Evaluating Usual Intake Estimation Methods

1. Introduction

The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) is a public health nutrition program that safeguards the health of women, infants, and children in low-income households who are at nutritional risk (U.S. Department of Agriculture [USDA] & Food and Nutrition Service, 2022). The program currently serves about 7 million women, infants, and children (Kline et al., 2022). Between 2011 and 2025, USDA funded a nationally representative, longitudinal study called the Infant and Toddler Feeding Practices Study (ITFPS-2). The study, now known as WIC ITFPS-2, followed a prospective cohort from birth through age 9, focusing on caregiver feeding practices and children’s diet-related health outcomes in the context of WIC service provision (Harrison et al., 2014). To address the study’s research objectives (Borger et al., 2025), researchers needed an analytic method that not only accurately reflects children’s diet quality but also captures the relationship between children’s dietary outcomes and family and environmental factors.

Dietary analysis is essential for understanding the relationship between nutrition and human health. Assessment of diet quality requires following people’s long-term consumption to determine usual intake (UI), which accounts for day-to-day variation. UI reflects the interactions among multiple foods and beverages reported in estimates for nutrients, energy, and other dietary components. Even though self-report measures commonly involve extensive measurement error (Kirkpatrick & Collins, 2016), intake estimates tend to be less biased when using short-term instruments, such as 24-hour dietary recalls and food records or diaries, than long-term instruments like food frequency questionnaires, which measure the frequency of consumption directly (Tooze, 2020). Over decades, various statistical models have been proposed and developed to better understand and address measurement error in dietary intake estimation from 24-hour dietary recalls (Dodd et al., 2006; Nusser et al., 1995; Tooze et al., 2006; Zhang et al., 2011a, 2011b). Some models attempt to tackle the issues of within-person variation and episodically consumed foods, including the methods developed by the National Cancer Institute (NCI).

The purpose of this study was to illustrate the use of the NCI’s Markov Chain Monte Carlo (MCMC) method for various types of UI analyses, comparing MCMC UI estimates with results from other NCI methods. The comparison between the MCMC method and other NCI methods is compelling because it informs the possibility of using the MCMC method to support more general dietary intake estimation and assessment. Moreover, NCI recently decided that it would no longer update the univariate and bivariate approaches, and it is important to understand the implications of this decision.

1.1. The NCI Approach to Estimating UI

The NCI approach accounts for measurement error in dietary intake by separating within-person variation from between-person variation. The NCI approach requires that at least a subset of respondents provide two or more recalls to enable estimation of usual dietary intake patterns. It accommodates episodically or rarely consumed foods using a two-part model in which the probability of consumption is estimated in addition to the amount consumed. The technique allows researchers to incorporate covariates, facilitating the use of covariates in generating UI estimates for subpopulations (Tooze et al., 2010), and to assess the effect of UI on health outcomes (Kipnis et al., 2009).

The UI estimation starts by fitting the NCI measurement error model (Brassard, 2022; NCI, 2013) to the intake data to obtain parameter estimates. Subsequently, the approach generates a pseudo population by drawing a random sample from the distribution using the parameter estimates from the first step. Lastly, it involves calculating desired statistics or running models using the pseudo population. For data obtained from a complex sample survey such as WIC ITFPS-2 or the National Health and Nutrition Examination Survey (NHANES), these steps incorporate sampling weights and are repeated across replicates created for variance estimation so that estimates accurately represent the population.

NCI has created different SAS macros for different types of dietary analyses. Selecting a macro for a given analysis depends on the number of dietary constituents involved in UI estimation (i.e., single, two, multiple) and how frequently they are consumed (i.e., regularly, episodically, rarely). NCI discusses which macros to select for specific types of analyses (NCI, n.d., 2024).

For multivariate analyses (i.e., estimating >2 dietary components), NCI extended its methodology to develop the MCMC method (Zhang et al., 2011a, 2011b). It simultaneously models multiple constituents, which could be a mixture of daily, episodically, or rarely consumed foods and beverages, accounting for correlations among them. In the MCMC method, researchers fit a multivariate measurement error model using the MCMC algorithm. Then, they use the resulting parameter estimates to generate a multivariate Monte Carlo draw of UI estimates for the multiple dietary constituents. This method can capture the complexity and dynamics of diet behaviors and variability in food and nutrition. One promising application of the MCMC method is estimating the Healthy Eating Index (HEI) scores, which are functions of multiple dietary components, including total energy (Gelfand & Tangney, 2021; Hutchinson et al., 2023; Wambogo et al., 2020).

1.2. The MCMC Method for HEI Calculation

The HEI is a widely used tool for assessing diet quality in relation to the recommendations in the Dietary Guidelines for Americans (DGA) (USDA & U.S. Department of Health & Human Services, 2020). The HEI is updated every 5 years, and the latest version is the HEI-2020, which provides HEI scores for individuals aged 2 years or older (National Institutes of Health et al., 2025).¹ Shortly after the most recent update to HEI, a new HEI-Toddlers-2020 for children under age 2 was released. The overall HEI-2020 and HEI-Toddlers-2020 scores are the sum of 13 component scores. Nine of 13 components are categorized as adequacy components, which means that there is no limit on the amount recommended for consumption, and people are encouraged to eat more for good health. Four of the 13 components are categorized as moderation components, which means that limits are recommended for good health. All but one component is density based (i.e., intake amounts per 1,000 kcal). The exception is the score for fatty acids, for which the HEI component is expressed as a ratio of poly- and monounsaturated to saturated fatty acids. The process of calculating HEI scores involves estimating the intake of multiple dietary constituents consumed either daily or episodically. Given the multivariate nature of HEI, the NCI recommends the MCMC method because it can jointly account for relationships among dietary constituents, including energy.

Because the MCMC method does not allow overlap among dietary constituents, the HEI components must be disaggregated into mutually exclusive constituents for UI estimation and then added together to form components before scoring. For example, legumes contribute to five adequacy components and are modeled as individual constituents in the macro. Researchers must identify and separate any dietary constituents consumed daily or episodically. They can also include covariates such as demographic characteristics and feeding practices to model the probability of consumption and the consumption quantity. The detailed steps and SAS macros they used include the following:

• Obtain the Box-Cox transformation parameters for each dietary constituent using the BOXCOX_SURVEY macro with the full-sample weights
• Run the STD_COV_BOXCOX24HR_CONDAY_MINAMT macro to prepare the input file for MULTIVAR_MCMC
• Using the file outputted in step 2, run the MULTIVAR_MCMC macro with the adjusted full-sample weights (i.e., original weight * total number of observed individuals/sum of original weights) to fit the multivariate measurement error model (NCI, 2013), which corrects for error in dietary intake data
• Run the MULTIVAR_DISTRIB macro using the parameter estimates from step 3 to generate a pseudo population with 100 pseudo persons per 1 observed individual
• Aggregate HEI components and calculate HEI scores for each individual in the pseudo population
• Calculate the distribution estimates and run regression models with adjusted weights (i.e., the weights outputted from MULTIVAR_MCMC divided by the number of pseudo persons per observed individual [100]), and store the point estimates
• Repeat steps 3 to 6 in each replicate (using the replicate weight provided in the input data file in place of the full-sample weight)
• Calculate standard errors (SEs) using the estimates from the full-sample run and the 40 replicate estimates

For documentation on the SAS macros, refer to the MCMC macro user guide (NCI, 2013).

At step 4, the output file contains the intake estimates for every dietary constituent later used to calculate the HEI component and total scores for each pseudo person generated from the MCMC method. It is unknown how using those estimates for other types of UI analysis (besides HEI calculation) compares with using UI estimates with the bivariate or univariate UI macros. For example, if the goal is to estimate the population distribution of a single dietary constituent or a ratio of two constituents or explore the relationship between dietary constituents and/or covariate information in a regression model, how do the results based on the MCMC method compare with those based on the bivariate or univariate UI modeling approaches?

2. Methods

WIC ITFPS-2 is a prospective cohort study that follows children from around the time of birth through age 6, with a follow-up at age 9. Harrison and colleagues (2014) describe the initial study design; Borger and colleagues (2022) present the study design after multiple study extensions. This study used 24-hour dietary recall data collected when the children in WIC ITFPS-2 were 5 years old and survey information from the longitudinal sample collected in multiple interviews through age 5.

2.1. Analytic Sample

WIC ITFPS-2 recruited study participants from study-eligible clinics during fall 2013 and followed them through the child’s sixth year, with a follow-up at age 9. Eligible participants were caregivers enrolling in WIC at a study-eligible clinic for the first time for their current pregnancy or their newborn; caregivers were at least 16 years old and spoke English or Spanish. Siegfried and colleagues (2023) describe the sampling and recruitment processes in detail.

The longitudinal sample used in this study comprises individuals who responded to every postnatal interview beginning with the 1- or 3-month interview (depending on the child’s age at WIC enrollment) through the fifth-year interview. Additionally, the current study used 24-hour dietary recall information from 1,030 children in the longitudinal sample, 11.8% of whom had second-day recalls; these dietary recalls were collected when the study children were aged 5 years.

Table 1 presents the sample characteristics. Data are weighted by statistical survey weights (full-sample weights and 40 replicate weights) that account for unequal selection probabilities and nonresponse to make inferences for the study-eligible population. Cases with missing values were excluded from the sample for consistency across all the methods discussed.

2.2. Dietary Recall Data

WIC ITFPS-2 collected 24-hour dietary recall information using USDA’s Automated Multiple-Pass Method (AMPM). Raper and colleagues (2004) detail the AMPM’s five-step approach. WIC ITFPS-2 used USDA’s Food and Nutrient Database for Dietary Studies 5.0 (FNDDS5) as the source of the nutrient values of food reported (Ahuja et al., 2012).

2.3. Analysis Design

The use of the MCMC method focused on two types of analyses: (1) estimating the distribution of intake in the population overall and among subpopulations, and (2) exploring the association between dietary intake and individual characteristics. Individual characteristics of particular interest for WIC ITFPS-2 included the child’s WIC participation, assessed either at a point in time or over time. Borger and colleagues (2020, 2022) and Au and colleagues (2025) indicate that most children consume the foods in the WIC food package, suggesting that nutrition outcomes would be associated with WIC participation. WIC participation over time is reflected in the child’s pattern of WIC participation, a variable that is included in models assessed. This study, therefore, included WIC participation as a focal individual characteristic.

The three dietary constituents selected for univariate analyses were added sugar, sodium, and whole grains. Among 5-year-old children, the first two are consumed daily, whereas the latter is episodically consumed. Each of the dietary constituents contributes to one of the HEI component scores (the first two are moderation components, and the latter is an adequacy component). Moreover, over- or underconsumption of these three dietary constituents has been associated with different health outcomes. For instance, strong evidence supports the association between added sugar consumption and dental caries in children (Chi & Scott, 2019), and high sugar intake is associated with reduced cognitive function in children (Gillespie et al., 2024). Evidence also shows that high sodium intake in childhood is associated with elevated blood pressure (Leyvraz et al., 2018). With increased consumption of whole grains, diet quality and nutrient intake significantly improve in children (O’Neil et al., 2011). As the denominator in all HEI component scores, dietary energy (calories) was also included in the univariate analysis.

The study assessed results from four modeling efforts using NCI and non-NCI methods:

• For univariate analysis, a linear regression model was fit to assess sodium intake as a function of the child’s sex, parity, the caregiver’s demographic characteristics, timing of food introduced to the child, and WIC or Supplemental Nutrition Assistance Program (SNAP) participation status.
• For bivariate analysis, the sodium model was extended by adding energy as a control of total dietary intake.
• A second model involving bivariate analysis was a logistic regression with a binary outcome determined by whether energy from added sugar was below (value = 1) or above (value = 0) 10% of total energy as recommended by the DGA, with the same set of covariates used in the linear regression model for sodium.
• Multivariate analysis focused on the total HEI score, its distribution in the population and subpopulations, and its association with the covariates.

Table 2 summarizes the intake methods considered for each type of analysis. All statistical analyses were conducted in SAS 9.4.

3. Results

3.1. Population Distribution Overall and by Subpopulation

3.1.1. Univariate Distribution

Table 3 presents the mean and quartiles of intake estimates for the three dietary constituents—added sugars, whole grains, and sodium—as well as for energy. The results show differences between the two non-NCI methods (single-day recall and average of 2 days’ recall) and the two NCI methods (the univariate NCI method and the MCMC method). The NCI methods result in less variability in the distribution of intakes than the non-NCI methods. Median intakes are closer among the four methods, but the mean intakes show the smallest difference. Surprisingly, whole grains are an exception. Estimated whole grain intake is much higher for the univariate NCI method than for the MCMC method and the two non-NCI methods across the mean and all three quartiles. The two NCI methods typically produce slightly larger values for the SEs than the non-NCI methods. The difference is particularly striking given how close the SEs are for the means. However, the differences are within one SE of each other for the four methods regarding added sugar, sodium, and energy.

3.1.2. Distribution of Ratios for HEI Component Scores

Because the univariate model cannot estimate ratios, Table 4 summarizes the mean and quantile estimates for the added sugars, whole grains, and sodium HEI components from four different approaches. Both the NCI and non-NCI methods yield similar estimates of the mean ratio scores, including both point estimates and SEs. The difference among the quartiles is consistent with the pattern observed in univariate analysis, whereby the bivariate NCI macro and the MCMC method produce higher estimates on the first quartile and median, but smaller estimates on the third quartile. The SEs from the two NCI methods are larger than those of the non-NCI methods for the mean and first quartile.

3.1.3. Percentage Meeting DGA Recommendation for Added Sugars

The methods examined in this study disagree on estimates of the portion of the study population with added sugars intake below the DGA recommendation of less than 10% of energy. The two NCI methods yield a smaller percentage (bivariate NCI macros, 56.7% [SE = 2.0 percentage points, or pp] and MCMC, 54.8% [SE = 2.3 pp]) than the two non-NCI methods (single-day recall, 61.7% [SE = 1.8 pp] and average of 2 days’ recall, 61.4% [SE = 1.9 pp]). The percentage is consistently the smallest for the MCMC method, even though the difference is within one SE of the bivariate NCI method.

3.1.4. Distribution of HEI Total Scores

Because the univariate and bivariate NCI approaches are not sufficient for multiple dietary components, Table 5 summarizes the mean and quantile estimates of the total HEI scores by the three methods: using only 1 day of recall, using the average of 2 days of recall, and using the MCMC method. The point estimates and SEs in the MCMC method are consistently larger than those in the non-NCI methods for the mean and the three quartiles. The difference in the total HEI score between the MCMC method and the two non-NCI methods ranges from 1.91 on the third quartile to 6.48 on the first quartile.

The same patterns observed in the overall distributions are also seen in subpopulations, such as estimates by WIC participation pattern (see Supplementary Figure S4).

3.2. Modeling Association Between Intake and Covariates

3.2.1. Linear Model With Sodium Intake as an Outcome

The univariate regression analysis explores the association of sodium consumption with demographic characteristics and feeding practice variables. Table 6 presents the covariates with significant or opposite signs of regression coefficient estimates across the four methods. The SEs all show similar magnitude. All four methods reached the same results regarding significance tests of association between the covariates and sodium consumption. All significant effects point in the same direction across the methods, and no difference in parameter estimates between methods is more than one SE. There is no apparent pattern or method that produces consistently higher values across the covariates. Though not statistically significant, the two non-NCI methods show that children receiving both WIC and SNAP benefits have nominally lower mean sodium consumption versus children who participated in neither of the programs, whereas the two NCI methods demonstrate the opposite results.

3.2.2. Linear Model With Sodium Intake as an Outcome, Controlling for Total Energy

In the univariate analysis, energy is added to the model as an extension of the regression model. The regression coefficients of the covariates then reflect the effect after controlling for the total intake (see Table 7). The four methods disagree on the significant effects. For instance, the number of snacks during the day is significant in the two non-NCI methods only. Parity appears to have a significant effect only when using the average of 2 days of recalls; a significant group difference is found between the firstborn and the third or subsequent born. The non-NCI methods and the two NCI methods also disagree on the direction of group differences. For example, the non-NCI methods show that children not introduced to salty snacks have higher energy-adjusted sodium intake levels than children introduced to salty snacks in the first 2 years of life. However, the two NCI methods nominally suggest the opposite, though this difference is not statistically significant in any of the four methods.

3.2.3. Logistic Regression with a Binary Indicator of Meeting Reference Intakes for Added Sugars

For this example, the ratio of added sugars to total energy is recoded as a binary variable depending on whether the ratio is below the DGA recommendation (<10% of total energy). The estimates from the four methods generally agree on which covariates are significant (see Table 8). Though not statistically significant, the non-NCI methods and the two NCI methods show nominal effects in opposite directions for group differences based on the child’s sex, caregiver’s ethnicity, and parity.

3.2.4. Linear Model with HEI Total Score as Outcome

Multivariate regression analysis explored the HEI total score as a function of demographic characteristics and feeding practices. Table 9 presents the regression coefficients for the three methods. The two non-NCI methods show no significant association between HEI total scores and any of the covariates selected, whereas the MCMC method identifies four: baby’s sex, TV on while eating, pattern of WIC participation, and age of the infant (in days) when the mother stopped breastfeeding. For comparisons among children with varying WIC participation patterns, all three methods agree that the longer children are enrolled in WIC, the nominally higher their HEI total score. The MCMC method produces the largest difference among all three methods. Moreover, MCMC results suggest that the group difference (coefficient = −3.37 [SE = 1.49]) between children who are on WIC for 2–3 years and those who are consistently on WIC is significant (p = .024), whereas such a difference is not significant in the two non-NCI methods.

4. Discussion

The application of the MCMC method for UI analyses was motivated by the complexity of dietary patterns comprising various foods and beverages. These should be assessed collectively (Zhang et al., 2011b). Although the estimation of HEI scores was a motivating factor for implementing the MCMC method, the MCMC method can be used for any study in which joint estimation of multiple dietary constituents is of interest (Tooze, 2020). When using data that represent a population, researchers can implement the MCMC method to construct a pseudo population that represents the intake distribution. This pseudo population provides UI estimates from multiple dietary constituents while considering covariates of interest.

This study explored the use of the pseudo population generated from the MCMC method for UI analyses beyond those involving HEI scores. The analyses considered were population and subpopulation intake distribution for a single dietary constituent and regression models with intake estimates as either the outcome or a covariate. To evaluate the performance of the MCMC method, three other methods were also considered: two non-NCI methods that use 1 day of dietary intake data or the average of 2 days of dietary intake data (when available), and the NCI method developed for one or two dietary constituents. Previous studies focusing on dietary intake overwhelmingly rely on data from NHANES. The current study investigated diet quality in children aged 5 using WIC ITFPS-2 dietary recall data.

Comparing the results of the two NCI methods and the two non-NCI methods, the distributions of single dietary constituents or ratios of intake to energy show similar patterns, whereby the two NCI methods usually produce higher estimates for the first quartile and the median, but lower estimates for the third quartile. This finding demonstrates the effectiveness of NCI methods for normalizing the intake distribution. Without UI estimation, the distribution using 1 day of intake data or the average of 2 days of intake data is usually right-skewed, with a larger median than the mean and a long tail at the third quantile and beyond. Such a pattern directly impacts deficiency detection, which relies on the ratio of the percentage of energy from a certain dietary constituent. In the current example, compared with the two NCI methods, the two non-NCI methods consistently report a higher percentage of the population as meeting the DGA recommendation for added sugars, which may lead to an overly optimistic conclusion about the diet quality of young children.

The four estimation methods examined generally agree on the association of intakes with covariates for most of the models assessed in this study. However, in certain situations, one method may report an effect to be significant when the others do not. Nonetheless, the difference in the magnitude is seldom over two SEs. As indicated by the two regression models in the bivariate analyses, the non-NCI and NCI methods report group differences in opposite directions for some effects. However, this occurred only for effects that were not statistically significant. These findings are consistent with those of other studies (Fulgoni et al., 2020; Herrick et al., 2018).

Of particular interest in the current study is the comparison between the two NCI methods. In most cases, the mean and median of intake estimates from the MCMC method are similar to those from the univariate or bivariate NCI methods. However, the study found an exception when examining episodically consumed food, for example, whole grains, because the distribution in population and subpopulation differs by the method used. UI estimation using the bivariate NCI method assumes the probability of consumption is correlated with consumption quantity, whereas the MCMC method does not explicitly incorporate this assumption. Further investigation is needed to identify the cause of the difference. With the incorporation of seafood in the WIC food package and the launch of the HEI-Toddler-2020, understanding the estimation issues around episodically consumed foods is crucial, as very young children in the United States do not regularly consume seafood.

However, the findings from the bivariate analyses suggest that the two NCI methods can reach comparable estimations on ratios between dietary constituents and energy. One possible explanation is that the magnitude of energy is much larger than the intake estimates of the dietary constituents. Given the similar energy distribution, dividing a dietary constituent by energy to develop a ratio reduces the difference between the NCI methods. In other words, the distribution of energy drives the distribution of ratios. Though there are other ways to compute a ratio, such as the population ratio method, they are not considered here because other studies have found that the estimation from these methods is similar to the NCI methods (Herrick et al., 2018; Wambogo et al., 2020).

One advantage of using the MCMC method is that, when working with episodically consumed dietary constituents, it rarely faces convergence failures commonly encountered in the univariate or bivariate NCI macros (Fulgoni et al., 2020; Herrick et al., 2018; Kipnis et al., 2009; Zhang et al., 2011b). For the intake estimation for whole grains, the univariate and bivariate NCI macros failed to converge for five and one replicate weights, respectively. When this occurs, the degrees of freedom are adjusted to the number of successful runs among the replicate weights for SE estimation using the univariate or bivariate NCI methods. Additionally, the computation time is shorter and the file sizes are smaller for the MCMC method relative to the other NCI methods when working on the same number of dietary constituents—another practical reason to choose the MCMC method for intake estimation.

4.1. Limitations

This study used a nationally representative sample of children aged 5 years. Importantly, their dietary intake patterns are substantially different from those of an adolescent or adult population. The findings presented could differ from those obtained by applying the MCMC method to other population groups. The sample used in this study challenges the MCMC method because dietary constituents are consumed daily or episodically. Many of the dietary constituents used to calculate the HEI score (e.g., seafood, legumes, dark vegetables, whole grains) are considered episodically consumed by young children. Large numbers of episodically consumed constituents could cause convergence failure in the application of the MCMC method. All constituents need to be carefully disaggregated to achieve a relatively balanced number of episodic and daily components. It is unclear whether disaggregation strategies could impact the final estimation results.

Although the current study shows that the MCMC method can produce UI estimation comparable to the other NCI methods using data from the WIC ITFPS-2 study, it does not assess how close these estimates are to the true UI. A simulation study is necessary to evaluate the bias and precision of UI estimates obtained from the MCMC method.

5. Conclusions

This study illustrates the use of MCMC for UI analyses that involve one, two, or more dietary constituents. In general, estimation based on the MCMC method is largely consistent with its NCI counterparts for univariate and bivariate analyses. More investigation is required to understand the cause of large differences in the distributions of episodically consumed dietary constituents. The examples used in this study demonstrate the applicability of the MCMC method for not only multivariate analysis but also a range of diet quality and intake evaluation. For practical reasons, including reduced computation time, smaller file sizes, and increased probability of model convergence, the MCMC method may be preferred.