Diet modelling: How it can inform the development of dietary recommendations and public health policy

Precision nutrition for type 2 diabetes in Benin: leveraging linear goal programming to optimize diets with emphasis on adequacy, affordability, accessibility, and culture

Background

Nutrition and diet are critical to managing Type 2 diabetes (T2D). Low-income households often face challenges maintaining a healthy and balanced diet due to food insecurity, availability, and cost. To address this issue, we used a linear goal programming (LGP) model to develop nutritionally adequate, affordable, accessible, and culturally acceptable diets for persons with T2D in Benin, a French-speaking sub-Saharan country. The goal was to help persons with T2D manage their condition more effectively.

Methods

We compiled a robust list of local commonly consumed foods in Benin, and calculated their nutritional value using West African food composition tables and food costs per serving from a market survey. Using mathematical optimization techniques, we designed dietary plans that meet the daily nutrient intake recommended by the World Health Organization (WHO) to prevent chronic diseases in normal adults. While adhering to dietary constraints of T2D, we developed optimized diet plans with varying energy levels that meet all nutrient requirements while considering availability, acceptability, and budgetary constraints.

Results

Fifty-two food items and recipes were evaluated to create six low-cost daily menus. Menu 1 was the most affordable at CFA 1,127 (USD 1.88), providing 1890 kcal of energy, while Menu 6 was the most expensive at CFA 1,227 (USD 2.05), providing 1749 kcal. All the menus met the daily WHO minimum requirements for carbohydrates, fat, cholesterol, and fiber content, while other nutrients such as protein, vitamin C, and iron reached the upper limits of the acceptable value range.

Conclusion

Linear goal programming can be an effective tool in helping to obtain optimized adequate, accessible, and culturally acceptable diets at minimal cost by interpreting and translating dietary recommendations into a nutritional model, based on local market prices.

Developing feasible healthy diets for Ethiopian women of reproductive age: a linear goal programming approach

OBJECTIVE

To develop a healthy diet for Ethiopian women closely resembling their current diet and taking fasting periods into account while tracking the cost difference.

DESIGN

Linear goal programming models were built for three scenarios (non-fasting, continuous fasting and intermittent fasting). Each model minimised a function of deviations from nutrient reference values for eleven nutrients (protein, Ca, Fe, Zn, folate, and the vitamins A, B1, B2, B3, B6, and B12). The energy intake in optimised diets could only deviate 5 % from the current diet.

SETTINGS

Five regions are included in the urban and rural areas of Ethiopia.

PARTICIPANTS

Two non-consecutive 24-h dietary recalls (24HDR) were collected from 494 Ethiopian women of reproductive age from November to December 2019.

RESULTS

Women's mean energy intake was well above 2000 kcal across all socio-demographic subgroups. Compared to the current diet, the estimated intake of several food groups was considerably higher in the optimised modelled diets, that is, milk and dairy foods (396 v. 30 g/d), nuts and seeds (20 v. 1 g/d) and fruits (200 v. 7 g/d). Except for Ca and vitamin B12 intake in the continuous fasting diet, the proposed diets provide an adequate intake of the targeted micronutrients. The proposed diets had a maximum cost of 120 Ethiopian birrs ($3·5) per d, twice the current diet's cost.

CONCLUSION

The modelled diets may be feasible for women of reproductive age as they are close to their current diets and fulfil their energy and nutrient demands. However, the costs may be a barrier to implementation.

Assessing the Quality of Simulated Food Patterns with Reduced Animal Protein Using Meal Data from NHANES 2017-2018

The nutritional consequences of progressively replacing meat products with plant-based foods need to be systematically evaluated. Modeling analyses provide insights into the predicted food consumption and nutritional adequacy of plant-based diets. We developed a novel methodology to simulate food patterns and evaluate diet quality. Meal data from the National Health and Nutrition Examination Survey (NHANES) 2017-2018 was used to create 100 7-day meal plans subject to various nutrient and food group optimization criteria. Omnivore (reference diet), flexitarian, pescatarian, and vegetarian food patterns were modeled using mixed integer linear programming. The modeled food patterns used the 25th and 75th percentiles of the US Usual Dietary Intakes to set the optimization constraints. The diet quality was determined using the Healthy Eating Index 2015 (HEI-2015). The modeled vegetarian, pescatarian, and flexitarian food patterns outperformed the omnivore diet on the HEI-2015, with the vegetarian pattern achieving the highest score (82 for females, 78 for males). Modeled flexitarian patterns, with a 25 to 75% reduction in animal protein, offer viable options for those seeking to reduce but not eliminate their animal protein intake while supporting the transition from omnivore to fully plant-based diets. This methodology could be applied to evaluate the nutrient and diet quality of different dietary patterns with various constraints.

A linear programming based method for designing menus for controlled feeding trials

BACKGROUND

Controlled feeding trials are an important method to determine cause-effect relationships between dietary intake and metabolic parameters, risk factors, or health outcomes. Participants of a controlled feeding trial receive full-day menus during a prespecified period of time. The menus have to comply with the nutritional and operational standards of the trial. Levels of nutrients under investigation should differ sufficiently between intervention groups, and be as similar as possible for all energy levels within intervention groups. Levels of other key nutrients should be as similar as possible for all participants. All menus have to be varied and manageable. Designing these menus is both a nutritional and a computational challenge that relies largely on the expertise of the research dietician. The process is very time consuming, and last-minute disruptions are very hard to manage.

OBJECTIVE

This paper demonstrates a mixed integer linear programming model to support the design of menus for controlled feeding trials.

METHODS

The model is demonstrated for a trial that involved consumption of individualized, isoenergetic menus with either a low or a high protein content.

RESULTS

All menus generated by the model comply with all standards of the trial. The model allows for including tight ranges on nutrient composition, and complex design features. The model is very helpful in managing contrast and similarity of key nutrient intake levels between groups and energy levels, and in coping with many energy levels and nutrients. The model helps to propose several alternative menus and to manage last-minute disruptions. The model is flexible; it can easily be adapted to suit trials with other components or different nutritional requirements.

CONCLUSIONS

The model helps to design menus in a fast, objective, transparent, and reproducible way. It greatly facilitates the design procedure for menus in controlled feeding trials and lowers development costs.

Development of an optimal grocery list based on actual intake from a cross-sectional study of First Nations adults in Ontario, Canada

A multi-stage sampling strategy selected 1387 on-reserve First Nations adults in Ontario. Foods from a 24-hour dietary recall were assigned to the 100 most common food groups for men and women. Nutrients from market foods (MF) and traditional foods (TF) harvested from the wild as well as MF costs were assigned based on the proportions of total grams consumed. Linear programming was performed imposing various constraints to determine whether it was possible to develop diets that included the most popular foods while meeting Institute of Medicine guidelines. Final models were obtained for both sexes with the top 100 food groups consumed while limiting the nutrient-poor foods to no more than the actual observed intake. These models met all nutrient constraints for men but those for dietary fibre, linoleic acid, phosphorus, and potassium were removed for women. MF costs were obtained from community retailers and online resources. A grocery list was then developed and MF were costed for a family of four. The grocery list underestimated the actual weekly food cost because TF was not included. Contemporary observed diets deviated from healthier historic First Nations diets. A culturally appropriate diet would include more traditional First Nations foods and fewer MF. Novelty ● Linear programming is a mathematical approach to evaluating the diets of First Nations ● The grocery list is representative of food patterns within Ontario First Nations and can be used as an alternative to the nutritious food basket used for public health food costing.

Using Linear Programming to Determine the Role of Plant- and Animal-Sourced Foods in Least-Cost, Nutritionally Adequate Diets for Adults

BACKGROUND

The respective roles of plant- and animal-sourced foods in sustainable healthy diets for humans remain unclear. Nutritional quality and the monetary cost of diets are key criteria among others for sustainable food production.

OBJECTIVE

Linear programming (LP) was used to determine the composition of nutritionally adequate dietary patterns formulated at the lowest cost. The hypothesis tested was that animal-sourced foods would be included in least-cost diets due to their high density of particular essential nutrients.

METHODS

The LP modeling work was based on eating patterns, retail food prices (2020), and the daily energy (11,150 kJ, 2665 kcal) and essential nutrient requirements (29 nutrients in total) of a reference adult in New Zealand (NZ). The LP modeling approach is publicly and freely available to readily illustrate the change in dietary profiles and daily diet cost, in the simulation of changes in energy and nutrient requirements, and price fluctuations within food groups.

RESULTS

A nutrient-adequate, least-cost dietary pattern formulated from 883 foods, with a daily cost of NZ $3.23, included both animal- and plant-based foods. The nutrients found to be equally first-limiting were biotin, calcium, molybdenum, potassium, selenium, vitamin A, pantothenic acid, and vitamin C. When a dietary scenario with no animal-sourced foods was modeled, by increasing the retail prices of animal-sourced foods by 1.05 to 10.3 times, the daily cost of this plant-only dietary pattern was NZ $4.34. Additional nutrients, such as zinc, vitamin B-12, and vitamin D, were met at their daily minimum required levels.

CONCLUSIONS

Dietary patterns formulated at the lowest cost and meeting the daily minimum requirements for energy and essential nutrients for an adult in New Zealand relied on foods sourced from animals and plants.

Addressing nutrient shortfalls in 1- to 5-year-old Irish children using diet modeling: development of a protocol for use in country-specific population health

BACKGROUND

Dietary habits formed in early childhood can track into later life with important impacts on health. Food-based dietary guidelines (FBDGs) may have a role in improving population health but are lacking for young children.

OBJECTIVES

We aimed to establish a protocol for addressing nutrient shortfalls in 1- to 5-y-old children (12-60 mo) using diet modeling in a population-based sample.

METHODS

Secondary analysis of 2010-2011 Irish National Pre-School Nutrition Survey data (n = 500) was conducted to identify typical food consumption patterns in 1- to 5-y-olds. Nutrient intakes were assessed against dietary reference values [European Food Safety Authority (EFSA) and Institute of Medicine (IOM)]. To address nutrient shortfalls using diet modeling, 4-d food patterns were developed to assess different milk-feeding scenarios (human milk, whole or low-fat cow milk, and fortified milks) within energy requirement ranges aligned with the WHO growth standards. FBDGs to address nutrient shortfalls were established based on 120 food patterns.

RESULTS

Current mean dietary intakes for the majority of 1- to 5-y-olds failed to meet reference values (EFSA) for vitamin D (≤100%), vitamin E (≤88%), DHA (22:6n-3) + EPA (20:5n-3) (IOM; ≤82%), and fiber (≤63%), whereas free sugars intakes exceeded recommendations of <10% energy (E) for 48% of 1- to 3-y-olds and 75% of 4- to 5-y-olds. "Human milk + Cow milk" was the only milk-feeding scenario modeled that predicted sufficient DHA + EPA among 1- to 3-y-olds. Vitamin D shortfalls were not correctable in any milk-feeding scenario, even with supplementation (5 µg/d), apart from the "Follow-up Formula + Fortified drink" scenario in 1- to 3-y-olds (albeit free sugars intakes were estimated at 12%E compared with ≤5%E as provided by other scenarios). Iron and vitamin E shortfalls were most prevalent in scenarios for 1- to 3-y-olds at ≤25th growth percentile.

CONCLUSIONS

Using WHO growth standards and international reference values, this study provides a protocol for addressing nutrient shortfalls among 1- to 5-y-olds, which could be applied in country-specific population health.

Sensitivity of Food-Based Recommendations Developed Using Linear Programming to Model Input Data in Young Kenyan Children

Food-based recommendations (FBR) developed using linear programming generally use dietary intake and energy and nutrient requirement data. It is still unknown to what extent the availability and selection of these data affect the developed FBR and identified problem nutrients. We used 24 h dietary recalls of 62 Kenyan children (4-6 years of age) to analyse the sensitivity of the FBR and problem nutrients to (1) dietary intake data, (2) selection criteria applied to these data and (3) energy and nutrient requirement data, using linear programming (Optifood©), by comparing a reference scenario with eight alternative scenarios. Replacing reported by estimated consumption frequencies increased the recommended frequencies in the FBR for most food groups while folate was no longer identified as a problem nutrient. Using the 10-90th instead of the 5-95th percentile of distribution to define minimum and maximum frequencies/week decreased the recommended frequencies in the FBR and doubled the number of problem nutrients. Other alternative scenarios negligibly affected the FBR and identified problem nutrients. Our study shows the importance of consumption frequencies for developing FBR and identifying problem nutrients by linear programming. We recommend that reported consumption frequencies and the 5-95th percentiles of distribution of reported frequencies be used to define the minimum and maximum frequencies.

Food-Based Dietary Guidelines around the World: A Comparative Analysis to Update AESAN Scientific Committee Dietary Recommendations

Food-Based Dietary Guidelines (FBDG) include dietary recommendations based on food groups according to the general and accepted nutrition principles and current scientific evidence. Adoption of FBDG contributes to the prevention of malnutrition in all its forms, promotes human health, and reduces environmental impact. The present review aims to perform an international comparative analysis of the FBDG adopted in different countries from three different continents (America, Asia, and Europe), with particular reference to the Spanish Food Safety and Nutrition Agency (AESAN, Agencia Española de Seguridad Alimentaria y Nutrición) Scientific Committee dietary recommendations. A total of twelve countries with the most updated FBDG and/or closest to the traditional and cultural preferences of Spain were finally selected. All the reviewed FBDG provided recommendations for fruits, vegetables, cereals, legumes, nuts, milk and dairy products, meat and derivatives, fish, eggs, water, and oil; however, remarkable differences regarding recommended amounts were found among countries.

What do Australian adults eat for breakfast? A latent variable mixture modelling approach for understanding combinations of foods at eating occasions

BACKGROUND

The patterning of food intake at eating occasions is a poorly understood, albeit important, step towards achieving a healthy dietary pattern. However, to capture the many permutations of food combinations at eating occasions, novel analytic approaches are required. We applied a latent variable mixture modelling (LVMM) approach to understand how foods are consumed in relation to each other at breakfast.

METHODS

Dietary intake at breakfast (n = 8145 occasions) was assessed via 24-h recall during the 2011-12 Australian National Nutrition and Physical Activity Survey (n = 3545 men and n = 4127 women, ⩾19 y). LVMM was used to determine breakfast food profiles based on 35 food group variables, reflecting compliance with Australian Dietary Guidelines. F and adjusted-chi2 tests assessed differences in timing of consumption and participant characteristics between the breakfast profiles. Regression models, adjusted for covariates, were used to examine associations between breakfast food profiles and objective adiposity measures (BMI and waist circumference).

RESULTS

Five distinct profiles were found. Three were similar for men and women. These were labelled: "Wholegrain cereals and milks" (men: 16%, women: 17%), "Protein-foods" (men and women: 11%) and "Mixed cereals and milks" (men: 33%, women: 37%). Two "Breads and spreads" profiles were also found that were differentiated by their accompanying beverages (men) or type of grain (women). Profiles were found to vary by timing of consumption, participant characteristics and adiposity indicators. For example, the "Protein-foods" profile occurred more frequently on weekends and after 9 am. Men with a "Bread and spreads (plus tea/coffee)" profile were older (P < 0.001) and had lower income and education levels (P < 0.05), when compared to the other profiles. Women with a "Protein-foods" profile were younger (P < 0.001) and less likely to be married (P < 0.01). Both men and women with a "Wholegrain cereals and milks" profile had the most favourable adiposity estimates (P < 0.05).

CONCLUSIONS

We identified five breakfast food profiles in adults that varied by timing of consumption, participant characteristics and adiposity indicators. LVMM was a useful approach for capturing the complexity of food combinations at breakfast. Future research could collect contextual information about eating occasions to understand the complex factors that influence food choices.

Improving health and carbon footprints of European diets using a benchmarking approach

OBJECTIVE

This study aimed to identify diets with improved nutrient quality and environmental impact within the boundaries of dietary practices.

DESIGN

We used Data Envelopment Analysis to benchmark diets for improved adherence to food-based dietary guidelines (FBDG). We then optimised these diets for dietary preferences, nutrient quality and environmental impact. Diets were evaluated using the Nutrient Rich Diet score (NRD15.3), diet-related greenhouse gas emission (GHGE) and a diet similarity index that quantified the proportion of food intake that remained similar as compared with the observed diet.

SETTING

National dietary surveys of four European countries (Denmark, Czech Republic, Italy and France).

SUBJECTS

Approximately 6500 adults, aged 18-64 years.

RESULTS

When dietary preferences were prioritised, NRD15·3 was ~6 % higher, GHGE was ~4 % lower and ~85 % of food intake remained similar. This diet had higher amounts of fruit, vegetables and whole grains than the observed diet. When nutrient quality was prioritised, NRD15·3 was ~16 % higher, GHGE was ~3 % lower and ~72 % of food intake remained similar. This diet had higher amounts of legumes and fish and lower amounts of sweetened and alcoholic beverages. Finally, when environmental impact was prioritised, NRD15·3 was ~9 % higher, GHGE was ~21 % lower and ~73 % of food intake remained similar. In this diet, red and processed meat partly shifted to either eggs, poultry, fish or dairy.

CONCLUSIONS

Benchmark modelling can generate diets with improved adherence to FBDG within the boundaries of dietary practices, but fully maximising health and minimising GHGE cannot be achieved simultaneously.

Designing healthier and acceptable diets using data envelopment analysis

OBJECTIVE

The objective of this research is to propose methodology that can be used to benchmark current diets based on their nutrient intakes and to provide guidelines for improving less healthy diets in a way that is acceptable for the studied population.

DESIGN

We discuss important limitations of current diet models that use optimisation techniques to design healthier and acceptable diets. We illustrate how data envelopment analysis could be used to overcome such limitations, and we describe mathematical models that can be used to calculate not only healthier but also acceptable diets.

SETTING

We used data from the Nutrition Questionnaires plus dataset of habitual diets of a general population of adult men and women in The Netherlands (n 1735).

PARTICIPANTS

Adult population.

RESULTS

We calculated healthier diets with substantial higher intakes of protein, fibre, Fe, Ca, K, Mg and vitamins, and substantially lower intakes of Na, saturated fats and added sugars. The calculated diets are combinations of current diets of individuals that belong to the same age/gender group and comprise of food item intakes in proportions observed in the sample.

CONCLUSIONS

The proposed methodology enables the benchmarking of existing diets and provides a framework for proposing healthier alternative diets that resemble the current diet in terms of foods intake as much as possible.

Animal-sourced foods are required for minimum-cost nutritionally adequate food patterns for the United States

The amounts of animal-sourced foods required to achieve a least-cost nutritious diet depend on the food prices prevalent in each country. Using linear programming, we determine least-cost dietary patterns in the United States and the constituent amounts of animal-sourced foods. We considered local foods and prices from 2009-2010, and the average energy and nutrient requirements of adults. Nutrient-adequate food patterns were estimated at US$1.98 per day and included animal and plant products. Limiting nutrients were α-linolenic acid, potassium, choline, and vitamins C, D, E and K. The prices of animal-based foods had to be increased by 2-11.5 times to be excluded from the modelled food pattern, with the least cost of a plant-only diet at US$3.61. Given relative food prices in the United States, we show that animal-based foods are needed to secure adequate nutrition at the lowest cost, underscoring the role of price and market mechanisms in the choice of nutrient-adequate, sustainable diets.

Optimisation modelling to improve the diets of First Nations individuals

We examined the feasibility of linear programming (LP) to develop diets that were economical, included traditional (cultural, non-market) foods and met the dietary reference intakes (DRI) in a Canadian Indigenous population. Diet optimisation using LP is a mathematical technique that can develop food-based dietary guidelines for healthy eating in Indigenous populations where food insecurity, availability and cost are important considerations. It is a means of developing nutritionally optimal food combinations that are based on economical and culture-specific foods. Observed food consumption data were derived using 24-h food recalls from the First Nations Food, Nutrition and Environment Study. The LP models were constructed to develop diets meeting DRI, cost and food constraints. Achieving the recommended food intake was not feasible in a model meeting all nutrient requirements. Models that met most nutrient requirements at reduced cost were designed for men and women, separately. In women, it was necessary to increase energy intake to meet most nutrient requirements. Nutrient requirements could not be met for fibre, linoleic and linolenic acids, vitamin D, Ca and K in both sexes, P in women, and Mg and vitamin A in men. Using LP to develop optimal diets for First Nations people, we found simultaneous achievement of all DRI was difficult, suggesting that supplementation might be necessary which goes against recommendations for individuals to meet their nutrient needs through healthy eating patterns. Additionally, to make diets feasible, programmes to reduce market food costs and to support First Nations people in traditional food harvesting are recommended.

Development of healthy and sustainable food-based dietary guidelines for the Netherlands

Objective:

To derive healthy and sustainable food-based dietary guidelines (FBDG) for different target groups in the Netherlands and describe the process.

Design:

Optimised dietary patterns for children, adolescents, adults and the elderly were calculated using an optimisation model. Foods high in saturated and trans-fatty acids, salt and sugar, and low in dietary fibre, were excluded. The dietary patterns resembled the current food consumption as closely as possible, while simultaneously meeting recommendations for food groups, nutrients, maximum limits for foods with a high environmental impact, and within 85 % of the energy requirement. Recommended daily amounts of food groups were based on the optimised dietary patterns and expert judgement.

Setting:

The Netherlands.

Participants:

FBDG were derived for Dutch people with different ages, genders, activity levels and food preferences.

Results:

For most target groups the optimisation model provided dietary patterns that complied with all requirements. For some food groups, the optimised amounts varied largely between target groups. For consistent messages to consumers, the optimised dietary patterns were adjusted to uniform recommendations per target group. Recommendations were visualised in the Wheel of Five. The advice is to eat the recommended amounts of foods according to the Wheel of Five and limit consumption of other foods.

Conclusions:

Based on an optimisation model, scientific evidence, information on dietary patterns and expert knowledge, we derived FBDG for different target groups. The Wheel of Five is a key food-counselling model that can help Dutch consumers to make their diets healthier and more environmentally sustainable.

International approaches to developing healthy eating patterns for national dietary guidelines

As part of the revision of the 2007 Eating Well with Canada's Food Guide, a literature scan on statistical modeling approaches used in developing healthy eating patterns for national food guides was conducted. The scan included relevant literature and online searches, primarily since the 2007 Canada's Food Guide was released. Eight countries were identified as utilizing a statistical model or analysis to help inform their healthy eating pattern, defined as the amounts and types of food recommended, with many common characteristics noted. Detail on international modeling approaches is presented, highlighting similarities and differences as well as strengths and challenges.

Healthy and sustainable diets that meet greenhouse gas emission reduction targets and are affordable for different income groups in the UK

OBJECTIVE

To model dietary changes required to shift the UK population to diets that meet dietary recommendations for health, have lower greenhouse gas emissions (GHGE) and are affordable for different income groups.

DESIGN

Linear programming was used to create diets that meet dietary requirements for health and reduced GHGE (57 and 80 % targets) by income quintile, taking account of food budgets and foods currently purchased, thereby keeping dietary change to a minimum.Setting/ParticipantsNutrient composition, GHGE and price data were mapped to 101 food groups in household food purchase data (UK Living Cost and Food Survey (2013), 5144 households).

RESULTS

Current diets of all income quintiles had similar total GHGE, but the source of GHGE differed by types of meat and amount of fruit and vegetables. It was possible to create diets with a 57 % reduction in GHGE that met dietary and cost restraints in all income groups. In the optimised diets, the food sources of GHGE differed by income group due to the cost and keeping the level of deviation from current diets to a minimum. Broadly, the changes needed were similar across all groups; reducing animal-based products and increasing plant-based foods but varied by specific foods.

CONCLUSIONS

Healthy and lower-GHGE diets could be created in all income quintiles but tailoring changes to income groups to minimise deviation may make dietary changes more achievable. Specific attention must be given to make interventions and policies appropriate for all income groups.

Perspective: Food-Based Dietary Guidelines in Europe-Scientific Concepts, Current Status, and Perspectives

Food-based dietary guidelines (FBDGs) are important tools for nutrition policies and public health. FBDGs provide guidelines on healthy food consumption and are based on scientific evidence. In the past, disease prevention and nutrient recommendations dominated the process of establishing FBDGs. However, scientific advances and social developments such as changing lifestyles, interest in personalized health, and concerns about sustainability require a reorientation of the creation of FBDGs to include a wider range of aspects of dietary behavior. The present review evaluates current European FBDGs with regard to the concepts and aspects used in their derivation, and summarizes the major aspects currently discussed to be considered in future establishment or updates of FBDGs. We identified English information on official European FBDGs through an Internet search (FAO, PubMed, Google) and analyzed the aspects used for their derivation. Furthermore, we searched literature databases (PubMed, Google Scholar) for conceptional considerations dealing with FBDGs. A total of 34 out of 53 European countries were identified as having official FBDGs, and for 15 of these, documents with information on the scientific basis could be identified and described. Subsequently, aspects underlying the derivation of current FBDGs and aspects considered in the literature as important for future FBDGs were discussed. Eight aspects were identified: diet-health relations, nutrient supply, energy supply, dietary habits, sustainability, food-borne contaminants, target group segmentation, and individualization. The first 4 have already been widely applied in existing FBDGs; the others have almost never been taken into account. It remains a future challenge to (re)conceptionalize the development of FBDGs, to operationalize the aspects to be incorporated in their derivation, and to convert concepts into systematic approaches. The current review may assist national expert groups and clarifies the options for future development of local FBDGs.

A Review of the Use of Linear Programming to Optimize Diets, Nutritiously, Economically and Environmentally

The "Diet Problem" (the search of a low-cost diet that would meet the nutritional needs of a US Army soldier) is characterized by a long history, whereas most solutions for comparable diet problems were developed in 2000 or later, during which computers with large calculation capacities became widely available and linear programming (LP) tools were developed. Based on the selected literature (52 papers), LP can be applied to a variety of diet problems, from food aid, national food programmes, and dietary guidelines to individual issues. This review describes the developments in the search for constraints. After nutritional constraints, costs constraints, acceptability constraints and ecological constraints were introduced. The 12 studies that apply ecological constraints were analyzed and compared in detail. Most studies have used nutritional constraints and cost constraints in the analysis of dietary problems and solutions, but such research begin showing weaknesses under situations featuring a small number of food items and/or nutritional constraints. Introducing acceptability constraints is recommended, but no study has provided the ultimate solution to calculating acceptability. Future possibilities lie in finding LP solutions for diets by combining nutritional, costs, ecological and acceptability constraints. LP is an important tool for environmental optimization and shows considerable potential as an instrument for finding solutions to a variety of very complex diet problems.

Food choices to meet nutrient recommendations for the adult Brazilian population based on the linear programming approach

OBJECTIVE

To identify optimal food choices that meet nutritional recommendations to reduce prevalence of inadequate nutrient intakes.

DESIGN

Linear programming was used to obtain an optimized diet with sixty-eight foods with the least difference from the observed population mean dietary intake while meeting a set of nutritional goals that included reduction in the prevalence of inadequate nutrient intakes to ≤20 %.

SETTING

Brazil.

SUBJECTS

Participants (men and women, n 25 324) aged 20 years or more from the first National Dietary Survey (NDS) 2008-2009.

RESULTS

Feasible solution to the model was not found when all constraints were imposed; infeasible nutrients were Ca, vitamins D and E, Mg, Zn, fibre, linolenic acid, monounsaturated fat and Na. Feasible solution was obtained after relaxing the nutritional constraints for these limiting nutrients by including a deviation variable in the model. Estimated prevalence of nutrient inadequacy was reduced by 60-70 % for most nutrients, and mean saturated and trans-fat decreased in the optimized diet meeting the model constraints. Optimized diet was characterized by increases especially in fruits (+92 g), beans (+64 g), vegetables (+43 g), milk (+12 g), fish and seafood (+15 g) and whole cereals (+14 g), and reductions of sugar-sweetened beverages (-90 g), rice (-63 g), snacks (-14 g), red meat (-13 g) and processed meat (-9·7 g).

CONCLUSION

Linear programming is a unique tool to identify which changes in the current diet can increase nutrient intake and place the population at lower risk of nutrient inadequacy. Reaching nutritional adequacy for all nutrients would require major dietary changes in the Brazilian diet.

Dietary changes needed to reach nutritional adequacy without increasing diet cost according to income: An analysis among French adults

OBJECTIVE

To explore the dietary changes needed to achieve nutritional adequacy across income levels at constant energy and diet cost.

MATERIALS AND METHODS

Individual diet modelling was used to design iso-caloric, nutritionally adequate optimised diets for each observed diet in a sample of adult normo-reporters aged ≥20 years (n = 1,719) from the Individual and National Dietary Survey (INCA2), 2006-2007. Diet cost was estimated from mean national food prices (2006-2007). A first set of free-cost models explored the impact of optimisation on the variation of diet cost. A second set of iso-cost models explored the dietary changes induced by the optimisation with cost set equal to the observed one. Analyses of dietary changes were conducted by income quintiles, adjusting for energy intake, sociodemographic and socioeconomic variables, and smoking status.

RESULTS

The cost of observed diets increased with increasing income quintiles. In free-cost models, the optimisation increased diet cost on average (+0.22 ± 1.03 euros/d) and within each income quintile, with no significant difference between quintiles, but with systematic increases for observed costs lower than 3.85 euros/d. In iso-cost models, it was possible to design nutritionally adequate diets whatever the initial observed cost. On average, the optimisation at iso-cost increased fruits and vegetables (+171 g/day), starchy foods (+121 g/d), water and beverages (+91 g/d), and dairy products (+20 g/d), and decreased the other food groups (e.g. mixed dishes and salted snacks), leading to increased total diet weight (+300 g/d). Those changes were mostly similar across income quintiles, but lower-income individuals needed to introduce significantly more fruit and vegetables than higher-income ones.

CONCLUSIONS

In France, the dietary changes needed to reach nutritional adequacy without increasing cost are similar regardless of income, but may be more difficult to implement when the budget for food is lower than 3.85 euros/d.

How low can dietary greenhouse gas emissions be reduced without impairing nutritional adequacy, affordability and acceptability of the diet? A modelling study to guide sustainable food choices

OBJECTIVE

To assess the compatibility between reduction of diet-related greenhouse gas emissions (GHGE) and nutritional adequacy, acceptability and affordability dimensions of diet sustainability.

DESIGN

Dietary intake, nutritional composition, GHGE and prices were combined for 402 foods selected among those most consumed by participants of the Individual National Study on Food Consumption. Linear programming was used to model diets with stepwise GHGE reductions, minimized departure from observed diet and three scenarios of nutritional constraints: none (FREE), on macronutrients (MACRO) and for all nutrient recommendations (ADEQ). Nutritional quality was assessed using the mean adequacy ratio (MAR) and solid energy density (SED).

SETTING

France.

SUBJECTS

Adults (n 1899).

RESULTS

In FREE and MACRO scenarios, imposing up to 30 % GHGE reduction did not affect the MAR, SED and food group pattern of the observed diet, but required substitutions within food groups; higher GHGE reductions decreased diet cost, but also nutritional quality, even with constraints on macronutrients. Imposing all nutritional recommendations (ADEQ) increased the fruits and vegetables quantity, reduced SED and slightly increased diet cost without additional modifications induced by the GHGE constraint up to 30 % reduction; higher GHGE reductions decreased diet cost but required non-trivial dietary shifts from the observed diet. Not all the nutritional recommendations could be met for GHGE reductions ≥70 %.

CONCLUSIONS

Moderate GHGE reductions (≤30 %) were compatible with nutritional adequacy and affordability without adding major food group shifts to those induced by nutritional recommendations. Higher GHGE reductions either impaired nutritional quality, even when macronutrient recommendations were imposed, or required non-trivial dietary shifts compromising acceptability to reach nutritional adequacy.

Beyond Wishful Thinking: Integrating Consumer Preferences in the Assessment of Dietary Recommendations

Convenience, taste, and prices are the main determinants of food choices. Complying with dietary recommendations therefore imposes a “taste cost” on consumers, potentially hindering adoption of those recommendations. The study presents and applies a new methodology, based on economic theory, to quantify this taste cost and assess the health and welfare effects of different dietary recommendations. Then, by comparison of those effects, we identify socially desirable recommendations that are most compatible with consumer preferences (i.e., that best balance health benefits against”taste cost”) and should be prioritized for promotion. The methodology proceeds in three-steps: first, an economic-behavioral model simulates how whole diets would change if consumers complied with dietary recommendations; second, an epidemiological model estimates the number of deaths avoided (DA) due to the dietary change; third, an efficiency analysis weighs the health benefits against the taste and policy costs of each recommendation. The empirical model is calibrated using French data. We find that recommendations to reduce consumption of red meat and soft-drinks, or raise consumption of milk products and fish/seafood impose relatively moderate taste costs. By comparison, recommendations related to F&V consumption and, to a lesser extent, butter/cream/cheese, snacks, and all meats impose larger taste costs on consumers. The F&V recommendation is the costliest for consumers to comply with, but it also reduces diet-related mortality the most, so that a large budget could be allocated to promoting F&V consumption while keeping this policy cost-beneficial. We conclude that promotion of most dietary recommendations improves social welfare. Our framework complements the programming models available in nutrition and public health: those models are best used to identify dietary targets, following which our framework identifies cost-beneficial ways of moving towards those targets.

Diet models with linear goal programming: impact of achievement functions

BACKGROUND/OBJECTIVES

Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost constraints. Results derived from GP models are usually very sensitive to the type of achievement function that is chosen.This paper aims to provide a methodological insight into several achievement functions. It describes the extended GP (EGP) achievement function, which enables the decision maker to use either a MinSum achievement function (which minimizes the sum of the unwanted deviations) or a MinMax achievement function (which minimizes the largest unwanted deviation), or a compromise between both. An additional advantage of EGP models is that from one set of data and weights multiple solutions can be obtained.

SUBJECTS/METHODS

We use small numerical examples to illustrate the 'mechanics' of achievement functions. Then, the EGP achievement function is demonstrated on a diet problem with 144 foods, 19 nutrients and several types of palatability constraints, in which the nutritional constraints are modeled with fuzzy sets.

RESULTS

Choice of achievement function affects the results of diet models.

CONCLUSIONS

MinSum achievement functions can give rise to solutions that are sensitive to weight changes, and that pile all unwanted deviations on a limited number of nutritional constraints. MinMax achievement functions spread the unwanted deviations as evenly as possible, but may create many (small) deviations. EGP comprises both types of achievement functions, as well as compromises between them. It can thus, from one data set, find a range of solutions with various properties.