presents further challenges due to the high frequency of zero records. Two-part mixed-effects models account for excess-zeros, daily variation and correlation arising from repeated individual dietary records. In practice, the application of the two-part model with random effects involves Monte Carlo (MC) simulations. However, these can be time-consuming and the precision of MC estimates depends on the size of the simulated data which can hinder reproducibility of results.

We propose a new approach based on numerical integration as an alternative to MC simulations to estimate the distribution of occasionally-consumed foods in sub-populations. The proposed approach and MC methods are compared by analysing the alcohol intake distribution in a sub-population of individuals at risk of developing metabolic syndrome.

The rate of convergence of the results of MC simulations to the results of our proposed method is model-specific, depends on the number of draws from the target distribution, and is relatively slower at the tails of the distribution. Our data analyses also show that model misspecification can lead to incorrect model parameter estimates. For example, under the wrong model assumption of zero correlation between the components, one of the predictors turned out as non-significant at 5 % significance level (p-value 0.062) but it was estimated as significant in the correctly specified model (p-value 0.016).

The proposed approach for the analysis of the intake distributions of occasionally-consumed foods provides a quicker and more precise alternative to MC simulation methods, particularly in the estimation of under- or over-consumption. The method is readily available to non-technical users in contrast to MC methods whereby the simulation error may be substantial and difficult to evaluate.