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4
A Theoretical Approach
Using Nutrient Density
to Plan Diets for Groups
SUMMARY
In this chapter the use of nutrient densities is proposed as a means
to plan diets for groups comprised of distinct subgroups with differ-
ent nutrient requirements and different usual energy intakes. Two
approaches are described. The first relates the median of the target
nutrient intake distribution to the mean energy intake of each sub-
group within the larger group, for which a diet is being planned.
These values are then compared to set a planning goal for the whole
group. This approach, however, does not consider the variability of
energy intakes within a subgroup, so it may require repeated itera-
tions of planning and assessment. The second approach involves
planning for an acceptable nutrient density ratio. This approach
takes into account the differences both in energy and nutrient needs
of the distinct subgroups to derive target nutrient intake distribu-
tions expressed as nutrient densities. The medians of the target
nutrient density intake distributions for the various subgroups are
then compared to set planning goals for the whole group. Impor-
tantly, the methods described here are not designed to plan for
desirable body weights (which might require weight loss or gain),
but to ensure that nutrients are provided in sufficient concentra-
tions in the diet to satisfy individuals' nutrient needs if they consume
sufficient food to maintain energy balance. These approaches are
theoretical in nature at this time and should be further explored.
89

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go
DIETARY REFERENCE INTAKES
INTRODUCTION
The methods presented in Chapter 3 assume that the planning
activity will be conclucteci for a group of people possessing similar
energy and nutrient requirements; for example, girls age ci 9 to 13
years or adult men age ci 31 to 50 years. Nutrient requirements are
specific to life stage and gentler, but there are many situations in
which planning diets for groups means planning for population
groups that include inclivicluals of different genders and ages and
thus different nutrient and energy requirements. Planning school
meals, for example, typically involves offering meals to both boys
and girls of ages ranging from ~ to 18 years. Planning the benefit
levels for the U.S. Food Stamp Program must include consideration
of the combination of ages and genders present in recipient house-
holcis. Planning the meals in institutional settings such as prisons or
hospitals must recognize differences in residents' requirements related
to age, weight, gentler, and possibly markoci differences in habitual
levels of physical activity.
When applying the concept of a target usual intake distribution to
planning for groups that include inclivicluals with different energy
and nutrient requirements, the heterogeneity of the group must be
consiclereci. One approach that has been used is to calculate the
average nutrient requirement for incliviclual group members and
use this average requirement in planning. The problem with this
approach, however, is that even if the planning appears to meet the
group neeci for the nutrient, there is no guarantee that nutrient
intakes will be clistributeci among inclivicluals in the group in a
manner to satisfy nutrient requirements. For example, in planning
for iron intakes for a group of men and women, simply computing
the average iron requirement and planning accordingly does not
ensure that incliviclual group members will have their iron require-
ment satisfied. In fact, when planning cliets or menus that provide
the average iron requirement, it is likely that food (anci iron) will
be clistributeci according to energy neecis of the inclivicluals in the
group. As a result, there will almost certainly be serious cleficits in
iron intakes for the women, who have lower energy requirements,
and surplus iron intakes for the men with their higher energy require-
ments (FAD/WHO, 1970~. Thus, to achieve a targeted group preva-
lence of inadequacy, subgroup differences in both nutrient and
energy requirements need to be taken into account in the planning
process.
The use of nutrient densities has been proposed as one means to
account for known differences in the energy and nutrient require-

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 91
meets of specific population subgroups (FAD/WHO, 1970; FAO/
WHO/UNU, 1985; TOM, 1995, 2002b). This approach involves cal-
culating the required nutrient density for the cliet such that when
inclivicluals' requirements for food energy are achieved, there is a
high likelihood that the nutrient requirement for inclivicluals within
the group also will be satisfied. In planning for nutrient acloquacy,
it must be assumed that inclivicluals' usual energy intakes are suffi-
cient for them to maintain energy balance with current levels of
physical activity and body energy stores, or in other words, that
their energy intake equals their energy expenditure.
Nutrient density is the ratio of the amount of a nutrient in foods to the
energy provided by these same foods. Nutrient density is frequently e~c-
pressed as the amount of the nutrient per 1, 000 kcal or M] of energy.
Although nutrient density may be used to describe foocis, meals,
cliets, or food supplies, its use in clietary planning is primarily to
describe daily intake targets.
Using the nutrient density concept, a number of approaches to
planning the cliets of heterogeneous groups could be consiclerecl.
The approach used clepencis in part on whether the intakes being
planned will be basest on consumption of a single food (e.g., an
emergency relief ration) or of varied amounts of multiple foocis,
the more common planning scenario. A method that can be used
to plan for cliets consisting of a single food is presented in Appen-
clix C, while two approaches are presented below that could be used
to plan intakes when the cliet consists of multiple foocis.
The first approach to planning using nutrient densities is based
on a comparison of the target meclian nutrient intake to the aver-
a~e ener~v requirement. This simple approach is based on the
methods presented in Chapter 3 and is referred to as the simple
nutrient density approach. It involves planning nutrient intakes for
the subgroup with the highest meclian nutrient neecis relative to
their energy neecis (e.g., the most vulnerable subgroup); it is assumed
that the other subgroups will obtain acloquate nutrient intakes if
they fulfill their energy requirements. This approach, while simple
and straightforward to implement, does not consider the variability
in energy intakes within a subgroup and may therefore result in a
prevalence of inacloquacy that differs from the planning goal.
The second approach to planning using nutrient densities is based
on the distribution of intakes expressed as a nutrient density.
Although this approach has not been tested in practical situations,
it considers the variability of energy intakes within a subgroup as
~ A 1

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92
DIETARY REFERENCE INTAKES
well as the distribution of nutrient intakes, and therefore offers the
most theoretically correct method of determining the appropriate
nutrient density to use for planning. It includes examining the clis-
tribution of intakes expressed as a nutrient density for each sub-
group and determining the target nutrient density distribution for
each. The nutrient density to be used for planning should be the
highest target nutrient density among the subgroups.
For each of these approaches, an assessment and adjustment of
the target distribution as neecleci should follow the planning activity.
For the first approach, which floes not consider variability in energy
intakes, several iterations of planning and assessment may be neecleci.
The second approach should more accurately identify the correct
target nutrient density so fewer assessment iterations would be
expected. In aciclition, each approach should include a comparison
of the projected target usual intake distribution to the Tolerable
Upper Intake Level (UL) for each subgroup. By planning for a
nutrient density that is acloquate for the subgroup with the highest
neecis, it is possible that a substantial proportion of some of the
other subgroups will consume cliets that exceed the UL.
Each of the methods proposed above requires an estimate of the
distribution of usual nutrient intakes in the various subgroups of
interest. As clescribeci in Chapter 3 and more fully elsewhere (IOM,
2000a), the distribution of usual nutrient intakes for each subgroup
can be estimated by assessing the nutrient intakes of a representa-
tive sample over at least two nonconsecutive or three consecutive
clays, and adjusting the observed distribution of nutrient intakes for
within-person variation.
An estimate of energy intake is also required. Assuming that the
group is in energy balance, one could use estimates of either energy
intake or energy expenditure. For the first approach, the mean energy
intake or expenditure in each subgroup of interest is used, while
for the more theoretically correct approach, an estimate of the dis-
tribution of usual energy intakes or expenditures is neecleci. As is the
case with nutrients, in principle, the distribution of usual energy
intakes in each subgroup can be estimated by assessing the energy
intakes of a representative sample over two or more clays and acljust-
ing the observed distribution of energy intakes for within-person
variation. The distribution of energy expenditures in each subgroup
can be estimated using the equations clevelopeci to estimate the
energy expenditure of inclivicluals in the group (IOM, 2002a).
However, both of these estimates (energy intake and energy
expenditure are subject to error. Estimates of energy expenditure
obtained using energy expenditure equations require ciata on

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 93
height, weight, age, and physical activity level. These estimates may
be biased if self-reporteci values for height and weight are used, as
height is frequently overreporteci and weight unclerreporteci, par-
ticularly among older adults (Kuczmarski et al., 2001~.
Error may also be introcluceci by assumptions regarding the phys-
ical activity level of group members. Because the energy expencli-
ture equations were clevelopeci very recently, no ciata are available
on the extent of this error.
On the other hanci, as cliscusseci in Chapter 1, problems of system-
atic underreporting of energy intakes in clietary intake surveys have
been clocumenteci repeatedly, suggesting that this is likely a wicle-
spreaci problem in intake assessments (Black and Cole, 2001~. There
is also evidence of systematic overreporting of energy intakes among
some inclivicluals (Black and Cole, 2001~.
The following discussion assumes that one can approximate the
distribution of usual energy intakes in the subgroup of interest by
using self-reporteci energy intake ciata. It is important to recognize,
however, that insofar as systematic reporting errors distort the clis-
tribution of usual energy intakes, these errors may seriously bias
estimates of the distribution of both nutrient requirements and
nutrient intakes expressed as densities. Bias would also exist in esti-
mates of the target meclian nutrient intake expressed in relation to
the mean energy intake. Unfortunately, well-establisheci, valiciateci
statistical methods to identify and correct for uncler- or overreport-
ing energy intakes are currently lacking. Implications of systematic
reporting errors on the planning methods presented here are
examined at the end of this chapter.
The methods described in this chapter are not designed to plan for
desirable body weights (which might require weight gain or loss), but
rather to ensure that the nutrients are provided in sufficient concentrations in
the individuals' diets to satisfy their nutrient needs if they consume su~i-
cient food to maintain energy balance (e.g., to maintain current body
weight).
PLANNING FOR HETEROGENEOUS GROUPS USING A
COMPARISON OF TARGET MEDIAN NUTRIENT INTAKE
TO MEAN ENERGY INTAKE (OR EXPENDITURE)
The approach presented in this section is an extension of the
approach presented in Chapter 3 to plan nutrient intakes of homoge-
neous groups. It is possible that it may be less accurate than the

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94
DIETARY REFERENCE INTAKES
approach clescribeci in the following section that uses the clistribu-
tion of nutrient intakes expressed as a density; however, because it
is less complex to implement, it may serve as an interim approach
for planners. Chapter ~ provides specific examples of the two
approaches and discusses the differences in results.
Four steps are necessary to derive a target meclian nutrient intake
relative to energy for a heterogeneous group:
1. Obtain the meclian of the target nutrient intake distribution
for each subgroup of interest (as clescribeci in Chapter 3~.
2. Divicle this target meclian nutrient intake by the mean energy
intake or expenditure in each subgroup to obtain the target meclian
nutrient intake relative to energy.
3. Compare the target meclian nutrient intakes relative to energy
for each discrete subgroup to identify the subgroup with the high-
est nutrient intake required relative to its mean energy intake. Use
this to set planning goals for the whole group, but ensure that nu-
trient intakes of other subgroups will not be above the Tolerable
Upper Intake Level.
4. Assess whether the plan was successfully implemented. (This
step is particularly important with this approach.)
Step I. Obtain the target median nutrient intake.
The first step in this approach is to obtain the median of the
target nutrient intake distribution for each subgroup, following the
approach clescribeci in Chapter 3. For nutrients for which an Esti-
mateci Average Requirement (EAR) has been cletermineci, the target
meclian nutrient intake is the meclian of the distribution obtained
by repositioning (if necessary) the usual nutrient intake distribu-
tion in the subgroup of interest so that an acceptably low propor-
tion of inclivicluals in the subgroup has intakes below the EAR. In
the case of iron, for which the requirement distribution is skewoci,
the probability approach is used in place of the EAR cut-point method
in order to estimate the target meclian nutrient intake.
For nutrients with an Acloquate Intake (AI), the AI may be used as
a target meclian nutrient intake. Meclian intake at the AI should
leaci to a low prevalence of inacloquacy if the AI was set as the
meclian intake of a healthy group and if the variability in usual
intake of the group of interest is similar to the variability in intake
of the population used to set the AI. When either of these concli-
tions is not satisfied, there will be less confidence that achieving a
meclian intake at the AI will result in a low prevalence of inacloquacy.

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 95
Step 2. Divide the target median intake by the mean energy intake
(or expenditure) for each subgroup of interest.
Once the target median nutrient intake has been identified for
each subgroup within the larger group, it is possible to express the
nutrient intake in relation to energy, typically per 1,000 kcal. This is
done by dividing the target median nutrient intake by the mean
ener~v intake or expenditure. For examole. if the target median
in, 1 1 ~
zinc intake tor a group ot girls Y to In years ot age was lu.l mg and
their mean energy intake was 2,200 kcal, this would represent a
target of 4.6 mg/1,000 kcal. This would be done for each subgroup.
Step 3. Identify the subgroup with the reference intake and set ~lan-
ning goals for the entire group.
Once the target median nutrient intakes have been expressed
relative to the mean energy intake or expenditure for each sub-
group, a decision can be made regarding which subgroup s needs
will be used to plan intakes for the entire group. In many cases, one
might choose to plan using the needs of the most vulnerable sub-
group (e.g., the subgroup with the highest target median nutrient
intake relative to mean energy intake or expenditure). Diets that
would 1eau to intakes providing that amount of the nutrient per
1,000 kcal would then be planned (e.g., for zinc, if the vulnerable
subgroup was girls 9 to 13 years of age, the goal for intake would be
4.6 mg of zinc/1,000 kcal). If the needs of this subgroup are met,
the needs of other subgroups should be satisfied and the group
prevalence of inadequacy should be low. Alternatively, if the needs
of the most vulnerable subgroup would 1eau to intakes by other
subgroups that are excessive (and perhaps above the UL), it may be
preferable to use a less vulnerable subgroup to plan for the group
as a whole and to target the most vulnerable subgroup using eauca-
tion programs, special foods, or targeted supplementation.
~ 1 ~ 1 1 ~ '
Step 4. Assess whether the plan was successfully implemented.
cat ,
Assessing the adequacy of the group's nutrient intakes is particu-
larly critical when this approach to dietary planning is used. By
using only the mean energy intake or requirement of each sub-
group, it fails to consider the variability of energy intakes among
members of a subgroup. Accordingly, those with very low energy
intakes may not meet their nutrient requirements. Planners using
this approach must be willing to alternate planning and assessment

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DIETARY REFERENCE INTAKES
until the goals are achieved because the actual prevalence of inacle-
quacy that results from this approach may be quite different from
the level that was the target.
PLANNING FOR HETEROGENEOUS GROUPS
USING THE DISTRIBUTION OF NUTRIENT INTAKES
EXPRESSED AS A DENSITY
This section describes an approach to establish a target nutrient
density intake distribution for each of the subgroups in a heteroge-
neous group, assuming multiple foocis with different densities are
consumed. It could also be used to plan for a group consisting of a
single life stage and gentler. The first step in the procedure is as
clescribeci in Chapter 3: obtain a target usual nutrient intake clistri-
bution in each of the subgroups so that an acceptably low propor-
tion of inclivicluals in each subgroup have an inacloquate intake of
the nutrient. The target distribution of usual intakes expressed as
nutrient densities in each of the subgroups is cleriveci relative to the
distribution of nutrient and energy requirements in each of the
subgroups directly, and provides the planning goal for each sub-
group.
Three steps are necessary to derive a target usual density intake
distribution.
1. Obtain the target distribution of usual nutrient intakes for each
subgroup of interest.
2. Combine the target distribution of usual nutrient intakes with
the usual energy intake (or expenditure distribution in each sub-
group to obtain the target distribution of usual nutrient intakes
expressed as densities.
3. Compare the estimated target median density intake for each
discrete subgroup to identify the reference nutrient density and set
planning goals for the whole group, but ensure that nutrient intakes
by other subgroups do not exceed the Tolerable Upper Intake Lev-
el (UL).
Step I. Obtain the target distribution of usual nutrient intake.
The first step in planning intakes for a heterogeneous group is to
obtain the target usual nutrient intake distributions for each sub-
group, following the approach clescribeci in Chapter 3. For nutri-
ents for which an Estimated Average Requirement (EAR) has been
cletermineci, the target usual nutrient intake distribution is obtained

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 97
by repositioning (if necessary) the usual nutrient intake clistribu-
tion in the subgroup so that an acceptably low proportion of incli-
vicluals in the subgroup have intakes below the EAR. In the case of
iron, for which the requirements distribution is skewoci, the proba-
bility approach is used in place of the EAR cut-point method in
order to estimate the position of the target usual nutrient intake
distribution.
In Chapter 3 and in the simple approach clescribeci in the previ-
ous section in this chapter, the planning tool of interest was the
median of the target usual intake distribution. Here, however, the
entire target usual nutrient intake distribution is of interest. In order to
establish a target nutrient density intake distribution, it is necessary
to account for the variability in nutrient and energy intakes among
inclivicluals. If the goal is to plan intakes when each of the sub-
groups is provicleci a separate cliet (as would be the case, for example,
in an institution that houses men, women, and young inclivicluals
separately), then the planner neecis to proceed no further. The
methods presented in Chapter 3, and briefly revisited here, suffice
to plan intakes for a subgroup that is homogeneous with respect to
age and gentler. However, if a single cliet will be provicleci to a
larger group composed of inclivicluals from the various subgroups,
then the planner neecis to account for the differences in energy
consumption among inclivicluals in different life stage and gentler
groups.
Step 2. Obtain the target nutrient density intake distributions.
Once the target usual nutrient intake distribution for each life
stage and gentler subgroup of the larger group has been estab-
lisheci (Step 1), it is possible to determine the target usual intake
distribution of the nutrient expressed as a density. The target clistri-
bution of usual intakes estimated in terms of nutrient densities will
be such that an acceptably low proportion of inclivicluals in each
subgroup (in the example, 2 to 3 percent) have inacloquate nutri-
ent intakes.
While the method presented in Chapter 3 essentially consisted of
repositioning the usual nutrient intake distribution, an aciclitional
step is neecleci when planning for a heterogeneous group. The
target usual nutrient intake distribution must be combined with the
distribution of usual energy intakes in each subgroup to obtain the
target nutrient density intake distribution. The difference here is
that while the objective is to obtain a target intake distribution for
the nutrient expressed as a density, the density intake distribution

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98
DIETARY REFERENCE INTAKES
cannot be directly compared to the nutrient requirement clistribu-
tion to determine how it should be repositioned. Thus it is neces-
sary to acici an intermediate step to the procedure which consists of
deriving first the target usual nutrient intake distribution for each
subgroup, as was clescribeci in Step 1 above. The steps necessary to
carry out this derivation are explained in detail below.
Recall that nutrient density intake is clefineci as the units of a
nutrient consumed per 1,000 kcal. Thus, if an incliviclual consumes
2,000 kcal and 104 mg of vitamin C, then that incliviclual consumes
a cliet with a vitamin C density of 52 mg/1,000 kcal. Therefore, if
one knows an incliviclual's usual nutrient intake and her or his usual
energy intake, it is possible to calculate the nutrient density intake
for that incliviclual. The calculation above can be taken one step
further if one considers a group in which inclivicluals vary in their
usual nutrient intake. In the unlikely case in which everyone in the
group has the exact same usual energy intakes, say 2,000 kcal, then
given the distribution of usual nutrient intakes in the group, it is a
simple matter to calculate the usual intake distribution of the nutri-
ent expressed as a density: simply clivicle each usual nutrient intake
in the group by 2,000 and multiply by 1,000. However, individuals
vary in the amount of energy they consume, and therefore the cler-
ivation of the distribution of usual intakes of the nutrient expressed
as a density given the usual nutrient and energy intake distributions
is a bit more challenging. In this more realistic scenario, it is neces-
sary to take into account that inclivicluals vary not only on the
amount of the nutrient they consume, but also on the amount of
energy they consume.
Suppose that an incliviclual from the subgroup has a vitamin C
intake of 70 ma. If it is assumed that the correlation between vita-
min C intake and energy intake is moderate to low, then that nutri-
ent intake level may correspond to different combinations of energy
intakes and thus vitamin C intakes per 1,000 kcal. For example, the
usual intake of 70 mg may result in a vitamin C density intake of
46.7 mg/1,000 kcal if the incliviclual consumes 1,500 kcal/ciay or in
a density intake of 31.8 mg/1,000 kcal if the incliviclual's energy
consumption is 2,200 kcal/ciay.
The simple example above illustrates the importance of account-
ing for the variability in usual energy intakes among inclivicluals in
the subgroups that comprise the larger group. Given each possible
usual nutrient intake in the subgroup, one must calculate each of
the nutrient density intakes that may result given the distribution of
energy intakes in the same subgroup. To account for the variability
in energy intakes among individuals in the subgroup, average the

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 99
nutrient density intakes over the distribution of energy intakes in
the subgroup. The average is weighted by the frequency of con-
sumption of each energy level in the group. To obtain this average
density intake corresponding to each nutrient intake in the sub-
group, the following calculation is used:
Average nutrient density intake = ~ 1 /Ij frequency I n = ~ (usual
nutrient intake/usual energy intakes) x frequencyj x lt',OOO (1)
where n denotes the number of energy intake levels in the sub-
group, and the subscript j indicates that for each nutrient intake in
the subgroup, the summation above must be carried out for each
energy intake level. The weights in the summation above are given
by the frequencies of consumption of each energy level. For exam-
ple, in a group of women age ci 19 to 50 years, consumption of
energy below 500 kcal or above 8,000 kcal would be associated with
low frequencies, whereas energy consumption of around 1,500 to
3,000 kcal would be observed more frequently. The calculation
above is carried out for each nutrient intake level in the subgroup.
As a result, a distribution of density intakes is obtained in the sub-
group by combining a target nutrient intake distribution and an
actual (unchangeci) usual energy intake distribution.
To illustrate this, consider a hypothetical group of 25 men. Intake
ciata were collected from each of these men on two nonconsecutive
clays, and the intakes were acljusteci to estimate usual intake of
nutrient Y and usual intake of energy. This group is very unusual, as
its nutrient intake distribution at baseline is flat: five men each have
usual intakes of 8 units, 9 units, 10 units, 11 units, and 12 units of
nutrient Y. The group's energy intake distribution is also unusual:
five men each have intakes of 2,000, 2,200, 2,300, 2,500, and 3,000
kcal. Further, these energy intakes are clistributeci so that each
nutrient intake level is represented by all five energy intakes.
The EAR for nutrient Y is 10 units, so at baseline, 10 of the men
have usual intakes below the EAR. In this scenario, the planning
goal is to have a prevalence of inacloquacy that is essentially zero.
Accordingly, the target usual nutrient intake distribution is obtained
by shifting the baseline distribution up by 2 units, leacling to usual
intakes of 10, 11, 12, 13, and 14 units of nutrient Y for the men.
To derive the target usual nutrient density distribution, each value
in the target nutrient intake distribution is paired with each value
from the energy intake distribution, as shown in Table 4-1. As shown
in the fourth column of the table, the target nutrient density intake
distribution ranges from 3.33 units/1,000 kcal to 7.0 units/1,000
, , ——— ~

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DIETARY REFERENCE INTAKES
TABLE 4-1 Deriving a Target Nutrient Density Distribution
for a Hypothetical Group of 25 Inclivicluals
Usual Target Target Intake
Nutrient Usual Nutrient Nutrient Resulting
Intake Energy Intake Density Intake from
Distribution Intake Distribution Distribution Meals with
(units of Distribution (units of (units/ Average
nutrient Y) (kcal) nutrient Y) 1,000 kcal) Density
8 2,000 10 5.0 10.18
8 2,200 10 4.55 11.20
8 2,300 10 4.35 11.71
8 2,500 10 4.0 12.72
8 3,000 10 3.33 15.27
9 2,000 11 5.5 10.18
9 2,200 11 5.0 11.20
9 2,300 11 4.78 11.71
9 2,500 11 4.4 12.72
9 3,000 11 3.67 15.27
10 2,000 12 6.0 10.18
10 2,200 12 5.45 11.20
10 2,300 12 5.22 11.71
10 2,500 12 4.8 12.72
10 3,000 12 4.0 15.27
11 2,000 13 6.5 10.18
11 2,200 13 5.91 11.20
11 2,300 13 5.65 11.71
11 2,500 13 5.2 12.72
11 3,000 13 4.33 15.27
12 2,000 14 7.0 10.18
12 2,200 14 6.36 11.20
12 2,300 14 6.09 11.71
12 2,500 14 5.6 12.72
12 3,000 14 4.67 15.27
Average 5.09
kcal, and has an average of 5.09 units/1,000 kcal. The intakes that
would result from meals planned to contain this density of nutrient
Y are shown in the fifth column of Table 4.1. It can be seen that
none of the men would have intakes below the EAR of 10 units, so
the planned-for very low prevalence of inadequacy would be
attained.
In practice, it is not really necessary to proceed with the average
over all energy consumption levels as above, nor is it necessary to

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 101
know the frequency of consumption associated with each energy
level. The average above can be more easily calculated using a sam-
pling, or Monte Carlo, approach as follows: first, for each usual
nutrient intake, randomly select a number m of usual energy in-
takes from the distribution of energy intakes, and second, compute
the following quantity:
Average nutrient density intake = (l/m) Im= ~ (usual nutrient
intake/energy intakes) x 1,600
(2)
Here, m is typically much smaller than n, so that the sum in
expression (2) is less computationally clemancling than that shown
in expression (1~. As a guideline, in the example presented in Chap-
ter 5, the value of n for women is approximately 4,500, but only 400
randomly selected energy consumption levels were drawn from the
usual energy intake distribution in the group in order to compute
the approximation in (2~. In fact, a value of m as low as 50 or 100
would have provicleci a good approximation to the average given in
(1) . If the m energy intakes are drawn at random from the clistribu-
tion of usual energy intakes in the subgroup, then the average in
(2) is self-weighting. This is because energy intake levels will be
drawn more or less frequently clepencling on the probability associ-
ateci with each energy intake level in the usual energy intake clistri-
bution. That is why the frequency associated with each level of
energy consumption floes not appear in equation (2~.
Either one of the two calculations presented above would pro-
cluce an average (over the incliviclual's likely levels of energy con-
sumption) nutrient density intake. To simplify the calculations even
further, the weighted average above floes not have to be computed
for each nutrient intake level in the subgroup in order to obtain an
approximation of the density intake distribution of the subgroup.
Just like in the case of the Monte Carlo average, it is possible to
draw at random a number q, also typically smaller than n, of usual
nutrient intakes from the target usual nutrient intake distribution
in the subgroup. The average (over the range of likely levels of
energy consumption) density for each of the q usual nutrient intakes
drawn from the distribution in the subgroup would then be calcu-
lateci as inclicateci in either of the two expressions presented above.
In the example in Chapter 5, q= 400, so that about 10 percent of
the usual vitamin C intakes for women were drawn from the target
usual intake distribution to compute the incliviclual weighted aver-
ages using equation (2~. Except in the unlikely event in which the
correlation between usual nutrient intakes and usual energy intakes

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DIETARY REFERENCE INTAKES
is high, the numerical approach cletaileci in either expression (1) or
(2) will produce a usable approximation of the distribution of target
nutrient density intakes for a group.
Step 3. Identify the reference nutrient density distribution and set
planning goals for the whole group.
Once the target nutrient density distributions have been clefineci
for each distinct subgroup in the population of interest, it is recom-
mencleci that the distribution with the highest meclian nutrient clen-
sity intake among the subgroups be consiclereci the reference nutri-
ent density distribution for the population for planning purposes.
For the subgroup with the highest target meclian nutrient density,
the planned cliet should achieve the targeted prevalence of inacle-
quacy. For all other subgroups, the prevalence of inacloquacy will be
even lower since the nutrient density of the planned cliet will exceed
their neecis. Thus for the population as a whole, the risk of inacle-
quacy will be lower than the level set for the subgroup with the
highest target nutrient density.
~ 1
The target nutrient density intake distribution is obtained from an ade-
quate target nutrient intake distribution, and therefore the resulting target
distribution of nutrient density intakes meets the criterion for adequacy
that was selected. It is also important to monitor the proportion of indiv?d-
uals whose intakes of the nutrient might exceed the UL.
For some nutrients (notably iron), prioritization of the neecis of
the subgroup with the highest requirement relative to energy can
result in the selection of a target meclian nutrient density that far
exceeds the neecis of all other subgroups. Uncler these circumstances,
planners must consider the risk that members of subgroups with
lower nutrient requirements relative to energy may achieve intake
levels in excess of the UL. They must also consider the cost-effectiveness
of providing such a nutrient-clense cliet for all subgroups. Uncler
some circumstances, it might be cleemecT more appropriate to select
a lower target nutrient density for the group as a whole and employ
direct interventions for the one or two population subgroups in
which the prevalence of inacloquacy would be above the clesirecT
level. This should not be seen as a weakness of the nutrient density
approach. Rather, this approach enables the identification of such
· ~
P Inning Issues.
The strength of the nutrient density approach to planning for
groups comprised of individuals from different life stage and gender

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 103
groups is that the method enables planners to systematically take
into account both the specific nutrient requirements of various sub-
groups and their differing energy neecis. The effectiveness of this
approach hinges on the ability to implement it and on the validity
of the assumptions that underpin it.
TECHNICAL CONSIDERATIONS OF THE NUTRIENT
DENSITY DISTRIBUTION APPROACH
Although the nutrient density distribution approach clescribeci
above is a promising tool for planning group cliets, several impor-
tant issues must be consiclereci.
Nutrients for Which an Adequate Intake Has Been Established
The nutrient density distribution approach to planning group diets can-
not be used for nutrients with an Adequate Intake (AU. The reference
nutrient density ratio links the requirement distribution of the nutri-
ent and the usual intake distribution of the nutrient to obtain a
target nutrient intake distribution (as clescribeci in Chapter 3), and
then expresses this distribution as a density. Thus, this approach
cannot be used in planning for nutrients with AIs because in these
cases there is no knowledge of the requirement distribution of the
nutrient. Although the simple approach using the median nutrient
density presented in the previous section can be used for nutrients
with an AI, planners neeci to be aware of the limitations of this
method.
Correlation Between Nutrient Intakes and Energy Intakes
A premise of the nutrient density distribution approach to plan-
ning intakes of heterogeneous groups is that the correlation
between usual nutrient intakes and usual energy intakes is mocler-
ate to low. This assumption permits computing the simple Monte
Carlo average that results in a target distribution of nutrient density
intakes in each subgroup. The low correlation assumption may not
hold since it would be expected that, in general, higher energy
consumption would imply higher intake of the nutrient. However,
as cliscusseci above, planning intakes for a group in terms of clensi-
ties would most often imply a change in the relationship between
energy and nutrient consumption, one objective being to provide
more units of the nutrient per 1,000 kcal of energy in the cliet. If,
however, assuming low correlation between nutrient and energy

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DIETARY REFERENCE INTAKES
intake is cleemeci unrealistic, in principle their relationship could
be mocleleci, and the Monte Carlo average presented in equation
(2) above could be improved. Otherwise, the target density intake
distribution in each subgroup could be cleriveci directly from the
target joint intake distribution of the nutrient and energy. In the
latter case, the methods presented in Chapter 3 for a single nutri-
ent would neeci to be extencleci accordingly to aciciress the problem
of estimating the target intake distribution of two nutrients jointly
(one of them being energy). A simplified first approximation of the
density approach to planning intakes for heterogeneous groups is
presented here, on the assumption that the correlation between
energy and nutrient intakes may not be so high as to significantly
affect the derivation of the target meclian nutrient density for the
group. However, more research is neecleci to explore the full impli-
cations of this assumption.
The Impact of Reporting Errors
As noted previously, there is ample evidence to suggest that uncler-
reporting is a serious problem in clietary intake surveys. The use of
doubly labeled water methods to determine energy expenditure has
facilitated identification of underreporting in energy intakes, but it
is unclear how the reporting of other nutrients is affected by this
phenomenon. At present, well-establisheci, valiciateci methods are
lacking to identify and correct for systematic reporting errors in
incliviclual intakes. Thus it is impossible to determine the impact of
underreporting on the planning methods proposed here. Nonethe-
less, the sources and probable direction of errors associated with
underreporting are explored below, considering the particular ways
in which self-reported intake data are used in the proposed applica-
tion of the distribution of nutrient densities to plan for heteroge-
neous groups. Note that while the discussion below relates primarily
to the nutrient density distribution approach, the issues raised are
equally relevant to the simple approach that relies on the estimated
meclian energy intake.
The estimated distribution of usual energy intakes is required to
derive a distribution of nutrient requirements expressed as clensi-
ties when planning intakes of a single food or of a cliet composed of
a variety of foocis with similar nutrient density. In planning for
heterogeneous groups uncler normal circumstances (e.g., where
individuals consume diets that comprise multiple foods with varying
nutrient clensities), both nutrient and energy intake ciata are
required. The estimated distribution of usual nutrient intakes is

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A THEORETICAL APPROACH USING NUTRIENT DENSITY 105
required to estimate the target nutrient intake distribution (see
Chapter 3~. The estimated distribution of usual energy intakes is
necessary to express the target usual nutrient intake distribution in
terms of target nutrient densities. Underreporting may bias both
the nutrient and energy intake distributions.
The impact of underreporting on estimates of target usual intake
distributions expressed as nutrient densities is likely to vary clepenci-
ing on the nutrient of interest. If some of the energy intakes are
systematically unclerreporteci, but the target nutrient intake clistri-
bution is less affected by underreporting, then some overestimation
of nutrient requirements in relation to energy would occur. If
energy and nutrient intakes have both been unclerreporteci to the
same extent, then the target density intake distribution may be less
biased. However, this assumption of "proportional underreporting"
is probably not valid. A more likely scenario is that intakes of energy
and the nutrient in question have been disproportionately uncler-
reporteci. The distribution of target usual nutrient intakes expressed
as densities will then also be estimated with error, but the nature
and magnitude of the error is unknown. The extent of this problem
would clepenci on the number of unclerreporteci intakes, the extent
of underreporting in energy versus nutrient intakes, and the magni-
tucle of underreporting in the intake ciata used.
One way to avoid the potential for systematic errors in self-
reporteci energy intakes to skew the distribution of nutrient density
requirements might be to approximate the distribution of usual
energy intakes from the distribution of energy requirements in the
group. Given the high correlation between individuals' energy
intakes and energy expenditure, usual energy intake should equal
energy expenditure if individuals are in energy balance. Thus, the
distribution of usual energy intakes could be constructed by esti-
mating the distribution of energy requirements for the subgroup.
Equations to predict energy requirements are provided for individ-
uals with a body mass index (BMI) of > 18.5 and < 25 (IOM, 2002a).
Another set of equations is provided to predict total energy expen-
diture for individuals with BMI 2 25. Application of these equations
requires knowledge of each individual's age, sex, height, and weight,
and sufficient information to classify the individual into one of four
broad categories of physical activity levels. In applying the equa-
tions to estimate the distribution of usual energy intakes, it is also
necessary to take into account the variation in requirements of indi-
viduals, estimated by the standard deviation of the prediction.
While this approach provides an alternative to the use of self-
reported intake data, it also has some serious limitations. The accu-

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DIETARY REFERENCE INTAKES
racy of the energy expenditure estimates hinges on the applicability
of the equations (anci their variance estimates) for the particular
group of interest and on the accuracy of the available ciata on an
incliviclual's height, weight, and physical activity level. All of these
parameters are subject to measurement error, particularly if self-
reporteci ciata are used. Furthermore, use of the energy expencli-
ture equations floes not eliminate the neeci to use self-reporteci
nutrient intake ciata to obtain an estimate of the target nutrient
intake distribution.
The use of self-reporteci clietary intake ciata is likely to be unavoici-
able in planning for groups. Clearly, more research is neecleci to
enable planners to identify the nature and magnitude of systematic
reporting errors in these ciata and to statistically adjust planning
applications when such errors are present.
An algorithm for the group planning applications presented here
and in Chapter 3 is summarized in Figure 4-1. It should be noted,
however, that the approaches clescribeci are largely theoretical at
this stage. More research is required to aciciress specific technical
issues, test the effectiveness of the proposed approaches in "real-
life" settings, and refine their practical application.
1~
· Does group have generally similar EARs and energy needs?
Yes
Is the requirement distribution skewed?
Yes No
1 ~ 1
Use the probability
approach to plan for
X% below
requirement
No
, l- ,
Use EAR cut-point
method to plan for X%
below requirement
(and no more than Y%
above the UL)
for others · Yes
in the group
Target vulnerable subgroup (e.g.,
fortified food, supplements, and/or
education)
Can the vulnerable subgroup
be identified?
i I
Yes
Is the vulnerable
subgroup an
appropriate
intervention target?
No
FIGURE 4-1 Schematic decision tree for planning group diets.
No
R~-
t