## Task 3: Key Concepts about Estimating Distributions of Usual Intake for a Single Episodically-consumed Dietary Constituent

Because the dietary assessment queries intake only on a single day or a few days, measures of usual intake from 24-hour recalls are prone to measurement error.  Using a simple average of 2 days does not adequately represent usual intake, particularly for episodically-consumed foods and nutrients.  Thus, more sophisticated methods based on statistical modeling are necessary. All of the statistical methods that have been developed to estimate usual intake from 24-hour recalls make the assumption that the 24-hour recall is prone to random, not systematic error (see Module 18, Task 2 for more details on these methods).

Two statistical methods have been developed to model the distribution of usual intake of episodically-consumed foods, adjusting for measurement error.  These are the method developed at Iowa State University for foods (ISUF method), and the method developed at the National Cancer Institute (NCI method). Both methods operate under the premise that usual intake is equal to the probability of consumption on a given day times the average amount consumed on a consumption day.

To estimate the usual intake of episodically-consumed dietary constituents, a method must meet several challenges.  These include the challenges for ubiquitously consumed dietary constituents plus additional challenges. It must:

A. Distinguish within-person from between-person variation,
B. Account for consumption-day amounts that are positively skewed, and
C. Account for reported days without consumption of the dietary constituent.

Challenge C is met by estimating the probability of consumption as well as the amount consumed on a consumption day.  For most episodically-consumed foods, there is a positive correlation between the probability and amount.  Therefore, a method must meet the following additional challenge:

D. Allow for the correlation between the probability of consuming a dietary constituent and the consumption-day amount.

The ISUF method meets challenges A-C, but cannot be used for foods for which probability of consumption is correlated with amount, and it does not incorporate covariates.

This  task describes the use of the NCI method to model the distribution of usual intake of episodically-consumed dietary constituents. It involves a two-part model with correlated person-specific effects. The first part of the model estimates the probability of consuming an episodically-consumed dietary constituent using logistic regression with a person-specific random effect. The second part of the model specifies the consumption-day amount using linear regression on a transformed scale, also with a person-specific random effect. Parts I and II are then linked by allowing the two person-specific effects to be correlated and by including common covariates in both parts of the model.

The macros to fit the NCI method may be downloaded from the NCI website.