# Estimation of habitual intake of infrequently consumed nutrients using the mixture distribution method

## TL;DR

A new method called MDM is proposed to estimate the habitual intake of nutrients that are not consumed regularly, using statistical models to simplify the process.

## Contribution

The MDM provides a computationally simpler approach to estimate habitual intake of infrequently consumed nutrients.

## Key findings

- The MDM and ISUF methods produced similar median habitual intakes for vitamins B6 and B12.
- The MDM estimates increase with higher proportions of positive intakes, outperforming arithmetic mean when positive intakes are below 60%.

## Abstract

The habitual intake of infrequently consumed nutrients typically exhibits a highly skewed distribution, primarily driven by the reported consumption and non-consumption of nutrients in repeated 24-h dietary recalls. The current methods for estimating this distribution are often computationally intense.

A mixture distribution method (MDM) was proposed to estimate habitual intake distribution of infrequently consumed nutrients, in which the frequency of consumption of a nutrient was modeled using a beta-binomial distribution and the amount consumed using a gamma distribution. The habitual intake using this method was compared to the Iowa State University Foods (ISUF) method using sample data consisting of four non-consecutive 24-h diet recalls collected from 120 children aged 6–59 months in Bihar, India. To assess the impact of zero inflation on the estimation of habitual intake, nutrient intakes were simulated with varying percentages of positive intakes, and habitual intakes were calculated using both methods.

The median (IQR) habitual intakes estimated from the MDM and ISUF methods were 0.47 mg (0.29, 0.65) and 0.46 mg (0.29, 0.62) for vitamin B6 and 0.38 mcg (0.14, 0.68) and 0.40 mcg (0.18, 0.69) for vitamin B12, respectively. Similarly, comparable results were found for other nutrients such as vitamins B3, B5, B12, and A and iodine. The simulated data showed that the estimated habitual intake by the MDM increased with the proportion of positive intakes considering the higher probability of consumption. When the proportion of positive intakes was below 60%, the estimates using the MDM, which considers the probability of consumption, were higher than the arithmetic mean calculated from 15 recalls.

The proposed MDM offers a computationally simpler approach to estimate habitual intake distribution by modeling the probability distribution of non-consumption and the distribution of positive intakes. The procedure can be easily implemented using standard statistical software and estimates habitual intake for infrequently consumed nutrients from multiple 24-h dietary recalls.