# Single regularly-consumed or episodically-consumed food or nutrient

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• MIXTRAN
• INDIVINT

## Procedure

Because replication methods (bootstrap or BRR) are used to estimate standard errors of calculated statistics, the following tasks must be performed repeatedly – once for the original data set (or using the base sampling weight variable) to obtain point estimates and again for each resampled data set (or using each of the bootstrap/BRR weight variables in turn):

1. Use the MIXTRAN macro to fit the measurement error model and store parameter estimates, then

2. Use the parameter estimates as input to the INDIVINT macro to compute the conditional expectation of usual intake of each individual given their FFQ response, then

3. Fit an appropriate health outcome-exposure model, using the conditional expectations as the dietary exposure.

After calculating desired statistics for all data sets/sampling weights, use the appropriate bootstrap/BRR algorithms to estimate standard errors for the coefficients in the health outcome–exposure model by taking the square root of the (adjusted, if BRR) variance across replicates.

## Notes

• The conditional expectations produced by INDIVINT are not true intakes for a particular individual. The computations involve averaging over an assumed (i.e., not observable) distribution of individual effects. Two individuals may have very different true usual intakes, yet report the same on FFQ. Their corresponding output from the INDIVINT macro would be the same. Thus, categorizing the two individuals based on their INDIVINT output would be subject to potentially extreme misclassification. However, under the assumptions required of the regression calibration method, using the output from INDIVINT yields a measurement-error-corrected estimate of the regression slope in a health outcome-exposure model.

• Using resampling methods to calculate standard errors of the coefficient for exposure in the health outcome-exposure model properly accounts for variability in all stages of the estimation.

• INDIVINT can estimate conditional expectations of (Box-Cox) transformed usual intake, if the health outcome-exposure model is nonlinear in the exposure. Second-degree and higher polynomial terms of exposure can be obtained by repeated calls to the INDIVINT macro and some algebra.

## Example Code

Example

• univar_epidemiology_example5a_mle_mainffq.sas - fit measurement error model using MLE with FFQ as main instrument; predict intake and fit logistic model to assess the relationship between a dietary component and a health outcome.

• univar_epidemiology_example5b_mle_mainffq.sas - perform bootstrap variance estimation.