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3 INRA, UMR1260 Nutriments Lipidiques et Prévention des Maladies Métaboliques, Marseille, F-13385 France; 4 INSERM, U476, Marseille, F-13385 France; 5 Université Aix-Marseille 1, Faculté de Médecine, IPHM-IFR 125, Marseille, F-13385 France; 6 Department of Human Nutrition, University of Otago, Dunedin, New Zealand; and 7 Nutritional Sciences Program, School of Public Health and Community Medicine, University of Washington, Seattle, WA 98195-3410
* To whom correspondence should be addressed. E-mail: nicole.darmon{at}univmed.fr.
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ABSTRACT |
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 TOP ABSTRACT IntroductionMethodsResultsDiscussionLITERATURE CITED |
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/100 kcal). We developed linear programming models to design diets that fulfilled increasing levels of nutritional constraints at a minimal cost. The median NDS:LIM values of foods selected in modeled diets increased as the levels of nutritional constraints increased (P = 0.005). In addition, the proportion of foods with a good nutritional quality for price indicator was higher (P < 0.0001) among foods selected (81%) than among foods not selected (39%) in modeled diets. This agreement between the linear programming and the nutrient profiling approaches indicates that nutrient profiling can help identify foods of good nutritional quality for their price. Linear programming is a useful tool for testing nutrient profiling systems and validating the concept of nutrient profiling.
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Introduction |
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TOPABSTRACTIntroductionMethodsResultsDiscussionLITERATURE CITED |
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Nutrient profiling aims to classify individual foods based on their nutrient content and their contribution to a healthy diet. This concept was originally proposed by the European Commission for the regulation of nutrition and health claims (16), but it can be used for different purposes, including nutrition information and education. The nutrient profile of a given food is a synthetic indicator of its overall nutritional quality. Various nutrient profiling systems have been proposed (17–22). Despite their differences, they have been shown to correlate well, both with one another and with expert opinion (23–25). A recent study showed good agreement between foods classified as healthy by nutrient profiling systems and foods consumed in larger quantities by healthy eaters based on a global index of dietary quality (26). However, both expert opinion and self-selected healthy diets are likely to be influenced not only by nutritional consideration but also by individual, socioeconomic, and cultural considerations. More objective external standards are therefore needed to validate nutrient profiles. Using modeled diets instead of self-selected diets as external validation standards could overcome this drawback, because diet modeling techniques make simulated food choices based on a set of well-defined and purposefully selected constraints (15).
The objective of this study was to use diet modeling with linear programming to demonstrate that foods with good nutritional quality relative to their price can be easily identified using their nutrient profiles and their energy cost. In this study, a nutrient profiling system based on the previously published (8) nutrient density score (NDS)8 and limited nutrient score (LIM) was used as an example of nutrient profile.
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Methods |
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TOPABSTRACTIntroductionMethodsResultsDiscussionLITERATURE CITED |
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The input data used in this analysis were based on dietary data collected in a cross-sectional dietary survey of a nationally representative sample of 1985 French adults (called the INCA survey), aged 15–92 y, conducted in 1999 by the French National Agency for Food Safety (27). Usual food intakes were estimated using a 7-d food record completed by all participants, aided by a photographic manual of portion sizes (28). After excluding under- and overreporters, using standard procedures (29), the dietary data from 1332 participants (596 men; 736 women) were available for analysis.
Drinking water, diet beverages, tea, coffee, and fortified foods were excluded from all analyses, because they are not food sources of nutrients or, for fortified foods, their artificially elevated nutrient content excludes them from nutrient profiling systems. The nutritional composition of the remaining 614 foods was computed from the INCA food composition database (30), the Suvimax food composition database (31), or from other appropriate databases to complete them (32–35). A column of French mean national 1997 retail prices primarily obtained from marketing research (SECODIP) was added to this table. The prices were those paid by a representative panel of French consumers (SECODIP); therefore, the mean price reflected the most frequently purchased forms of each food. After adjusting for preparation and food wastage, the food costs were expressed in /100 g of edible portion.
The foods were aggregated into 7 major food groups (meat, fruit and vegetables, mixed dishes and snacks, dairy, starches and grains, sweets and salted snacks, and added fats), 20 subgroups (e.g. subgroups in the fruit and vegetable group were: fruits, vegetables, and dried fruits), and 36 families (e.g. families in the fruit subgroup were: fresh fruits, fruit juices, and other processed fruits).
Nutrient profiling of foods
A synthetic indicator of the nutritional quality of each food was specifically developed for this study. It was based on 2 previously published indicators: the NDS, a positive score based on qualifying nutrients only, and the LIM score, a negative score based on disqualifying nutrients only (8,17). NDS was an unweighted arithmetic mean of the percent adequacy for 23 nutrients based on 100 kcal of food.
The NDS was calculated as follows:
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where Nutrienti is the quantity (in g, mg, or µg) of nutrient i provided by 100 kcal of each food and RDAi is the mean of the 2001 French recommended dietary allowances (RDA) for men and women (36). The 23 nutrients used to calculate each food item's NDS and their mean RDAs are given (Table 1).
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where MRVi is the maximum recommended value for nutrient i and Li is the content of limiting nutrient i in 100 g of edible portion. The 3 limited nutrients were sodium, simple added sugars, and SFA. The maximum recommended values for SFA and added sugars corresponded to 10% of a recommended energy intake of 2000 kcal, i.e. 22 and 50 g, respectively (37). The maximum recommended value for sodium corresponded to a daily intake of 6 g NaCl (i.e. 2365 mg of Na). The final nutrient profile for each food was computed as the ratio between NDS and LIM whenever LIM > 1%. In cases where LMI 
1%, the nutrient profile was equal to NDS to avoid instability in ratio-based measures whenever the denominator tended toward 0.
Description of optimization models
Linear programming for modeling human diets has been described in detail elsewhere (38). In this study, linear programming models were developed to select 21 isocaloric diets for each gender, which differed in the nutritional (3 sets) and social acceptability (7 sets) constraints introduced into the models. In all models, an equality constraint fixed the energy constant (1800 kcal for women and 2200 for men) and total diet cost was minimized to obtain the strict lowest cost needed to fulfill all the constraints introduced in each model.
Increasingly stringent levels of nutritional quality of the modeled diets were achieved by 3 sets of constraints on nutrients (Table 2), which ensured the achievement of macronutrient recommendations (level A), macronutrient recommendations plus estimated average requirements (EAR) for 25 nutrients (level B) or macronutrient recommendations plus RDA recommendations (level C), respectively. In levels B and C, constraints limiting the content of SFA, simple added sugars, and sodium were also introduced, as well as safe upper limits for 9 nutrients (Table 2).
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Two approaches to identify foods with a good nutritional quality relative to their price
Identification of foods based on their nutrient profiles and energy cost.
Nutrient profiles and energy cost (in /100 kcal) were calculated for each food and the relationship between these variables was used to identify foods that have a good nutritional quality relative to their price. A regression analysis was performed between the 2 variables (after they had been log-transformed to normalize their distribution) with NDS:LIM as the dependent variable and energy cost as the independent variable. Based on previous studies that have shown a positive correlation between the nutritional quality of individual foods and their cost (17,39), a positive relationship was expected. The regression line was drawn on a scatter plot upon which the position of each food was indicated, as well as that of the median of each food subgroup. Each food's residual from the regression line defined its nutritional quality for price indicator (NQPI). Foods with a positive residual value (i.e. foods above the regression line) had a better nutritional quality relative to their price than foods with a negative residual value (i.e. foods below the regression line). Moreover, foods with the highest positive residual values had the highest nutritional quality relative to their price.
Identification of foods using linear programming. Linear programming models designed to select a nutritionally adequate diet at the lowest cost achievable will, by definition, preferentially select foods that have high nutritional quality relative to their price. Thus, the proportion of foods with a positive NQPI value will increase with increasing levels of nutritional constraints but not necessarily with increasing levels of social acceptability constraints. Moreover, independent of cost considerations, the nutritional quality of foods selected in modeled diets will increase with increasing levels of nutritional constraints but not necessarily with increasing levels of social acceptability constraints.
Comparison of the 2 approaches
We tested the general agreement between the 2 approaches in different ways. First, all foods in the database were classified as having either a positive or negative NQPI value (i.e. a residual value either above or below the regression line, respectively, in the regression analysis performed between NDS:LIM and energy cost) and the proportion of foods with a positive value was calculated for each of the 21 possible combinations of nutritional and social acceptability constraints.
Second, all foods in the database were also classified as having either been selected or not selected in at least 1 linear programming model and a chi-square analysis was performed between the 2 dichotomous variables (above or below the regression line; selected or not selected in a modeled diet) to test the equality of proportions of foods with a positive NQPI value among the foods selected in linear programming diets and among the foods that were not selected by linear programming. We used the nonparametric Mann-Whitney U test to compare medians of energy cost, NDS/LIM and the nutritional quality for price indicator (i.e. residual values of the linear regression) between foods selected by linear programming and foods that were not selected.
Third, we analyzed the impact of increasing the level of nutritional constraints on the nutritional quality and price of the foods selected by linear programming by comparing the medians of NDS:LIM, energy cost, and the NQPI of the foods selected at each level of nutritional constraint (and grouping all levels of social acceptability constraints).
Finally, the impact of increasing the level of social acceptability constraints on the nutritional quality and price of the foods selected by linear programming was analyzed by comparing the medians of NDS:LIM, energy cost, and the NQPI for all foods selected in diets fulfilling either levels 1 and 2, or levels 3, 4, and 5, or levels 6 and 7 of social acceptability constraints, respectively (and grouping all levels of nutritional constraints). Medians of NDS:LIM, energy cost, and NQPI were also calculated among unselected foods.
For each variable (energy cost, NDS:LIM, and NQPI), equality of medians was tested using the Kruskal-Wallis test. P < 5% was considered significant.
The SAS system version 9.1. (SAS Institute) was used for all the analysis, including linear programming analysis (simplex algorithm of the operational research product).
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Results |
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TOPABSTRACTIntroductionMethodsResultsDiscussionLITERATURE CITED |
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Impact of nutritional and social acceptability constraints on the minimum cost of modeled diets and the number of selected foods.
The minimum cost of modeled diets increased as the nutritional and social acceptability constraint levels increased (Fig. 2). At the highest level of social acceptability constraint (level 7), the lowest cost required to fulfill the RDAs was 3.32 /d. In contrast, without social acceptability constraints, the minimum cost required to fulfill the RDA was 1.24 /d. The number of foods selected increased as the levels of nutritional constraints increased (Fig. 2). It also increased with increasing levels of social acceptability constraints until level 5 and then decreased at levels 6 and 7, in which foods consumed by <2.5 and 5% of the total population were excluded from the list of food variables, respectively. This reduction in the number of foods selected indicates that rarely consumed foods were selected in the modeled diets unless constraints were introduced to exclude them.
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/d) with increasing levels of these constraints (Fig. 2).
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Discussion |
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TOPABSTRACTIntroductionMethodsResultsDiscussionLITERATURE CITED |
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The NDS nutrient profiling system used in this study included up to 23 different essential nutrients, which gives a relatively precise description of each food's nutritional content. To be enforceable for health claim regulation, marketing, or advertising, nutrient profiles should be based on a more restricted number of nutrients. Indeed, number of nutrients selected to be included in a nutrient profiling system is a fine balance between the need to include nutrients of importance to public health and the need for a manageable number of nutrients in a field setting (22).
More importantly, our results indicate that the linear programming approach is useful for validating the concept of nutrient profiling itself, i.e. its ability to discriminate foods according to their contribution to a healthy diet. In previous studies, global indices of dietary quality were used to validate nutrient profiling systems by examining the classification agreement of healthy and unhealthy foods (40,41). However, in 1 study, a significant proportion of foods were classified differently by the global dietary approach compared with the nutrient profiling approach (41). In another study, the contribution of "unhealthy" foods increased as the general level of healthiness of the diet decreased, but the differences were small for foods classified as "healthy" by nutrient profiling (40). Such discrepancies were partially attributed to positive associations between the consumption of healthy and unhealthy foods in the self-selected diets used to develop the global indices of dietary quality (41). The diets of healthy and unhealthy eaters are likely to differ for a number of reasons not necessarily related to nutrition; in particular, socioeconomic factors often influence food choices (42). For example, cheese may be present in healthy diets mainly as a marker of higher social class. When self-selected diets are used to create global indices of dietary quality, it may result in an important classification bias that attenuates inter-method measures of agreement. The advantage of using a linear programming approach to validate nutrient profiling systems is that modeled diets are not subject to this type of bias.
The limitations of this study must be noted. First, the use of mean retail prices does not take into account food price variability related to season, place of purchase, or brand. However, it is the hierarchy of prices rather than their absolute values that will affect the results. In addition, the lowest cost achievable in this study for a socially acceptable diet fulfilling all the nutritional recommendations for an adult, i.e. 3.32 /d, was strikingly similar to the minimal cost calculated previously based on an earlier French dietary survey and a food database that included only 60 food items (15). Another limitation is that the modeled diets were likely to be unrealistic, because the objective function minimized diet cost instead of the difference between the modeled diet and existing food habits, as was done previously (15,43). In this study, the selection of realistic modeled diets was not the primary purpose of the analyses. Instead, the linear programming approach was used to identify diets containing foods of good nutritional quality for their price. Further, the diets selected via linear programming were consistent with previous studies that have shown nutrient adequacy is associated with higher dietary variety (44) and that nutrient-dense diets are more expensive than those of low nutrient density (45). The definition of the nutritional quality for price indicator also has its limitations. In particular, it was dependent on the dataset used to calculate it. Finally, only a limited number of foods were selected in the modeled diets (105 of 614 foods variables), which limits the conclusions that can be drawn about the foods that were not selected. This limitation was also noted in 1 of the 2 other validation studies based on a global indicator of dietary quality (41). It is a technical limitation of the methods used, suggesting that more research is needed to develop methods to validate the nutrient profile concept itself.
In this study, the agreement between the linear programming approach and the nutrient profiling system suggests that the nutrient profiling approach identifies foods with a good nutritional quality for their price. The linear programming approach is also a useful tool for evaluating alternative nutrient profiling approaches and validating the concept of nutrient profiling itself, because unlike other approaches used (40,41), it is not influenced by the biases inherent in self-selected diets. The selection of a healthy diet on a low food budget will require the selection of a number of foods with high nutritional quality for price. The nutrient profiling approach is useful in identifying such foods.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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2 Author disclosures: M. Maillot, E. L. Ferguson, A. Drewnowski, and N. Darmon, no conflicts of interest.
8 Abbreviations used: EAR, estimated average requirement; LIM, limited nutrient score; MRV, maximal recommended value; NDS, nutrient density score; NQPI, nutritional quality for price indicator; RDA, recommended dietary allowance.
Manuscript received 15 January 2008. Initial review completed 30 January 2008. Revision accepted 20 March 2008.
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