Dietary intake data generated from con­ventional dietary assess­ment methods have been severely criticized in the past because both random and systematic errors occur in measuring intakes of food and calculating their nutrient con­tent (Subar et al., 2015). The data are also frequently misinter­preted. This is particularly unfortunate because the careful evaluation of food- and nutrient-intake data has important uses and applications, provided that the limitations of the methods are clearly understood.

This chapter describes the assess­ment of nutrient intakes and the planning of nutritious diets at both the indi­vidual and population level. Most of the approaches used are based on comparison of the usual daily intake of an indi­vidual or group with the appropriate Nutrient Reference Values (NRVs) or the Acceptable Macro­nutrient Distri­bution Ranges (AMDRs). The tables of NRVs have now been expanded in many countries and regions to include:

• An Average Require­ment (AR), referred, in some countries, as an Estimated Average require­ment (EAR).
• A Recom­mended Intake (RI₉₈), termed a Recommended Dietary Allowance (RDA) in Canada and the U.S.
• An Ade­quate Intake (AI) and/or an Upper Intake Level (UL),

Each NRV has a specific use as a reference standard for diet assess­ment and planning; their derivation is described in Chapter 8a. The AI is used for those nutrients for which there is insufficient available info­rmation to set an AR. Development of the UL arose because of the increasing availability of fortified foods and dietary supplements worldwide, and con­cern about ingesting too much of a nutrient.

8b.1 Applications of Nutrient Reference Values in diet assess­ment and planning

Many countries have adopted a new paradigm and set multiple NRVs rather than just a single value for the Recom­mended Intake (RI₉₈) or equiv­alent (Chapter 8a). Nutrient Reference Values are used for assessing the adequacy of nutrient intakes and planning nutritious diets for both apparently healthy indi­viduals and population groups as shown in Figure 8b.1. However, care must be taken to ensure the appropriate NRV is selected and the data inter­preted correctly.

Table 8b.1. Uses of Nutrient Reference Values for planning and assessing nutrient intakes of apparently healthy indi­viduals and groups. Modified from Barr (2006).

NRV	Assessment of nutrient intakes of healthy indi­vidual or groups
AR Individual	Use (with infor­mation on variability of require­ment and intake) to examine the prob­ability that the usual intake is inade­quate
AR Group	The pro­portion of the group with usual intake below the AR is an esti­mate of the group preva­lence of inade­quacy
RI Individual	Usual intake at or above the RI has a low prob­ability of inade­quacy
RI Group	Do not use to assess intakes of groups
AI Individual	Intake at or above the AI can be assumed ade­quate; no assess­ment can be made if intake is below the AI
AI Group	Median usual intake at or above the AI implies a low prev- alence of inade­quate intakes; no assess­ment can be made if median intake is below the AI
UL Individual	Usual intake above the UL may place an indi­vidual at risk of adverse effects from excessive intake
UL Group	The pro­portion of a group with usual intake above the UL may be at potential risk of adverse effects of excessive intake
NRV	Planning for nutritious diets for healthy indi­viduals or groups
AR Individual	Do not use the AR as an intake goal; usual intake at this level has a 50% prob­ability of inade­quacy
AR Group	Plan for an acceptably low pro­portion of a group with intakes below the AR. Note that mean intake will likely be above the RI
RI Individual	Aim for this intake; usual intake at or above the RI has a low prob­ability of inade­quacy
RI Group	Do not use the RI to plan mean intakes for groups. In almost all cases, mean intake at the RI will lead to an unacceptably high preva­lence of inade­quate intakes
AI Individual	Aim for this intake; usual intake at or above the AI has a low prob­ability of inade­quacy
AI Group	Plan for median intake at this level; median usual intake at or above the AI implies a low preva­lence of inade­quate intakes
UL Individual	Plan for usual intake to remain below the UL to avoid potential risk of adverse effects from excessive intake
UL Group	Plan to minimize the pro­portion of a group with intakes above the UL to minimize the risk of adverse effects of excessive intake

Assessment of nutrient intakes and planning nutritious diets at the indi­vidual level is especially chal­lenging because neither the require­ments of the indi­vidual nor their usual nutrient intake are known with any certainty. A quantitative method has been developed to esti­mate the prob­ability that an indi­vidual's intake or diet meets his or her require­ment. This method can be used provided NRVs for the nutrient of inter­est exist and the day-to-day variation in intake of the nutrient is not high.

Alternatively, health professionals can use published guidelines to provide a more practical qualitative assess­ment based on the likelihood that the intake of an indi­vidual is not ade­quate. Both methods can be used for dietary counseling and nutrition education and for developing a dietary plan that the indi­vidual can follow.

At the group level, with the inclusion of both an Average Require­ment (AR) and Upper Intake Level (UL) in the expanded NRV framework, the focus is no longer on the group mean intake alone, but also takes into account the distri­butions of usual intake within a group. With this new focus, the preva­lence of inade­quate and potentially excessive intakes can be assessed by estimating the pro­portion within the group whose usual intakes are less than the AR, and above the UL, respectively, by using either the prob­ability approach or the simpler EAR cutpoint method. To ensure a nutritious diet for the group, a plan can be devised to alter the current distri­bution of usual intakes to reduce the preva­lence of undesirable intakes.

Guidance on the correct uses of NRVs for planning and assessing nutrient intakes of indi­viduals and groups to avoid their misuse is summarized in Table 8b.1. A more detailed discussion of the correct use of each com­ponent of the NRVs for the assess­ment of nutrient intakes and planning nutritious diets of indi­viduals and groups follows.

With the development of more reliable statistical methods to assess the risk of inade­quate or excessive intakes of nutrients, vulnerable indi­viduals and subgroups in the population can be more accurately identified and targeted during inter­vention programs. Table 8b.2

Table 8b.2. Critical health applications that depend on the NRVs in the United States, Canada, and the United Kingdom.
WIC: U.S Special Supplemental Nutrition Program for women infants, and children.
SNAP: U.S Supplemental Nutrition Assistance Program.
Data from Murphy et al. (2016).

Application	Examples
Dietary guidelines	Important in formulating food-based dietary guidance, e.g.:   • US Dietary Guidelines for Americans   • Eating Well with Canada's Food Guide (2007)   • USDA Food Patterns   • UK Eatwell Guide
Nutrition monitoring	Needed to asses nutritional health on a national level.   • US NHANES and What We Eat in America analyses   • Canadian Community Health Survey analyses   • UK Diet and Nutrition Survey Rolling Program
Food assistance programs	Important to guide the design of healthier federal nutrition assistance programs   • School meals, WIC, SNAP, child and adult care programs   • Administration on Aging programs
Health Professionals	Used for dietary counseling and education and to design:   • healthy diets for institutions such as hospitals   • healthy diets for long-term care facilities and prisons
Nutrition research	Needed to study how diet can help prevent disease and provide a frame of reference in research
Military	Used to   • Ensure nutrient needs are met for armed forces   • Plan healthy meals   • Procure food, including military rations
Nutrition labeling	Can be used for the nutrition facts supplement facts labels. Such labels can help con­sumers make healthier food choices
Food/supplement industries	Used to develop healthy foods and safe supplements
Global nutrient standards	Provide a framework for other countries and inter­national organizations when setting their own standards

summarizes some of the uses and health applications that depend on the NRVs using examples from the United States, Canada, and the United Kingdom.

8b.2 Using the NRVs to assess nutrient intakes of an indi­vidual

None of the methods of assessing nutrient-intake data described below are capable of identifying with certainty that an indi­vidual's recorded nutrient intake is ade­quate or excessive. This is because the actual nutrient require­ment of an indi­vidual is not known. In addition, the recorded nutrient-intake data only approx­imate the indi­vidual's “usual” nutrient intake, because of normal day-to-day variation in the diet (Chapter 6) combined with mea­sure­ment errors (Chapter 5). For these reasons, dietary data alone can only provide an esti­mate of the prob­ability of an inade­quate or excessive intake of a nutrient. The reliability of this risk esti­mate depends on the quality of the dietary data collected and the method used to calculate the esti­mate of risk. However, only when biochemical, anthro­pometric, and clinical assess­ments are combined with the dietary investigation can a valid assess­ment of an indi­vidual's nutritional status be made.

Table 8b.1 summarizes the appropriate Nutrient Reference Values for assessing the nutrient intakes of indi­viduals. Details on planning diets for indi­viduals are given in Section 8b.4.1. The outline in this table should always be followed when assessing nutrient intakes (and planning diets) for indi­viduals.

8b.2.1 Using the Average Require­ment

It is not possible to compare the intake of an indi­vidual with his or her own require­ment, because the actual require­ment for any given indi­vidual is not known, as noted earlier. Moreover, the reported nutrient intake of an indi­vidual is unlikely to represent their mean usual intake because of within-person variation in nutrient intakes combined with mea­sure­ment errors, as discussed in Chapters 5  and 6. In view of these uncertainties, two approaches have been developed to assess the nutrient intakes of an indi­vidual. The first approach involves a statistical method that esti­mates the level of confidence that the usual nutrient intake of an indi­vidual meets the corres­ponding AR and is discussed below. The second approach is a qualitative interpretation of the nutrient intakes of an indi­vidual and is described in Section 8b.2.4.

The statistical approach is based on the following assumptions:

• The AR is the best esti­mate of an indi­vidual's require­ment.
• There is person-to-person variation in the require­ments (i.e., between-person variation), best described by the standard deviation of the require­ment esti­mate (SD_R). The latter indicates how much the indi­vidual's require­ment for a nutrient can deviate from the median require­ment in the population. In the absence of data for SD_R, IOM (2003) has assumed a CV of 10% for most nutrients. The SD_R is then calculated from the AR and CV as: SD_R = CV × AR.
• Mean reported intake of an indi­vidual is the best esti­mate of the usual intake of an indi­vidual.
• Day-to-day variation in intake (i.e., within-person variation) for an indi­vidual exists and can be described by the within-person standard deviation of intakes (SD_within). The latter indicates how much the reported intake may deviate from the usual intake.

The statistical approach standardizes the difference between the reported intake of a young woman for zinc, as an example, and the AR for zinc, by dividing the difference by the standard deviation of the difference (SD_D) . The latter takes into account the day-to-day variability in zinc intake for the young woman under study, and the variability of the require­ment (her zinc require­ment could differ from the AR) (Barr et al., 2002; Murphy and Poos, 2002). For details of the equation and worked examples using the ARs, see Appendix B in IOM (2000). Note this statistical approach cannot be used when the within-person variation is not normally distributed, or when the require­ment distri­bution is skewed (e.g., iron require­ments for pre­meno­pausal women).

Table 8b.3. Selected standardized difference values and corres­ponding probability of correctly concluding that the observed usual intake is ade­quate. Modified from IOM (2000).

Standardized Difference (Diff/SDD) i.e. Z-score	Inter- pretation	Probability of correct interpretation
+ 2.0	Usual intake is ade­quate	0.98
+ 1.65		0.95
+ 1.5		0.93
+ 1.0		0.85
+ 0.5		0.70
0.0		0.50
− 0.5		0.30
− 1.0		0.15
− 1.5		0.07
− 1.65		0.05
− 2.0		0.02

The result of this calculation is a Z‑score. In general, Z‑scores represent a difference divided by its standard deviation, and corres­pond to probability values associated with the normal distri­bution. Selected Z‑values corres­ponding to different levels of assurance are given in Table 8b.3). From the Z‑score the probability value (p) reflects the degree of confidence that, for example, the usual zinc intake of the young woman meets her zinc require­ment. As shown in Table 8b.3) when Z = +0.50, p = 0.70; when Z = −1.0, then p = 0.15, and when Z = −2.0, then p = 0.02 (Barr et al., 2002).

8b.2.2 Using the Adequate Intake

The approach described in Section 8b.2.1 cannot be used for those nutrients for which there is insufficient available infor­mation to set an AR. Instead, a statistically based hypothesis testing procedure can be used to compare an indi­vidual's intake to the AI. Details are also given in IOM (2000). Again, the procedure con­sists of a Z‑test involving the difference between the intake of the indi­vidual and the AI, relative to the esti­mated within-person standard deviation of the daily intake of the nutrient of interest.

If there is a high degree of confidence that the usual nutrient intake of an indi­vidual equals or exceeds the AI, after applying the appropriate statistical test, the diet is almost certainly likely to be ade­quate in a given nutrient. In con­trast, no evaluation can be made of the prob­ability of an inade­quate nutrient intake when the intake of the nutrient falls below the AI because the require­ment is unknown. In such cases, the inter­pretation must rely solely on the judgment of nutrition professionals. In general, to eliminate the possibility of nutrient inade­quacy, an indi­vidual should be encouraged to increase his or her nutrient intake to meet the AI (Barr et al. 2002; Murphy and Poos, 2002).

8b.2.3 Using the Upper Intake Level

The Upper Intake Level (UL) can be used to determine whether the usual intake of an indi­vidual is so high that it poses a risk of adverse health effects. Another statistical test can be used to determine the level of con­fidence that the usual intake of an indi­vidual is below the UL; details of this test are also given in (IOM, 2000). Whether the UL applies to the intake from supplements, fortificants, or medications or to the total intake from all sources depends on the nutrient (Barr et al. 2002; Murphy and Poos, 2002).

Hypothetical examples of assessing the adequacy or excessive intakes of riboflavin, folate, calcium, vitamin D and zinc for an elderly woman are given in Barr et al. (2002). In these examples, the appropriate statistical methods were employed to determine the level of confidence that the woman's usual intake met her require­ments (for riboflavin, folate, and zinc based on an AR), or exceeded the AI (for calcium and vitamin D at that time), but was below the UL; see Barr et al. (2002) for more details. Note that an AR has now been set for calcium and vitamin D by IOM (2011).

8b.2.4 Using the qualitative interpretation of an indi­vidual's nutrient intake

Table 8b.4: Guidelines for the qualitative inter­pretation of indi­vidual intakes. Modified after IOM (2003).

Recommended Intake (RI98)
If the intake is > RI98 there is a high level of confid- ence that intake is ade­quate if observed over a large number of days
If the intake is between the Average Require- ment (AR) and the RI98, the intake prob­ably needs to be improved because the prob­ability of adequacy is less than 97.5%
If the intake < AR, then the intake very likely needs to be improved because the prob­ability of adequacy is less than 50%
Adequate Intake (AI)
If the intake > AI, then the mean intake is likely ade­quate if observed over a large number of days
If the intake < AI, then the adequacy of intake cannot be determined
Upper Intake Level (UL)
If the intake > UL, there is a potential risk of adverse effects if observed over a large number of days
If the intake < UL, the intake is likely safe if observed over a large number of days

For practical purposes, a qualitative interpretation of the nutrient intakes of an indi­vidual in relation to the AR, RI₉₈, AI, and UL can be made, using the guidelines given in Table 8b.4. To apply this approach, the intakes of an indi­vidual must be assessed over a large number of days. Again, it is preferable to combine such a qualitative assessment with infor­mation based on biochemical, clinical, and anthropometric data, where possible.

8b.2.5 Using the Acceptable Macro­nutrient Distri­bution Range

If Acceptable Macro­nutrient Distri­bution Ranges (AMDRs) have been set for indi­viduals for carbo­hydrate, protein, total fat, linoleic acid, and α-linolenic acid, e.g., by IOM (2003) (see Section 8a.5.6), then the usual intake of macro­nutrients (expressed as a percentage of total energy intake) for an indi­vidual should fall within these ranges. If the usual intake of a macro­nutrient is below the AMDR, there is potential for an increased risk of both inade­quate intake of the essential macro­nutrient and chronic diseases. The potential for an increased risk of chronic diseases may also occur if the usual intake of a macro­nutrient exceeds the AMDR (IOM, 2000).

8b.2.6 Using Energy Intakes

The average esti­mated energy require­ments (EER) are based on a defined age, sex, height, weight, and physical activity level. Hence, a mean usual energy intake for an indi­vidual either above or below their calculated EER, would theoretically result in either weight gain or weight loss, respectively. However, even based on several days of energy intake from an indi­vidual, it is difficult to determine energy balance. Therefore, in practice recent body weight is often used to assess the likely adequacy of the energy intake of an indi­vidual (Barr, 2006). Note that no prob­ability of adequacy can be assessed for energy, because the intake of energy is almost always related to energy require­ments, violating one of the assumptions of the prob­ability approach (see Section 8b.3.1).

8b.3 Using NRVs to assess nutrient intakes of groups

infor­mation is often required on the pro­portion of a group with usual intake of a nutrient below their own require­ment. An esti­mate of the pro­portion of the group with an excessive usual nutrient intake is also important, as it exposes that portion of the group to the risk of adverse effects (See Table 8b.1). Unfortunately, there are some examples in the literature in which the use of the NRVs to determine the preva­lence of inade­quate intakes has been incorrect, leading to misleading interpretations (Trumbo et al., 2010). These may include:

Comparison of the usual intakes of the indi­viduals with the RI₉₈. Reporting the proportion of a group with usual intakes below the RI₉₈ is inappropriate because it will always lead to an over­esti­mate of the true preva­lence of inade­quacy. By definition, the RI₉₈ is set at 2SD above the AR, and thus exceeds the require­ments of more than 97% of all indi­viduals in the group.

Comparison of the group mean or median intake with the AR. This is inappropriate because even if the mean intake equals the AR, a high pro­portion of the population (≈ 50%) will be expected to have inade­quate usual intakes based on the definition of the AR.

Comparison of the group mean or median intake with the RI₉₈. This is inappropriate because it does not take into account the wide variation in the distri­bution of usual intakes within the group, which almost always exceeds the variability in the require­ment distri­bution. Hence, even if the mean/median intake equals or even exceeds the RI₉₈, there may still be a substantial pro­portion of the group who will have intakes less than their own require­ments, as shown in Box 8b.1. Indeed, to ensure a low preva­lence of intakes below the AR, the mean or median nutrient intakes of the group should exceed the RI₉₈, often by a considerable amount.

Comparison of the usual intakes of indi­viduals with the AI . This cannot be used to assess the preva­lence of inade­quate intakes.

Comparison of the group mean or median intake with the AI. Provided the AI used has been set based on the mean intake of a healthy population, then if the mean or median intake of the group is at or above the AI, the group can be assumed to have a low preva­lence of inade­quate intakes. However, if the mean or median intake of the group is below the AI, it is not possible to make any assumptions about the preva­lence of inade­quacy.

Note that in cases when the mean or median intake is compared with the NRVs, the distri­bution of nutrient intakes does not need to be adjusted for day-to-day variation because only the mean or median intake is being examined. However, the only situation in which this approach is appropriate is for nutrients with an AI based on the mean/median intake of a healthy population, or for energy (see Section 8b.4.2).

When the objective is to compare the adequacy of nutrient intakes for two groups, then the preva­lence of inade­quate intakes for each group should be determined, and not the mean intake for each group. The latter can be the same as shown in Figure 8b.2, even though there were differences in the pro­portions in each group with inade­quate intakes. This situation occurs when the intakes in one group are much more variable than in the other group (Murphy and Poos, 2002, Figure 8b.2).

The recom­mended approach for evaluating the adequacy of nutrient intakes of population groups is to use the average require­ment (AR). Two methods based on the AR have been developed: the full prob­ability approach and the EAR cutpoint method; they are described below. Neither of these methods requires that the intakes be normally distributed, although other assumptions described below must be satisfied (Murphy and Vorster, 2007).

Note that these methods cannot be used to identify actual indi­viduals with inade­quate intakes because some of the indi­viduals will have require­ments that are lower than the AR, and others have higher than average require­ments.

8b.3.1 Full Probability Approach

The full prob­ability approach was first described by Beaton (1972), with the goal of providing a more reliable esti­mate for the pro­portion of indi­viduals within a population group with inade­quate intakes (i.e., intakes below their require­ments). Because there is no infor­mation about the actual require­ments of each indi­vidual, this procedure does not identify with certainty which indi­viduals have inade­quate intakes. Hence, it cannot be used to screen those indi­viduals for nutrient inade­quacy.

The statistical approach combines the distri­butions of both require­ments and indi­vidual usual nutrient intakes for the group to esti­mate the pro­portion of indi­viduals with inade­quate intakes. The probability of inade­quacy for each indi­vidual in the group is calculated first, followed by an esti­mate of the average of the indi­vidual probabilities for the group. This yields the group preva­lence of inade­quate intakes. The statistical approach is based on three key assumptions:

• Intakes and require­ments are independent
• The median and the variance of the distri­bution of require­ments are known
• The shape of the require­ment distri­bution follows some known statistical model (normal, lognormal etc) (IOM, 2003).

To adopt the probability approach for evaluating nutrient intakes, the following infor­mation is required:

• The AR for each nutrient for the particular sex and life-stage group of indi­viduals.
• The distri­bution of require­ments for each nutrient among similar indi­viduals: for most nutrients, this is not precisely known. In the absence of such infor­mation, the distri­bution of require­ments for most nutrients is assumed to be normal with a coefficient of variation of 10% (or 15% for niacin) about the AR. Notable exceptions are the iron require­ment distri­butions for men­struating adolescent women 14–18y; and men­struating adult women, both of which are positively skewed. The iron require­ment distri­butions for children 1–3y, and 4–18y are also esti­mated by the US IOM (2001) to be skewed.
• Reliable data on the distri­bution of usual nutrient intakes for the group being assessed.
• Knowledge of the expected correlation between intakes and require­ments among indi­viduals: for all nutrients (except energy); this is assumed to be very low.

Reliable infor­mation on the distri­bution of usual intakes of the nutrient in the group can be obtained by adjusting the distri­bution of observed intakes statistically in an attempt to partially remove the effects of day-to-day variability in intakes (i.e., within-person variation) (Chapters 6). This yields an adjusted intake distri­bution, as discussed in detail in Chapter 3; Section 3.3.2. Such an adjustment can be applied, provided at least two independent days or three consecutive days of dietary intake data for a representative subsample of indi­viduals in the group, have been collected. Four statistical methods are available for estimating the distri­bution of usual intakes. The methods have different features which are summarized in Box 3.3; Chapter 3; Section 3.3.2.

Figure 8b.3

shows an example of observed (unadjusted) and adjusted zinc intakes for a group of Malawian women. The intakes were obtained from two independent 24h recalls from each woman and adjusted to remove the effects of day-to-day (within-person) variability in intake following the procedure outlined in Chapter 3. Note that the adjust­ment process has yielded a distri­bution with the same mean (6.6mg/d) but reduced variability. Note that any bias arising from under- or over-reporting of food intakes is not removed by this adjust­ment process.

In this statistical approach, a prob­ability of inade­quacy can be calculated for any level of usual intake because infor­mation on the distri­bution of require­ments for the group is known. Inade­quate intakes associated with the usual intake of each indi­vidual in the group is determined first, followed by the average for the group as a whole. The latter is esti­mated as the weighted average of inade­quate intakes for each indi­vidual, as outlined below (Barr et al. 2002).

The calculations for the prob­ability approach can be performed manually or by a computer. For the manual calculation, first the nutrient intakes are classified into six classes defined by the AR and the associated SD limits as shown in Table 8b.5

Table 8b.5. Assignment of “risk” or prob­ability statements to six classes of observed intakes expressed as pro­portions of the Estimated Average Require­ment. An assumption in this model is that the distri­bution of require­ments for most nutrients is symmetrical with the coefficient of variation at 10% or 15%. Compiled from Beaton (1985).

Class	A. Individual's intake in terms of the distri­bution of require­ments	B. Probability that indi­vidual intake doesn't meet the require­ment
1	< −2SD	1.00
2	−2SD to −1SD	0.93
3	−1SD to mean	0.69
4	mean to + 1SD	0.31
5	+ 1SD to + 2SD	0.07
6	> +2SD	0.00

(column A). The number of indi­viduals with intakes of the nutrient within each class is then determined; this number is then multiplied by the appropriate prob­ability for each class (Table 8b.5, column B) to give the number of indi­viduals per class who were likely to have intakes below their own require­ments. The numerical prob­abilities are derived from the area beneath the “normal” curve between the stated SD limits. The sum of the numbers in the six classes gives the total number of indi­viduals in the population group with inade­quate intakes for the nutrient. This sum can be expressed as a percentage of the total population group to give a prob­ability esti­mate for the population group as a whole. For example, assume that in a population group of n = 4600, the numbers of indi­viduals with usual intakes of vitamin C within classes one to six, respectively, are 300, 500, 800, 900, 1400, and 700. When multiplied by the appropriate prob­abilities for each class (Table 8b.5, column B), the number of indi­viduals per class likely to have vitamin C intakes below their own require­ments becomes 300, 465, 552, 279, 98, and 0. The sum of these numbers equals 1694, and this represents the total number of indi­viduals with inade­quate intakes for vitamin C. When expressed as a percentage, 37% of the total population are predicted to have intakes of vitamin C below their own require­ments.

The full prob­ability approach must be used for assessing the preva­lence of inade­quate intakes of iron for women between the ages of menarche and menopause because the distri­bution of iron require­ments for this life-stage group is highly skewed: some women have high menstrual iron losses. Calculations can be performed by using one of the four computer programs itemized in Box 3.3  Chapter 3; Section 3.3.2. Alternatively, for iron a spread­sheet can be used for these calculations in conjunction with tabulated data presented in Gibson and Ferguson (2008), provided the distri­bution of observed intakes have been adjusted statistically to yield infor­mation on the usual intakes. See: Gibson and Ferguson (2008). Tables in this publication provide data for the prob­ability of inade­quate intakes of iron (mg/d) for adolescent girls age 14–18y, adult women prior to men­opause, and children age 1–3y and 4–8y. Different ranges of usual iron intakes are presented at three levels of bio­avail­ability: low (5%), inter­mediate (10%); and high (15%).

Table 8b.6. List of nutrients with dietary reference intakes (DRIs) for the United States and Canada. The √ indicates that the specific DRI has been defined for that nutrient. EAR, Estimated Average Require­ment; RDA, Recommended Dietary Allowance; AI, ade­quate Intake; UL, Tolerable Upper Intake Level. From IOM (2000a); IOM (2000b); IOM (2001).

Nutrient	EAR	RDA	AI	UL
Calcium	√	√		√
Copper	√	√		√
Chromium			√
Iodine	√	√		√
Iron	√	√		√
Magnesium	√	√		√
Manganese			√	√
Molybdenum	√	√		√
Phosphorus	√	√		√
Selenium	√	√		√
Zinc	√	√		√
Thiamin	√	√
Riboflavin	√	√
Niacin	√	√		√
Vitamin B6	√	√		√
Folate	√	√		√
Vitamin B12	√	√
Vitamin C	√	√		√
Vitamin A	√	√		√
Vitamin E	√	√		√
Vitamin D	√	√		√
Fluoride			√	√
Sodium			√	√
Potassium			√
Biotin			√
Choline			√	√
Vitamin K			√
Pantothenic Acid			√

An example of how to use the table to esti­mate the preva­lence of inade­quate intakes of iron for men­struating women con­suming a diet with 5 percent average bio­avail­ability of iron is also given in Chapter 10 of Gibson and Ferguson (2008). Comparable tables for U.S. adolescent girls (14–18y) and men­struating women classified as non-oral con­traceptive users or con­traceptive users (assuming 60% reduction in menstrual iron loss) and based on 18% bio­avail­ability are available in IOM (2001).

Note that the full prob­ability approach should not be used for energy. Energy intake is highly correlated with require­ment among non-obese indi­viduals (even after age, sex, and weight adjust­ments have been made).

At present, the absence of reliable esti­mates of the ARs for all nutrients limits the general applicability of the prob­ability approach to esti­mate the preva­lence of inade­quacy for every nutrient. Table 8b.6 summarizes the nutrients for which an AR and CV% of the require­ment have been set by the U.S. Food and Nutrition Board (IOM, 2003). In the United Kingdom, ARs have been documented for iron, calcium, zinc, vitamin C, vitamin B₁₂, folate, riboflavin, and vitamin A (COMA, 1991). The WHO / FAO (2004) report also provides ARs for selected nutrients.

8b.3.2 EAR Cutpoint Method

A shortcut to the prob­ability approach has been devel­oped by Beaton (1994), and adopted by the U.S Food and Nutrition Board (IOM, 2000) for assessing the pro­portion of inade­quate intakes in a group. This simpler version is termed the EAR cutpoint method and does not require infor­mation on the exact require­ment distri­bution. The EAR cutpoint method can be used, providing the following three con­ditions are met:

• Intakes and require­ments of the nutrient are independent (assumed to be true for all nutrients, but is not true for energy).
• The distri­bution of intakes in the population group must be more variable than the distri­bution of require­ments (which is generally the case in free-living Individuals).
• The distri­bution of require­ments in the group is approx­imately symmetrical about the AR (but this is not the case for the iron require­ments of children aged 1 to 8y or women between the ages of menarche and menopause).

Again, data on the usual nutrient intakes are required, and these are best obtained by statistically adjusting the observed intakes for day-to-day variation (i.e., within-person variation), as discussed in Chapter 3. In this simplified version, the preva­lence of inade­quate intakes within the group is simply esti­mated by counting the number of indi­viduals in the group with usual intakes below the AR, instead of estimating the level of inade­quate intakes of each indi­vidual separately. This preva­lence is represented by the shaded area to the left of the AR under the curve showing the distri­bution of usual intakes, as shown in Figure 8b.4. The larger area to the right of the AR represents the majority with usual intakes above the AR. Further theoretical justification for this approach can be found in Carriquiry (1999) and IOM (2003).

This EAR cutpoint method is especially useful when the actual preva­lence of inade­quate intakes in the group is close to 50%. As the true preva­lence approaches zero, or 100%, the performance of this method declines, even if the con­ditions listed above are met.

In addition, in circum­stances when the variability in intakes is very low, as may occur for groups fed similar diets, then the full prob­ability approach should be used instead of the EAR cutpoint method. Some examples of simulations used to assess the performance of the EAR cutpoint method in different situations are given in (IOM, 2000).

Currently, the EAR cutpoint method based on the U.S Food and Nutrition Board Dietary Reference Intakes (NRVs equiv­alent) can be applied to assess the preva­lence of inade­quate intakes among population subgroups for the following nutrients: calcium, copper, iodine, magnesium, molybdenum, phosphorus, selenium, zinc, thiamin, riboflavin, niacin, vitamin B₆, folate, vitamin B₁₂, vitamin C, vitamin A, vitamin D, and vitamin E (Table 8b.6). As noted earlier the EAR cutpoint method cannot be used for assessing iron intakes for men­struating adolescents aged 14–18y and men­struating women because their distri­bution of iron require­ments is skewed, although it can be used with these groups for the other nutrients listed above.

The EAR cutpoint method has been used to identify nutrients of con­cern when revising the USDA food assistance programs based on US national survey data (Trumbo et al., 2010), as well as for assessing the adequacy of usual zinc intakes from national food con­sumption surveys con­ducted in several low- and middle-income countries (Hess, 2017).

8b.3.3 Using 77% Percent of the Recommended Intake (RI₉₈) as a Cutoff Value

In some tables of NRVs, esti­mated average require­ments (i.e, ARs) for nutrients are not specified, as noted earlier. In such cases, approximations for the esti­mated average require­ments can be calculated, provided the RI (or equiv­alent) for each nutrient approx­imates the mean require­ment esti­mate plus two standard deviations, with a specified coefficient of variation (i.e., RI₉₈) (NRC, 1986). The pro­portion of the population with usual intakes below the derived AR is then calculated, as described in Section 8b.3.2.

A cutoff value of 77% of the RI is sometimes used. This approach assumes a CV for the nutrient of 15% about the AR. Such an assumption will yield a con­servative esti­mate of nutrient inade­quacy compared to that based on a CV for the nutrient of 10% about the AR. Use of the latter CV corres­ponds to a cutoff of approx­imately 83% of the RI instead of 77%; hence, it will yield a larger percentage of the group likely to have inade­quate intakes. Briefel et al. (2000) used 77% of the 1989 U.S RDA values for zinc as a cutoff to evaluate the zinc intakes of the U.S population in the National Health and Nutrition Examination Survey III 1988–1994, prior to the release of the EAR for zinc by the IOM (2001).

Few ARs have been published by WHO / FAO. However, a table of con­version factors that can be used for calculating ARs from the WHO / FAO (2004) RNIs (equiv­alent to RIs) is available in WHO (2006) (Annex C) along with a table in the text depicting the calculated AR values. No ARs can be calculated from the WHO / FAO RNIs for iron for adolescent girls, men­struating women (19–50y), or children (< 9y) because of the skewed distri­bution of require­ments for iron for these groups. The con­version factors that have been used in WHO (2006) to calculate the WHO/FAO ARs are based on standard deviations derived by the U.S Food and Nutrition Board of the Institute of Medicine and used to calculate the U.S and Canadian Recom­mended Dietary Allowances (RI equiv­alent).

8b.3.4 Use of Adequate Intake

The Adequate Intake (AI) is esti­mated in a number of different ways, depending on the nutrient and the life stage group. When the AI has been set based on the mean intake of a healthy population, then if the study group's mean intake is at or above the AI, the group can be assumed to have a low preva­lence of inade­quate intakes (Table 8b.1), although the actual preva­lence of inade­quate intakes cannot be established. When the AI is used in this way, the distri­bution of intakes does not have to be adjusted for within-person variation because only the mean or median intake is being examined for comparison. However, no assumptions can be made about the preva­lence of inade­quate intakes when the mean or median intake of a group falls below the AI because the distri­bution of require­ments is unknown (Barr et al. 2002; Murphy and Poos, 2002).

8b.3.5 Use of Upper Intake Level

When any comparison is made with the Upper Intake Level (UL), it is important to note if the UL assess­ment for the nutrient of interest is based on infor­mation on usual daily intakes from all sources or only from supplements, fortificants, and medications. The preva­lence of potentially excessive intakes is esti­mated by assessing the pro­portion of the group with usual intakes above the UL. The goal is to have a low pro­portion of a group with intakes above the UL (Barr et al. 2002; Murphy and Poos, 2002). Before an assess­ment is made, the intake distri­bution must be adjusted to remove the effect of within-person variation in intakes (see Chapter 3). Because of the uncertainties and the variability in indi­vidual sensitivities to the adverse effects, the actual preva­lence of adverse health effects in the group will seldom be equal to the pro­portion with intakes above the UL. Moshfegh et al. (2005) assessed the pro­portion of the population in the U.S NHANES (2001–2002) survey with intakes above the UL for eleven nutrients.

Table 8b.7. Data and evaluation of a hypothetical group's diet. Data for children 4–8y, from 1994–1996 Continuing Survey of Food Intakes by Individuals. UL, Upper Intake Level; AR, Average Require­ment; AI, ade­quate Intake; RI, Recommended Intake; inade­quacy, percentage of intakes below the AR; Excessive intakes, percentage of intakes above the UL. The intakes were adjusted to remove the effects of day-to-day variation before these assess­ments were made. Note that the AI for calcium was replaced by an AR in 2011, so the appropriate assessment method now would be to determine the proportion of the group with intakes below the AR. From Murphy and Poos (2002).

	Thiamin (mg)	Magnesium (mg)	Calcium (mg)	Vitamin C (mg)
Group Mean intake	1.44	212	838	96
Require­ment	0.5 (AR)	110 (AR)	800 (1997 AI)	22 (AR)
inade­quacy (%)	< 1	5	Low	< 1%
UL	None set	110	2500	650
Excessive intake (%)	Unknown	Unknown (supps only)	< 1	< 1

Table 8b.7 provides an example of the use of all the approaches described above for assessing nutrient intakes of a group derived from a national nutrition survey. Further details are given in Murphy and Poos (2002).

8b.3.6 Energy Intakes

As noted for indi­viduals (Section 8b.2.6), the prob­ability approach cannot be used to esti­mate the preva­lence of inade­quate or excessive intakes of energy in a group because of the expected high correlation between energy intake and energy require­ments among indi­viduals. The latter violates one of the assumptions required for the adoption of the prob­ability approach. Instead, the group mean energy intake can be compared with the mean esti­mated energy require­ment (EER) for the group, taking into account the ages, sexes, heights, weights, and physical activity levels of the indi­viduals in the group. If the mean intake is equal to the mean EER, energy intake can assumed to be ade­quate, whereas if the mean intake exceeds or falls below the EER, then the group on average is likely to be gaining or losing weight, respectively. Again, because only the mean is calculated, the intake distri­bution does not need to be adjusted for within-person variation in intakes, as noted for the AI (Section 8b.3.4).

Alternatively, as under-reporting of energy intake in dietary assess­ment is ubiquitous, the adequacy of the group's energy intake can also be assessed using the body mass index (BMI). The pro­portion of a group of U.S adults with a BMI below or above the normal range of 18.5–25kg/m² would be classified as having inade­quate or excessive energy intakes, respectively for their activity level, whereas for U.S children and adolescents, the pro­portion with BMI-for-age < 5^th percentile or ≥ 85^th percentile should be used (Kuczmarski and Flegal, 2000).

For inter­national use for children 0-5y, underweight and overweight are defined as BMI-for-age <−2 Z‑score and above +2 Z‑score, respectively, of the WHO Child Growth Standards 0–5y (WHO, 2006), but <−2 Z‑score and above +1 Z‑score for the BMI-for-age WHO Growth Reference for children 5–19y (de Onis et al, 2006).

8b.3.7 Macro­nutrient Intakes

For macro­nutrients with a reference intake range, the pro­portion of the group with usual intakes (adjusted for within-person day-to-day variation) outside the AMDR can be assessed. If the preva­lence outside the range is high, then an inter­vention may be needed.

8b.4 Using the NRVs for planning nutritious diets

As shown in Figure 8b.1, NRVs can also be used to plan diets at the indi­vidual or group level. Planning for an indi­vidual involves setting intake targets that ensure a nutritionally ade­quate diet, while also being acceptable, whereas for a group, the goal is to determine a desirable intake distri­bution that minimizes the preva­lence of inade­quate or excessive intakes. Numerous applications for planning nutritious diets exist, including dietary counseling for indi­viduals, developing menus for institutions, or designing inter­ventions for high-risk groups, as shown in Table 8b.2.

8b.4.1 Using the NRVs for planning nutritious diets of indi­viduals

The goal of planning a diet for an indi­vidual is to ensure there is a low prob­ability of inade­quacy and the potential risk of an excessive intake is small. This can be achieved by ensuring that the usual intake of the indi­vidual meets the RI₉₈, because by definition, the intake at that level should be ade­quate for almost all (98%) indi­viduals. Use of the AR as a goal for the nutrient intake of an indi­vidual is not appropriate because an intake at this level would be ade­quate for only 50% of indi­viduals. When setting the RI₉₈, however, knowledge about the distri­bution of require­ments for many nutrients remains limited, so an assumption about the coefficient of variation of the require­ment is often made, as noted in Chapter 8a. This has led to debate over the use of the RI₉₈ as the goal for planning diets at the indi­vidual level (Beaton, 2006; Murphy et al. , 2006). Nevertheless, at present the RI₉₈ remains the most appropriate target for the nutrient intake for indi­viduals, at least until more accurate data on the require­ment distri­butions are available.

To avoid a potential risk of adverse effects, the nutrient intakes of an indi­vidual should not exceed the UL. This means that the diet of an indi­vidual should have usual nutrient intakes that fall between the RI₉₈ and the UL. For those nutrients with only an AI, then nutrient intakes for an indi­vidual should fall between the AI and the UL.

Planning for an indi­vidual's energy intake is unlike other nutrients. For most nutrients, there is essentially no risk if an indi­vidual consumes an intake that may marginally exceed his or her require­ment (i.e., the RI₉₈ exceeds the require­ments of almost all (97–98%) indi­viduals in a group). However, in the case of energy, consuming an energy intake that met the require­ments of 97–98% of a group would lead to weight gain in that proportion of indi­viduals. Accordingly, energy require­ments of indi­viduals are best monitored by assessing their body weight status — those with BMI in the normal range who are maintaining their weight (or gaining weight appropriately during growth) are considered to be meeting their energy require­ment. If an esti­mate of energy needs is required for planning purposes, an approximation can be provided by using the equations for EER, which consider age, sex, height, weight and physical activity level. However, because there is variability in energy require­ments even among indi­viduals with the same characteristics, body weight must be monitored and intake adjusted where necessary (Barr et al., 2003). For macro­nutrients (expressed as percentage of energy), the goal is to ensure that the intakes from the indi­vidual's diet falls within the AMDR ranges.

Table 8b.8. Data and assess­ment of the nutrient intakes of a hypothetical indi­vidual's diet. Data for a 30y man observed for 3 days and thus assumed to reflect the usual intake. DFE: Dietary folate equiv­alent. RI₉₈ recommended intake. UL Upper Intake Level. From Murphy and Vorster (2007).

	Thiamin (mg)	Ribo- flavin (mg)	Folate (µg) DFE	Zinc (mg)	Phos- phorus (mg)
Man's avg. daily intake	1.3	1.1	400	10.3	3,800
RI98	1.2	1.3	400	11.0	700
UL	None	None	1,000	40	4,000
Proposed change in in intake	None	Inc- rease	None	Inc- rease slightly	None

Planning a nutritious diet at the indi­vidual level may involve counseling indi­viduals with special needs such as vegetarians and athletes, or those requiring therapeutic diets, as well as providing food-based dietary guidance. Table 8b.8 provides an example of how to plan to change the nutrient intakes of a hypothetical 30y male indi­vidual. In this example, provided the three days of intake collected represented his usual intake, the indi­vidual has been advised to increase his intake of both riboflavin and zinc so that they meet the RI₉₈; no other changes were needed as none of the intakes exceeded the UL (Table 8b.8). Note that in this example, the evaluation of the indi­vidual's nutrient intake was conducted using the more practical qualitative approach described in 8b.2.4, rather than the statistical approaches described in 8b.2.1 through 8b.2.3.

8b.4.2 Using NRVs for planning nutritious diets for groups

Planning diets for groups is more complex than for indi­viduals because of the wide range of nutrient intakes in a group arising from differences in the amount and types of food con­sumed. The goal is to alter the distri­bution of current nutrient intakes within the group to reduce the preva­lence of inade­quate and excessive intakes, where necessary. The three NRVs used for planning nutrient intakes for a group are the AR, the AI, and the UL; the RI₉₈ should not be used for groups. For more details on planning diets for groups, the reader is referred to IOM (2003) and Murphy and Barr (2005).

The EAR cutpoint method described in Section 8b.3.2 is also used for planning the diets of groups, with the goal of minimizing the pro­portion of the group with intakes below the AR and above the UL. Steps in planning diets for groups, using the EAR cutpoint method are shown in Box 8b.2. The method can only be used for those nutrients with a defined AR and UL, and for which the require­ment distri­bution is approx­imately symmetrical.

As noted earlier, because iron require­ments for certain life-stage groups are skewed, the full prob­ability approach must be used to calculate the preva­lence of inade­quate or excessive intakes for these groups using software described earlier (Chapter 3; Section 3.3.2). Alternatively, published tables of the distri­bution of iron require­ments can be used to esti­mate manually the prob­ability of inade­quacy for each indi­vidual within the group, from which the prob­ability of inade­quacy for the whole group can be calculated; refer to Section 8b.3.1 for more details.

Note that irrespective of which method is used, the distri­butions of observed intakes, both before and after the intervention, must always be adjusted statistically to yield the usual intake distri­bution and thus remove the effects of day-to-day variations; see Chapter 3 for details of the statistical techniques to use.

When only an AI has been set for a nutrient, it is not possible to esti­mate the preva­lence of inade­quate intakes in the group for that nutrient, and instead the goal is to ensure that the average intake of the group for that nutrient is at or above the AI.

Table 8b.9. Current and target usual zinc intake distri­butions (mg/d from food) for girls 9–13y.
* NHANES III data. The distri­bution is for food intake only, assuming that the girls for which planning is being done do not take supple­ments.
† AR = 7mg/d, ‡ UL = 23mg/d
From Murphy and Barr (2005).

	Current Intake*	Target Intake	Change
Mean	9.6	10.4	+0.8
Percentile
2nd	6.2	7.0	+0.8
5th	6.5	7.3	+0.8
10th	7.1	7.9	+0.8
25th	8.1	8.9	+0.8
50th	9.4	10.2	+0.8
75th	10.9	11.7	+0.8
90th	12.5	13.3	+0.8
95th	13.5	14.3	+0.8
99th	15.5	16.3	+0.8
% below EAR†	9%	2%	−7%
% above UL‡	0%	0%	None

When planning the energy intakes of groups, the goal is for the mean intake of the group to be approx­imately equal to the EER. The latter represents the average energy require­ment for the group. No RI₉₈ is set for energy because intakes above require­ments lead to weight gain. The EAR cutpoint method should not be used for planning energy intakes (Murphy and Barr, 2005). Because only the mean intake for the group is calculated, the intake distri­bution does not need to be adjusted for day-to-day variation, as noted earlier.

When con­sidering the AMDR, the diets of groups should be planned to minimize the preva­lence of intakes outside the AMDR. In this way, the risk of chronic diseases will be reduced, while ensuring ade­quate intakes of other essential nutrients (Murphy and Barr, 2005).

Example of the process for planning zinc intakes using the EAR cut-point method

In the example shown in Table 8b.9, the first step is to select the planning goal, which in this example will be to have no more than 2–3% of girls aged 9–13y to have usual zinc intakes less than the AR (i.e., 7mg) and no more than 2–3% above the UL (i.e., 23mg/d). Step 2 is to esti­mate the target intake distri­bution. To complete this step, infor­mation on the current intake distri­bution for zinc is needed. In this example, data on the usual zinc intake distri­bution of girls aged 9–13y from NHANES III is used (Table 8b.9). Note that the esti­mated preva­lence of inade­quate intakes based on this current intake distri­bution is 9%, above the goal of no more than 2–3% below the AR. Note also that the AR for zinc of 7mg approx­imates the 10th percentile of the current usual intake distri­bution. Hence, assuming our planning goal is to reduce the preva­lence of inade­quate intakes to 2%, then the distri­bution of usual intake needs to be shifted such that the current intake at the 2nd percentile (currently 6.2mg/d) is increased to corres­pond to the AR of 7mg. Thus, an increase of 0.8mg is needed, and assuming that the shape of the distri­bution does not change, then intake at every percentile would also increase by 0.8mg/d. This would yield a target median intake of 9.4 + 0.8 = 10.2mg as shown in Table 8b.9. Figure 8b.5 shows the current usual intake distri­bution and the proposed target usual intake distri­bution for this group of girls aged 9–13y.

The next step is to plan a menu to meet the target intake distri­bution, which in this example could be achieved by substituting some of the foods currently con­sumed with those higher in zinc, recognizing that not all food will be con­sumed. In the final step, the effect of the new menu is examined. This can be achieved by collecting dietary intake data from each girl in the group, calculating zinc intakes, and after adjust­ing the distri­bution of observed intakes to usual zinc intakes, estimating the preva­lence of inade­quate and possible excessive intakes. If the planning goal of 2% with intakes below the AR has not been met, then a new plan will be required.

In this example only zinc is con­sidered whereas in practice intakes of all nut­rients would be con­­sidered. The planner then has the task of deciding which of the nut­rient intakes need to change necessitating the use of a nut­rient calculation software package. The nutrient profiles of the proposed menus can be calculated using the software, so that the necessity of further changes can be assessed.

Health Canada followed the process outlined above when planning diets for their publication entitled “Eating Well with Canada's Food Guide” (Health Canada, 2011). Their goal was to ensure a low preva­lence of nutrient intakes below the AR when a life-stage and sex group chooses foods from food groups following the recom­mended dietary pattern; see Katamay et al. (2007) for more details of the methods applied. However, the process to develop the subsequent Canadian Food Guide, released in 2019, did not include a comparable assessment of the nutrient adequacy of the recommended dietary pattern (Barr, 2019). A modification of this approach has also been used in the U.S to identify nutrient targets for school meals (IOM, 2010b).

There are several other challenges that may be encountered when planning diets for groups. These are summarized in Murphy and Barr (2005) and discussed in more detail in IOM (2003). As an example, all the approaches described above for planning diets for groups assume that the age and sex of the indi­viduals within the group are similar, thus permitting a single set of ARs and ULs to be applied. However, in some circum­stances, groups are hetero­geneous making the planning process more challenging. Currently the recom­mended approach for hetero­geneous groups is to first identify the subgroup with the greatest nutrient require­ment per 1,000kcal (i.e., nutrient density) and second, apply the approaches described above to plan the intakes for each nutrient. Here care must be taken to ensure that no subgroups within the group have the potential for excessive intakes. Finally, after the new menus or food patterns have been implemented, then the actual nutrient intake distri­butions must be checked to ensure that the preva­lence of inade­quate and potentially excessive intakes remains low.

Applications for groups include planning diets for institutional feeding such as school lunch programs, residential schools, hospitals, prisons, nursing homes, the military etc, and in some cases, emergency food assistance programs (Murphy and Barr, 2005). The approach is also used for establishing appropriate levels of nutrient fortification of foods and described in detail in WHO (2006). For more details of these applications, the reader is advised to con­sult Murphy and Vorster (2007).

Acknowledgments

RSG would like to thank Professor Susan Barr who kindly reviewed this chapter and suggested some helpful improvements, as well as collaborators, particularly my former graduate students. RSG is grateful to Michael Jory for the HTML design and his tireless work in directing the trans­ition to this HTML version.