In this paper, the use of the amount part of the NCI method to obtain estimates of the distribution of usual intake of nutrients has been presented and illustrated using examples from the EATS and simulations. The NCI method performs similar to the ISU method for the example nutrients and simulations considered, and both methods are superior to the simple individual mean. Although we used 24HR as the dietary assessment instrument in these analyses, it would be possible to apply this methodology to other dietary assessment tools that meet the model assumptions, such as repeat weighed food records. Additionally, this method requires at least two dietary assessments on at least a subset of individuals. In this paper, we used four days of measurement from the EATS data because it was available and covered a full year of intake; however, we have also illustrated that the method works well with only 2 days of data.

One limitation of the use of the 24HR is the possible violation of the assumption that it is unbiased for the consumption day amount. Validation studies of the 24HR using biomarkers for total energy (doubly labeled water) and protein (urinary nitrogen) have demonstrated biases in 24HRs [

18,

19]. Freedman

*et al.* demonstrated that incorporating adjustment for protein intake can reduce the bias in 24HRs for total energy [

20]. Yanetz

*et al.* describe how to use doubly labeled water data in a validation study to adjust the estimated distribution of usual energy intake in a national survey [

21]. Unfortunately, currently there are no adequate biomarkers that produce unbiased estimates of true intake for nutrients other than energy, protein, and possibly potassium. However, the requirement of unbiasedness is essential for the suggested methodology. Therefore, the degree to which the estimation of the distribution of usual intake may be biased for most nutrients is unknown. In this paper, we have assumed that the 24HR meets the assumption of unbiased estimation for the nutrients we examined; however, this is a potential limitation of this instrument for use with this model.

One advantage of using the NCI method over the ISU method is the efficiency in making estimates for subgroups, by being able to fit common parameters for the subgroups. It is apparent, however, that in some cases fitting different variance parameters by subgroup may be necessary. Even if different variance components are fit, efficiency may be gained by fitting other common parameters, as was demonstrated in the analyses of the EATS data in which a model with some common parameters was superior to a fully stratified model. It is also possible to compare nutrient intake of population subgroups, adjusted for other factors that affect intake if necessary. In addition, the ability to incorporate covariates into the model allows the analyst to make adjustments simultaneously for day of the week, season, and sequence effects, and individual covariates, using a straightforward extension of the model [

22].

Standard errors of estimates were calculated for the NCI method using the bootstrap method; they were calculated for the ISU method using Taylor linearization assuming that the transformation is fixed and known [

13] and a simple bootstrap in some cases. The assumption of a fixed and known transformation leads to standard errors for the ISU method that ignore the variability due to choosing the normality transformation, which may explain some of the negative bias shown over the percentiles near the median in . However, it is important to note that the ISU method’s linearization-based standard errors are intended only for analysis of simple random samples. For analysis of complex survey data, alternative estimation methods, such as the bootstrap and balanced repeated replication methods, will most likely be equally suitable for both the NCI and ISU methods.

The NCI method and ISU method performed similarly in estimating the percent of the sample below a cutoff on the nutrients we examined. However, although this paper provides evidence for the utility of the NCI method for nutrient estimation, further investigation is warranted on the comparison of the NCI method with the ISU method. In particular, further investigation into the impact of sample size, how easily data may be transformed to meet the model assumptions, and estimation of standard errors in the tails is needed. One difference we discovered between the two methods was the type of approximation used in the backtransformation. In the simulations based on calcium, the Taylor series approximation worked well; however, for nutrients with a large amount of within-person variation this method does not appear to work as well as the nine-point approximation. Therefore, the nine-point quadrature approximation is recommended for general use.

The NCI method provides a unified framework for estimating the usual intake of dietary constituents, with application to estimating the distribution of foods [

15], nutrients, and applications for relating usual intake to disease [

23]. We have shown here that the NCI method, although originally devised to estimate distributions of the usual intake of episodically consumed foods [

15], also provides a flexible framework for estimating the distribution of usual intake of nutrients. It thus provides a unified framework for estimating the distribution of usual intakes of any dietary component of interest.