**ORIGINAL ARTICLES**

**Assessing usual dietary intake in complex sample design surveys: the National Dietary Survey**

**Avaliação do consumo alimentar usual em pesquisas com amostras complexas: Inquérito Nacional de Alimentação**

**Evaluación del consumo alimentario usual en investigaciones con muestras complejas: pesquisa nacional de alimentación**

**Flávia dos Santos Barbosa ^{I}; Rosely Sichieri^{II}; Washington Leite Junger^{II}**

^{I}Departamento de Nutrição Social. Instituto de Nutrição. Universidade do Estado do Rio de Janeiro. Rio de Janeiro, RJ, Brasil ^{II}Departamento de Epidemiologia. Instituto de Medicina Social. Universidade do Estado do Rio de Janeiro. Rio de Janeiro, RJ, Brasil

Correspondência | Correspondence

**ABSTRACT**

The National Cancer Institute (NCI) method allows the distributions of usual intake of nutrients and foods to be estimated. This method can be used in complex surveys. However, the user must perform additional calculations, such as balanced repeated replication (BRR), in order to obtain standard errors and confidence intervals for the percentiles and mean from the distribution of usual intake. The objective is to highlight adaptations of the NCI method using data from the National Dietary Survey. The application of the NCI method was exemplified analyzing the total energy (kcal) and fruit (g) intake, comparing estimations of mean and standard deviation that were based on the complex design of the Brazilian survey with those assuming simple random sample. Although means point estimates were similar, estimates of standard error using the complex design increased by up to 60% compared to simple random sample. Thus, for valid estimates of food and energy intake for the population, all of the sampling characteristics of the surveys should be taken into account because when these characteristics are neglected, statistical analysis may produce underestimated standard errors that would compromise the results and the conclusions of the survey.

**Descriptors:** Food Habits. Nutrition Assessment. Diet Surveys, utilization. Complex samples.

**RESUMO**

O objetivo do estudo foi indicar uma adaptação do método do Instituto Nacional do Câncer (INC), utilizando-se dados do Inquérito Nacional de Alimentação. Esse método estima a distribuição do consumo usual de nutrientes e alimentos e pode ser aplicado em estudos com amostra complexa. Entretanto, são necessários cálculos adicionais, tais como a replicação repetida balanceada, a fim de obter os erros padrão e intervalos de confiança para os percentis e a média da distribuição de consumo usual. A aplicação desse método foi exemplificada analisando o total de energia (kcal) e frutas (g), comparando as estimativas das médias e seus respectivos erros padrão obtidos, considerando o desenho do inquérito e supondo amostra aleatória simples. Embora os resultados das estimativas pontuais para a média tenham sido similares, houve aumento de até 60% nos respectivos erros padrão na amostragem complexa, comparada à amostragem simples. Desse modo, para estimativas válidas de consumo de alimentos e de energia devem-se levar em conta todas as características de amostragem dos inquéritos, porque, quando essas características são negligenciadas, a análise estatística pode produzir erros padrão subestimados que podem comprometer os resultados e conclusões da pesquisa.

**Descritores:** Hábitos Alimentares. Avaliação Nutricional. Inquéritos sobre Dietas, utilização. Amostras Complexas.

**RESUMEN**

El objetivo del estudio fue indicar una adaptación del método del Instituto Nacional del Cáncer (NCI), utilizándose datos de la pesquisa nacional de alimentación. Ese método estima la distribución del consumo usual de nutrientes y alimentos y puede ser aplicado en estudios con muestra compleja. Mientras, son necesarios cálculos adicionales, tales como la replicación repetida balanceada, a fin de obtener los errores estándar e intervalos de confianza para los percentiles y el promedio de la distribución de consumo usual. La aplicación de este método fue ejemplificado analizando el total de energía (Kcal) y frutas (gr), comparando las estimaciones de los promedios y sus respectivos errores estándar obtenidos considerando el diseño de la pesquisa y suponiendo muestra aleatoria simple. A pesar que los resultados de las estimaciones puntuales para el promedio hayan sido similares, hubo aumento de hasta 60% en los respectivos errores estándar en el muestreo complejo, comparado con el muestreo simple. De ese modo, para estimaciones validas de consumo de alimentos y de energía se deben tomar en cuenta todas las características de muestreo de las pesquisas, porque cuando estas características son descuidadas, el análisis estadístico puede producir errores estándar subestimados que pueden comprometer los resultados y conclusiones de la investigación.

**Descriptores:** Hábitos Alimenticios. Evaluación Nutricional. Encuestas sobre Dietas, utilización. Muestras Complejas.

**INTRODUCTION**

For most epidemiological diet analyses, usual intake is required, and in many situations, such as in large surveys, only one or two 24-hour recalls (24HR) or food records are collected. These methods yield an excessive amount of within-person variation,^{4} and early attempts to compensate for this limitation by averaging over a small number of days^{1} do not adequately represent usual individual intakes. Thus, more sophisticated methods based on statistical modelling were developed,^{2} paying special attention to the problems that are inherent in modelling usual intake of foods or food groups that are episodically consumed. Challenges for the statistical modelling of usual intake include the following: the ratio of within-person and between-person variation; the reported days that are without consumption or the consumption-day amounts that are positively skewed, with extreme values in the upper tail; the correlation between the probability of consumption and the consumption-day amount; and covariate information on usual intake.

The National Cancer Institute (NCI) method was designed to meet all of these challenges by allowing efficient estimation of the usual intake distributions of daily and episodically consumed items.^{13} The method also allows the prediction of individual intakes to be used in a model to assess the relationship between diet and disease or another variable^{6} and by performing an assessment of the effects of individual covariates on consumption.^{12} An extension of the NCI method has also been used to estimate the population distributions of the ratios of usual intakes of dietary components.^{5}

The objective of this article is to indicate the necessary adaptations of the NCI method when estimating the distributions of usual intakes of nutrients and foods.

**THE NATIONAL CANCER INSTITUTE METHOD**

The premise of the NCI method is that usual intake is equal to the probability of consumption on a given day times the average amount that is consumed in one day. For the dietary components that are consumed nearly every day, the probability is one: if less than 5% of the population had zero intake of a food, this amount-only model can be used and is referred to as a one-part model. For a two-part model, the first part estimates the probability of consumption using logistic regression with a person-specific random effect. The second part specifies the consumption-day amount using linear regression on a transformed scale, with a person-specific effect. The two parts are linked by allowing the two person-specific effects to be correlated and by including common covariates in both parts of the model. Covariates may be included, particularly if there is interest in subpopulations.^{13}

The NCI method requires a minimum of two non-consecutive 24HR or records for at least a representative sample of individuals from the population of interest, i.e., it is intended for use on large datasets with sample sizes of at least 1,000 or more, especially if distributions in population subgroups are to be estimated.^{5,13}

Macros developed by the NCI^{a} in Statistical Analysis System (SAS) program in short, for a single dietary component, two macros are available: The first macro, *MIXTRAN*, transforms the data and fits the model. The second macro, *DISTRIB,* uses the parameters that are estimated by *MIXTRAN* to estimate the usual intake statistics through simulation. *DISTRIB* can also provide the estimated percentage of the population whose usual intake falls below a given value.^{13}

The standard errors and p-values output of the Mixtran macro are only valid for an analysis of a simple random sample. Special care must be taken when using the NCI SAS macros to analyze data from a complex survey, because in analysis of complex surveys, calculation of these standard errors requires additional programming to implement a replication method such as Balanced Repeated Replication (BRR).

**Standard Errors in complex samples**

Complex samples (CS) differ from simple random samples (SRS) in that SRS designs assume independence of observations, while CS does not. In complex sample design surveys, the standard error estimates are generally small and biased if the differential weighting of individuals and the complexity of a sample design (i.e., the identification of stratum and primary sample units (PSU) are ignored.^{7} The replication methods represent one approach to handling this problem, with standard errors computed from each subsample, and the variability among these subsamples (or replicate estimates) is used to compute the standard errors of the full estimate.^{14}

There are various replication methods for creating subsamples. In this study, a variation of the Balanced Repeated Replication (BRR) method known as Fay's BRR method was used.^{3,8} The BRR is a variance estimation method for two PSU/stratum designs. BRR makes a half-sample replicate by selecting one unit from each pair of PSUs and weighting the selected unit by 2 so that it represents both units. Consequently, estimates from every PSU are in each replicate, although half of them are weighted to zero.

In Fay's BRR method, observations in the sample PSUs that are not chosen for replication are not zeroed out, in contrast to BRR. Instead, their sampling weight is diminished by a multiplicative factor *K* (*K* is a proportion), whereas the observations in the sample PSU that are chosen for the replication have their sampling weights enhanced by the multiplicative factor (2 - *K*). Setting *K* = 0 yields the standard BRR technique. A commonly recommended value is *K* = 0.3 for Fay's method. For example, when K = 0.3, the weights are reduced to 30% of their original values in one half sample and are increased to 170% of the original value in the other half sample.

The Fay's BRR method was developed for the specific situation in which there are two PSUs per stratum design; however, the Brazilian Dietary survey has more than two PSUs per stratum. To overcome this restriction, the usual way is to randomly group the PSU in each stratum into two groups and then apply the BRR procedure. This is the so-called grouped balanced half-sample (GBHS) method.

To exemplify the GBHS method, consider stratified random sampling without replacement from a finite population of ^{N} units divided into ^{H} strata, with ^{Nh} units in stratum . Let ^{nh} be the sample size in stratum ^{h}. In the GBHS method, the sample in each stratum is first divided at random into two groups containing units. A set of R half-samples balanced on the groups is formed as follows: Let if group 1 in stratum ^{h} is in the *r*_{th} half-sample, otherwise, and More details on this method may be found in Kish & Frankel^{b} (1968) and Wolter^{14} (1985). An SAS macro was utilized to perform the random grouping of PSUs within stratum.

We applied all of these procedures in the following example using the 2008-2009 Brazilian Dietary Survey, which has a complex sample design. This survey was performed as a part of the 2008-2009 Household Budget Survey (HBS), which was conducted by the Brazilian Office of Statistics and Geography (IBGE - *Instituto Brasileiro de Geografia e Estatística*) as a two-stage sampling process. In the first stage, PSUs were selected according to the number of households that were in a unit, and in the second stage, the households were selected by simple random sampling. The Individual Dietary Intake was conducted in 24% of the households that were selected in the 2008-2009 HBS. Two non-consecutive days of food records were collected among 34,003 individuals. For this analysis, 1,254 women who were pregnant or lactating were excluded. This resulted in a final sample size of 32,749 individuals. Number of individuals in each days of food record for energy and total fruit by sex and age group is shown in Table 1.

The application of the NCI method varies for dietary components that are consumed daily and those that are episodically consumed. We exemplified both of the situations, analyzing the total energy (kcal) and fruits (g). The means, standard errors for means, and intakes at the 10^{th}, 50^{th}, and 90^{th} percentiles and standard errors for gender/age groups were estimated for the two examples, comparing estimations that were based on simple random sampling (considering only weights) and complex sampling (considering the weights and the complexity of sample design). For complex sampling, standard errors were estimated using Fay's BRR method, and twelve sets of BRR replicate weights were generated with a factor 0.3. As an additional step, the sampling weights were rounded before being fed into macros, because the MIXTRAN macro can only work with integer sampling weights. The weights were post-stratified to control totals in each replicate.

The models were fitted to the data using the statistical software package SAS (Version 9.2).

More than 50% of the individuals in each sex-age group reported no consumption of fruits indicating how episodic fruit consumption is. For energy, more than 96% in each sex-age group provide two days (Table 1). As expected, point estimates were similar when complex sampling and simple random sampling were compared, but there was an important difference in the standard errors, which vary according to the subpopulations. The percentiles of usual intakes were also quite similar because the NCI method corrects for within-person variability (Table 2).

**DISCUSSION**

The NCI method is one way of estimating usual intake. Recently, four methods (Iowa State University Method - ISU, National Cancer Institute - NCI, Multiple Source Method - MSM, and Statistical Program for Age-adjusted Dietary Assessment - SPACE) were compared, and all of them provided similar estimates of usual food intake. Nevertheless, when a nutrient has a high within-person variation or has a highly skewed distribution, and when the sample size is small, the estimates could be biased.^{10}

One limitation of the NCI and other methods is the assumption that the 24HR records represent an unbiased instrument for measuring food intake. Studies with doubly labeled water have found misreporting of the energy intake on the 24HR record, almost always in the direction of underreporting.^{11} This observation suggests that at least some foods are underreported as well.^{10,11}

Greater understanding of the effect of each characteristic of the sampling on the results should stimulate researchers to use adequate methods for data analysis. The Brazilian Dietary Survey is stratified to account for variation in intakes over the entire year, and stratification has an important effect on weighting but also in the degrees of freedom of the analysis. Clustering at the PSU level is the most important factor, increasing by more than twice the SE. On the other hand, the NCI process of accounting for intra-individual variability in food intake and weighting corrected almost all of the skewedness in the subpopulation that was analyzed.

Valid estimation of food and energy intake for the population must account for all of the sampling characteristics of the surveys because when these characteristics are neglected, statistical analysis might produce underestimated standard errors that would compromise the results and the survey's conclusions.

**REFERENCES**

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▲ **Correspondência | Correspondence: ** Flávia dos Santos Barbosa

Instituto de Nutrição

Departamento de Nutrição Social - UERJ

Rua São Francisco Xavier, 524 - 12º Andar Bloco E Sala 12008 Maracanã

20550-900 Rio de Janeiro, RJ, Brasil

E-mail: barbosaflavia@bol.com.br

Received: 11/25/2011

Approved: 11/28/2012

The authors declare that there are no conflicts of interest. This manuscript was submitted for publication and underwent a peer review process as any other manuscripts submitted to this publication, and anonymity was guaranteed for authors and reviewers. Editors and reviewers declare no conflicts of interest that may affect the peer-review process.

a Usual Dietary Intakes: SAS Macros for Analysis of a Single Dietary Component. [cited 2013 Mar 6]. Available from: http://riskfactor.cancer.gov/diet/usualintakes/macros.html

b Kish L, Frankel MR. Balanced repeated replication for analytical statistics. In: Proceedings of the Social Statistics Section, 2-11. 1968. New York, United States. New York: American Statistical Association; 1968.