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OVERVIEW OF THE NCI METHOD 1. Input Day 1 and Day 2 intakes 2. Fit model and BoxCox transform to near normality 3. Simulate usual intakes based on model fitted 4. Backtransform to original scale 5. Derive percentiles and proportions above/below cutpoints More information on general features of this process is below. All model types that estimate group usual intake distributions use both the mixtran and distrib macros to perform the five basic steps above. A model is fit to the input data set (steps one and two) in the first of the two NCI method SAS macros (the mixtran macro).^{6} The main purpose of the model is to estimate how much of the variation in the reported intakes is withinperson (or daytoday) variation, so that this can then be omitted from the usual intake distribution simulated in the second macro. The rest of the variation in the reported intakes (betweenperson variation) is described using covariates (if covariates are used), and a residualbetween person variation term. In fitting the model, a BoxCox transformation, withinperson variation, covariates (if used), and residual betweenperson variation terms are all jointly estimated (maximum likelihood method).^{2,8} Some information on each of these model terms is below.
Note that the twopart model is more complex. For episodically consumed nutrients, in the twopart model the NCI method also estimates the probability of consuming the nutrient on a given day, using logistic regression with an additional personspecific random effect, and covariates (if used).^{2} Information on the model fitted to the data is output from the ‘mixtran’ macro and passed to the second NCI method SAS macro (the ‘distrib’ macro).^{12} The distrib macro runs steps three, four, and five above, starting with a Monte Carlo simulation component.^{6} A number of pseudo persons (n=100) are generated to represent each individual in the ingoing data set, using the model estimated in the mixtran macro. Each of the 100 pseudo persons for an individual has the covariate information corresponding to that individual (such as the same age and gender), but different simulated personspecific effects.^{ 2,}^{9} Withinperson or daytoday variation is not included in the simulated intakes, as it does not contribute to usual intakes. The simulated pseudoperson intakes are backtransformed to the original scale (or units) to give a simulated population usual intake distribution. Population mean and percentiles of intake, along with proportions above and below cutpoints (NRVs), are derived empirically from this distribution. Sample weights are taken into account to ensure the results represent the population.^{2} NCI METHOD MACROS The NCI method website provides SAS macros that can be downloaded and used for usual intake calculations. The macros used by ABS, as programmed by NCI, were more recent versions of mixtran and distrib (version 2) provided by the NCI. This version uses a different backtransformation (ninepoint approximation) which is better able to handle very skewed nutrient intakes.^{2} ENDNOTES 1 National Cancer Institute, 2013, Usual dietary intakes: details of the method, <http://appliedresearch.cancer.gov/diet/usualintakes/details.html>, last accessed 16/02/2015. 2 Tooze, JA et al. 2010, ‘A mixedeffects model approach for estimating the distribution of usual intake of nutrients: The NCI method’, Statistics in Medicine, vol. 140, pp.111116, <http://jn.nutrition.org>, last accessed 09/02/2015. 3 Dodd, KW et al. 2006, ‘Statistical methods for estimating usual intake of nutrients and foods : a review of the theory’, Journal of the American Dietetic Association, vol. 106, pp. 16401650, <http://www.andjrnl.org/>, last accessed 09/02/2015. 4 Tooze, JA et al. 2006, ‘A new statistical method for estimating the usual intake of episodically consumed foods with application to their distribution’, Journal of the American Dietetic Association, vol. 106, pp. 15751587. 5 Kipnis, V et al. 2009, ‘Modeling data with excess zeros and measurement error: application to evaluating relationships between episodically consumed foods and health outcomes’, Biometrics, vol. 65, no. 4, pp. 10031010. 6 National Cancer Institute, 2013, Usual dietary intakes: SAS macros for analysis of a single dietary component, <http://appliedresearch.cancer.gov/diet/usualintakes/macros_single.html>, last accessed 16/02/2015. 7 The Box Cox transformation is a function that transforms data to a nearnormal distribution using a variable called a lambda (). This variable affects the strength of the transformation, so that the transformation can be adjusted to suit the characteristics of the input data set. In the NCI method, the lambda is selected such that the withinperson errors are normally distributed around mean zero on the transformed scale. For more information see endnote 2. The BoxCox function is , where r is the input nutrient intake. Note that a minimum lambda bound of 0.01 has been set when using this function. Therefore, although in a BoxCox transform the limiting case for =0 is formally defined as the natural logarithm, it has not been employed in the usual nutrient intakes publication. 8 Zhang, S et al. 2011. ‘Fitting a bivariate measurement error model for episodically consumed dietary components’, The International Journal of Biostatistics, vol. 7, no. 1, <http://www.bepress.com/ijb/vol7/iss1/1>, last accessed 01/03/2014. 9 A set seed was used in simulations in the distrib macro.

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