## Task 1: Key Concepts about Estimating Distributions of Usual Intake for a Single Ubiquitously-consumed Dietary Constituent

Because they measure intake only on a single day, measures of usual intake from 24-hour recalls are prone to measurement error.  Using a simple average of a few days does not adequately represent usual intake.  Thus, more sophisticated methods based on statistical modeling are necessary. All of the statistical methods that have been developed make the assumption that the 24-hour recall is prone to random, not systematic error.  For estimating ubiquitously-consumed dietary constituents, these methods must meet the following challenges.  They must:

1. Distinguish within-person from between-person variation, and
2. Account for consumption-day amounts that are positively skewed.

Four statistical methods have been developed to estimate the distribution of ubiquitously-consumed dietary constituents: the National Research Council (NRC) method (National Research Council, 1986), the method developed at Iowa State University (ISU method) (Nusser et al., 1996), a simplification of the ISU method called the Best Power Method (Dodd, 1996), and the NCI method (Tooze, 2006).  All of these methods meet challenges A and B.

The four methods differ in terms of the methods for transforming the data, estimating the distribution of usual intake based on the estimated variance of usual intake, and backtransforming the data.  In particular, the ISU method uses a sophisticated procedure to transform the data to approximate normality.  The other methods use a more simple power transformation; the NCI method uses the Box-Cox transformation estimated within the statistical model.  The NRC, ISU, and Best Power methods use a shrinkage estimator to estimate the distribution usual intake for the population.

Because it may include covariates in the model and may accommodate episodically-consumed dietary constituents, the NCI method uses a Monte Carlo procedure to estimate the distribution of usual intake.  In this procedure, 100 realizations of usual intake are generated for each person using the estimated distribution of usual intake from the statistical model.  This value is added to the linear predictor for each person, and then backtransformed to the original scale. The NRC method does not use a transformation to adjust the backtransformed mean to the mean on the original scale as the other methods do.  For more details on the methods see Module 18 Task 2 and Dodd et al (2006).

The macros to fit the NCI method may be downloaded from the NCI website.   Software for fitting the ISU method is available from the Center for Survey Statistics and Methodology at Iowa State University.