## Task 3: Key Concepts about Examining the Relationship Between Usual Intake of a Single Episodically-consumed Dietary Constituent and Some Outcome

Two of the primary challenges of dietary intake data are measurement error adjustment, and positively skewed data.  Regression calibration (see Module 21, Task 1 for more information on this topic) is a method for dealing with the former challenge.  In this method, the 24-hour recall data are replaced with a predictor of true intake, given the 24-hour recall data.  When the data are normally distributed, this estimate is fairly easy to obtain.  However, when data are positively skewed and must be transformed, the process for obtaining the regression calibration predictor involves numerical integration.  The NCI method uses adaptive Gaussian quadrature to obtain this estimate.

When interest is in modeling an episodically-consumed dietary component in relation to a health outcome, additional challenges arise.  These include many days of zero intakes, and a correlation between the probability of consuming a food and the amount consumed on a consumption day.  In addition, when modeling health parameters, it is almost always necessary to include covariates to adjust for potential confounders (see Module 17, Task 3 for a discussion of confounders).  The NCI method for relating usual intake of an episodically consumed food to a health parameter has been developed to meet these challenges, in addition to the challenges mentioned previously.  Essentially, a two-part model is used to model both the probability of consumption of the episodically-consumed dietary constituent and the consumption day amount, using the model that is at the core of the NCI method. After fitting the model, numerical integration is used to estimate the regression calibration predictor. When regression calibration is used, it is necessary to include the covariates that will be used in the health parameter model in the calculation of the regression calibration predictor, i.e.,

Furthermore, the covariates X may comprise covariates that will aid in the prediction of .These covariates may include data from a food frequency questionnaire (FFQ).  (It is assumed the food frequency information is not related to the health parameter if true dietary intake is known.) This predictor is then used to estimate the relationship between usual dietary intake and the health parameter, using an appropriate statistical model. Balanced repeated replication (BRR) (see Module 18, Task 4 for more information on this topic) is used to calculate standard errors.

IMPORTANT NOTE

Note: If a food frequency variable is used as a covariate, BRR weights for the FFQ sample should be used.

Software is available to apply this method, including the MIXTRAN, DISTRIB, and INDIVINT macros, which may be downloaded from the NCI website.