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2 Center for Nutrition and Health and 3 Expertise Center for Methodology and Information Services, National Institute for Public Health and the Environment, Bilthoven, the Netherlands
* To whom correspondence should be addressed. E-mail: patricia.waijers{at}rivm.nl.
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ABSTRACT |
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Introduction |
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TOPABSTRACTIntroductionMethodsDiscussionLITERATURE CITED |
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Therefore, we propose an age-dependent model to estimate habitual intakes. In an age-dependent model, habitual intake distributions in a population are estimated and described as a function of age. Also, consecutive steps in dietary assessment can be performed age-dependently, for example, relating habitual intakes to estimated average requirements (EARs)4 or upper safe levels of intake by estimating the proportion of individuals for whom intake is inadequate or too high.
We developed an age-dependent dietary assessment model, called AGE MODE, which is evaluated and compared with currently used methods. We showed the usefulness of this method using folate intakes from the third Dutch National Food Consumption Survey (DNFCS-3), conducted in 1997/98.
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Methods |
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TOPABSTRACTIntroductionMethodsDiscussionLITERATURE CITED |
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AGE MODE is a general methodology that can be used for intakes of micronutrients and other dietary compounds. It aims to estimate habitual intakes of dietary components in a population from short-term dietary data. In contrast to other proposed methodologies, this is accomplished by describing intakes as a continuous function of age. The methodology is based on ideas of Slob (7) and generalized as much as possible. The model has been programmed in S-PLUS (8).
AGE MODE contains several steps that will be explained in more detail later in this paper: 1) Box-Cox transformation of the observed intakes to obtain normally distributed data; 2) fitting a fractional polynomial to the transformed data; 3) obtaining a mixed effect estimate of the fractional polynomial, providing the inter-individual variance and the intra-individual variance; 4) identification of possible outliers; 5) back-transformation by Monte Carlo Simulations to obtain the habitual intakes on the original scale; and 6) additional steps in dietary assessment.
Box-Cox transformation of the observed intakes to obtain normally distributed data.
Intake data are generally skewed, whereas most statistical analyses require normally distributed data. The Box-Cox method estimates the transformation parameter 
using the maximum likelihood method, ensuring symmetrically and approximately normally distributed intake data after transformation (Eq. 1).
 | (Eq. 1) |
Note that for = 0, f(x) = ln(x).
Fitting a fractional polynomial to the transformed data. AGE MODE searches the best polynomial function to describe the data using fractional polynomial regression of order 2 (9).
Let n denote the number of observations and let p and q be the powers of the fractional polynomial y(xi). The fractional polynomial regression function (Eq. 2) is given by
 | (Eq. 2) |
where xi is the age of individual i, and yi the transformed intake; p and q can take the value of {–2, –1, –0.5, 0, 0.5, 1, 2}. In this way, the transformed intakes are described as a function of age by at most a 3-parameter family of curves, and the optimal fractions p and q are estimated as well as a, b, and c.
Obtaining a mixed-effect estimate of the fractional polynomial, providing the inter-individual variance and the intra-individual variance.
Because intake data for each person for at least 2 d are available, Equation 2 is refit with a mixed effect model. Each person is seen as a group with 2 or more observations, allowing estimation of the intra-individual day-to-day variance, 
2, and the inter-individual variance, denoted by 
2. We redefine Equation 2 for the case p 
q and define a as a random parameter, the individuals being the grouping variable. The intakes for an individual may differ by day so that Equation 2 can be reformulated into:
 | (Eq. 3) |
where yij is the transformed intake for individual i on day j, 
I 
N(0, 2), 2 being the inter-individual variance, and 
ij N(0, 2), 2 constituting the intra-individual variance. The residuals ij are assumed to be normally distributed with constant variance over age.
Identification of possible outliers. Outliers can seriously influence estimates. Therefore, Grubbs' method is used to automatically detect outliers, assuming that the residuals of Equation 3 are normally distributed (10,11). To check if the residuals are normally distributed, diagnostic plots of the Kolmogorov-Smirnov goodness of fit test from the S-PLUS module Environmental Stats are used (12).
Check of .
The Box-Cox transformation is used again, because the residuals, without the outliers, should be at least symmetrically distributed. The estimated Box-Cox parameter, reported as "-check," should be near 1, which means that no additional transformation is needed.
Iterations of steps 1–5. Outliers can influence the Box-Cox estimate, the powers of the fractional polynomial, and the estimates of the mixed-effect model. Therefore, if outliers have been removed, steps 1–5 need to be repeated until no further outliers are detected. Two or 3 iterations seem to be sufficient in practice.
Back-transformation by Monte Carlo Simulations to obtain the habitual intakes on the original scale. To obtain the usual intake for each individual, the intra-individual variance needs to be eliminated. Monte Carlo Simulations are performed to acquire the habitual intake distributions on the original scale, using the results of the fitted mixed-effect model.
Simulated intakes are generated on the transformed scale by drawing n individuals of each age and creating a time series of k intake days for each individual i with:
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resulting in a time series for each individual i
 | (Eq. 4) |
where di, and ei,t are realizations of I and i,t in Equation 3.
Then, each of the generated observations is back-transformed to the original scale:
 | (Eq. 5) |
The habitual intake distribution of a given age, with a corresponding CI, can subsequently be estimated from the individual mean intakes, averaging over t.
 | (Eq. 6) |
For every age, the distribution of n individuals is given by {x1, x2, ..., xn}, which implies that the mean of the population and all quantiles can be calculated.
Additional steps in dietary assessment. Generally estimating habitual intake distributions is only a first step in dietary assessment. Additional steps in dietary assessment can also be accomplished in AGE MODE. Population intakes are, for example, evaluated through comparison with dietary reference intakes or upper safe levels of intake. If information on required levels of intake is provided, it is straightforward to estimate the fraction of the population with a habitual intake above or below the requirements. Most straightforward is the use of a cut-off value, but also a probabilistic approach can easily be executed in our model applying Monte Carlo Simulations if a requirement distribution has been specified.
Application of AGE MODE to folate intakes from DNFCS-3
To illustrate the model, AGE MODE has been applied to estimate habitual folate intakes from the DNFCS-3. Resulting habitual folate intake estimates are also compared with estimates obtained with the method developed at Iowa State University (ISU) by Nusser et al. (6).
The DNFCS-3 data
DNFCS-3, carried out in 1997/98, comprised 6250 noninstitutionalized persons aged 1–97 y in 2564 households selected from a stratified random sample in the Netherlands (13). Because pregnancy and lactation may affect dietary habits, pregnant and lactating women were excluded. Analyses were restricted to individuals until the age of 70 y, as the number of older individuals was very small. In total, 5744 subjects (2716 men and 3028 women) remained for analyses.
Information on food consumption was obtained with a 2-d dietary record on 2 consecutive days. The foods consumed at home were recorded in a household diary for all individual members of the household by the person usually engaged in preparation of the meals. Consumption away from home was recorded by every participant in a personal diary (children <13 were assisted by 1 or both parents). Food consumption data were collected during 40 wk/y and evenly distributed over the seasons and the 7 d of the week.
Folate intake was calculated using the 2001 Dutch food composition table (14). For 179 products that were regularly consumed, folate content was missing. For these products, folate content was estimated through comparison with similar products.
Habitual intakes by the ISU method developed by Nusser et al. (6) were calculated with the software package C-SIDE (15). For this purpose, gender and age groups generally used in the Netherlands (1–3 y, 4–8 y, 9–13 y, 14–18 y, 19–50 y, and 51–70 y) were specified. For a fair comparison of results from the ISU method and results from AGE MODE, we removed outliers identified by AGE MODE from the data.
Folate intake assessment with AGE MODE
The steps in AGE MODE, as described above, were carried out. Three iterations were sufficient, as no additional outliers were removed in iteration 3 (Table 1). AGE MODE displays a histogram, a cumulative density function, and a QQ-plot (Supplemental Fig. 1). The large number of observations made the Kolmogorov-Smirnov test significant, but the QQ-plot showed satisfactory results. Also, "-check" (Table 1) differed only slightly from 1 (no additional transformation needed). AGE MODE produced various plots, showing the fitted polynomial through the intakes on the transformed scale (Supplemental Fig. 2) and the estimated habitual folate intakes as a function of age after back-transformation (Fig. 1). The mean observed folate intakes of all individuals of a given age are depicted in the same figure to get clear insight into the fit of the polynomial function. The resulting habitual intake distributions become slightly wider with increasing age (Fig. 2).
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Direct comparison of estimates from AGE MODE and the method developed by Nusser et al. at ISU (6) is somehow artificial, as estimates by the latter method can only be obtained for population subgroups. A depiction of the mean habitual intake estimates for AGE MODE and the ISU method as a function of age in 1 figure may make a strong appeal for an age-dependent approach (Fig. 4). When estimated habitual intake distributions from AGE MODE and the ISU method are compared (Supplemental Fig. 4), they strongly concur. For children, estimated habitual intake distributions from AGE MODE were somewhat wider than those from the method of Nusser et al. (6).
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Discussion |
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TOPABSTRACTIntroductionMethodsDiscussionLITERATURE CITED |
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AGE MODE estimates habitual intake distributions as a function of age. Also, subsequent estimates for the prevalence of inadequate intakes of micronutrients can be obtained for any given age. This approach has several advantages above current practice.
Most important may be that with an age-dependent model, it is not necessary to specify subgroups of age. Consequently, variation in intake caused by age is no longer an issue. Another reason to favor an age-dependent model is the fact that intakes of many dietary components are subject to extremely large variations in general. Therefore, estimated habitual intake characteristics may be prone to high uncertainties and be less reliable if numbers are small, for example if smaller subgroups are taken. In AGE MODE, all available data are used to estimate the parameters of the habitual intake distribution. This means that power of precision can be lent from adjacent ages, improving the reliability of the estimates.
In addition, the estimated habitual intake distributions for the individual ages are consistent, whereas transformation parameters can show important differences between adjacent subgroups when estimated individually.
AGE MODE is rather simple and transparent and allows us to gain insight into the underlying data. All steps in the estimation of the habitual intakes are clearly described and illustrated, and the final estimates are depicted in 1 figure with the means of the original observations. The method by Nusser et al. (6), designed to estimate habitual intake distribution for specified subgroups, is operational in statistical software packages developed at ISU (15,18), but the model is extremely complex. The available software generally works well with customary intake data but could be considered a black box, which may be a severe limitation for users, especially in the case of less customary data. It was shown that habitual intake distributions estimated with both methods are comparable.
The fundamental concept of AGE MODE, fitting an age-dependent function, is based on the ideas of Slob, implemented in STEM (19). However, the methodology is completely different. To obtain symmetrically distributed observations, AGE MODE applies the general Box-Cox transformation, whereas in STEM, the log-transformation is used. In our analyses, we often find estimates for in the range of 0.20–0.25, significantly different from = 0 (in the case of a natural log transformation).
In the next step, STEM chooses fixed functions with several unknown parameters to fit to the log-transformed data. But because no physical relation between habitual intake and age is known, we propose a more general approach by using fractional polynomial regression. This method simply searches for the best way to describe the data, but has also some drawbacks, like the nonmonotone increase at the lower ages for women. Also important is the back-transformation step. In STEM, the inverse of the forward-transformation is used, which results in estimates for the median, whereas AGE MODE uses Monte Carlo Simulations to obtain estimates for the mean habitual intakes.
Outliers are removed in AGE MODE based on the statistical test proposed by Grubbs and Beck (11). The problem of outliers is complicated. The central question is whether or not to remove outlying observations. On the one hand, they can disturb calculations, but on the other hand, they can contain true information (20).
We inspected the statistical outliers more closely. The lower outlying observations (4 in males, 7 in females) were all due to anomalous low consumption, mainly due to illness. As these observations are not representative for normal intakes, it can be argued to remove them. It should then be considered, however, to remove all individuals who reported lower intake than normal due to illness. High (outlying) folate intakes (8 in males, 7 in females) were mainly due to liver consumption. These high intakes really occur and seem not due to anomalous consumption. One should be aware that leaving out statistical outliers influences (reduces) the intra-individual and also the inter-individual variation. Handling these outliers is a matter of careful judgment. Options are to remove the outliers before transformation and reinclude them afterward, to consider different subgroups (e.g., liver and nonliver consumers), or to include extra covariates in the model.
We proposed a new approach to model the intake of dietary components. Although our methodology is now applicable, it still needs to be further developed. A major issue is the function describing the intakes age-dependently. We used a 2nd order polynomial, as this function appears well capable to describe our data. But the use of higher order polynomials and options to increase the flexibility of the polynomial need to be studied, so the data may be described even better. This is also necessary to obtain consistent results when the age range is extended or restricted.
Furthermore, at this moment, variances are assumed to be the same for all ages. This assumption may not be valid and could be relaxed by estimating inter- and intra-individual variances as a function of age. This will not greatly influence the results but may optimize the model. It should also be investigated how an additional module can be incorporated in AGE MODE to discern between consumers and nonconsumers and to estimate consumption frequency. The methodology for this has already been proposed and is available in S-PLUS (21). Furthermore, as mentioned earlier, the model could be extended with extra covariates. A broader application of AGE MODE may lead to new insights and further improvements.
In conclusion, we proposed an age-dependent methodology to assess the intake of dietary components, named AGE MODE. The model produces estimates for the habitual intake distribution and evaluates intakes in an age-dependent manner. The model may still be further extended, but the feature of age dependency shows clearly described advantages above currently used methods.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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4 Abbreviations used: AGE-MODE, age-dependent dietary assessment model; DNFCS-3, third Dutch National Food Consumption Survey; EARs, estimated average requirements; ISU, Iowa State University.
Manuscript received 16 May 2006. Initial review completed 2 June 2006. Revision accepted 14 August 2006.
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LITERATURE CITED |
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TOPABSTRACTIntroductionMethodsDiscussionLITERATURE CITED |
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