# Livro DRI 2006 (Micronutrientes)

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```reported energy intake.
Dietary Reference Intakes: The Essential Guide to Nutrient Requirements
http://www.nap.edu/catalog/11537.html
PART I: APPLYING THE DIETARY REFERENCE INTAKES 55
CASE STUDIES
Case Study One: Using the Probability Approach to
Assess Intakes in a Group
Using a group of 650 adult men aged 19 to 30 years and a hypothetical nutrient
with an EAR of 7 mg/day for this age and gender group illustrates the probabil-
ity approach. Individuals in this group, even though they are similar in age and
gender, differ in both their requirements for the nutrient and their usual intakes
of the nutrient. At a conceptual level, determining the prevalence of inadequate
nutrient intakes in the group would simply involve comparing each individual\u2019s
usual nutrient intake with his individual requirement, and totaling the number
of men with usual intakes below their individual requirements. For example, a
man with a usual nutrient intake of 9 mg/day and a requirement of 10 mg/day
would not meet his requirement and would be classified as inadequate, whereas
another man with a usual nutrient intake of 9 mg/day and a requirement of 5
mg/day would exceed his requirement. In practice, however, we almost never
know individuals\u2019 nutrient requirements. Instead, we may have information on
the distribution of requirements for a small group of individuals who are simi-
lar in age and gender, and who took part in studies to determine nutrient re-
quirements. From that information, we can determine the probability, or risk,
Knowledge of the distribution of requirements allows one to construct a
risk curve that defines the probability that any given intake is inadequate, whether
the requirement distribution is statistically normal or not. Figure 8 shows a risk
curve for the example nutrient with an EAR of 7 mg/day. The requirement dis-
tribution for this nutrient is statistically normal, and the SD is ~ 1.5 mg/day. As
described earlier, for nutrients with normal requirement distributions, 95 per-
cent of individuals have requirements within ± 2 SD of the EAR. In this ex-
ample, 95 percent of men aged 19 to 30 years would have requirements be-
tween 4 mg/day (7 mg/day minus twice the SD of 1.5 mg/day) and 10 mg/day
(7 mg/day plus twice the SD of 1.5 mg/day). The probability of inadequacy
associated with any intake can be determined by assessing where the intake
level intersects the risk curve.
As illustrated in Figure 8, the probability of inadequacy at a usual intake at
or below about 3 mg/day is associated with a probability of inadequacy of 1.0
(100 percent), meaning that virtually everyone with a usual intake in this range
does not meet their own requirement. When usual intakes are at or above about
11 mg/day, the probability of inadequacy is zero, meaning that virtually every-
one with a usual intake in this range would meet their own requirement. When
usual intake is between 4 mg/day and 10 mg/day, the probability of inadequacy
varies, and can be estimated by determining where the usual intake level inter-
sects the risk curve:
Dietary Reference Intakes: The Essential Guide to Nutrient Requirements
http://www.nap.edu/catalog/11537.html
56 DRIs: THE ESSENTIAL GUIDE TO NUTRIENT REQUIREMENTS
0
0.2
0.4
0.6
0.8
1.0
1.2
Usual Intake (mg/d)
Pr
ob
ab
ilit
y
of
In
eq
ua
cy
7 mg/d (EAR)
Probability = 0.5
1 2 3 4 5 6 7 8 9 10 11 12 13
5 mg/d
Probability = 0.9
9 mg/d
Probability = 0.1
FIGURE 8 Risk curve. This risk curve is from a normal requirement distribution with a mean
of 7 mg/day and a SD of 1.5 mg/day.
\u2022 It is relatively high at intakes that are just above the lower end of the
distribution of requirements (about 0.9 or 90 percent at a usual intake
of 5 mg/day in this example).
\u2022 By definition, the probability of inadequacy at the EAR is 0.5 or 50
percent (7 mg/day in this example).
\u2022 It is relatively low at intakes that are closer to the upper end of the
distribution of requirements (about 0.1 or 10 percent at a usual intake
of 9 mg/day in this example).
The information on the probability of inadequacy of different usual intake
levels is used to estimate the prevalence of inadequate intakes in the group.
This is done by determining the probability of inadequacy for each usual intake
level in the group, and then computing the average for the group as a whole.
Figure 9 and Table 5 illustrate this approach. Figure 9 shows the risk curve
from Figure 8, as well as a usual intake distribution for the group of 650 men in
the example (each \u201cbox\u201d in the figure represents 10 men and there are 65 boxes).
Table 5 shows the usual intake levels from the distribution shown in Figure 9,
the associated probability of inadequacy, and the number of men at that intake
level.
Dietary Reference Intakes: The Essential Guide to Nutrient Requirements
http://www.nap.edu/catalog/11537.html
PART I: APPLYING THE DIETARY REFERENCE INTAKES 57
To illustrate how Figure 9 and Table 5 work to determine the prevalence of
inadequacy, consider men with intakes of 5 mg/day and 9 mg/day. Twenty men
have usual intakes of 5 mg/day, and an intake of 5 mg/day intersects the risk
curve at a probability of inadequacy of 0.90. Because each individual with a
usual intake of 5 mg/day has a 90 percent (0.9) probability of being inadequate,
one would expect 18 of 20 men (90 percent) to be inadequate. In contrast, 80
men have usual intakes of 9 mg/day, and an intake of 9 mg/day intersects the
risk curve at a probability of inadequacy of 10 percent.
One would thus expect 8 men (10 percent of the 80 men with usual in-
takes of 9 mg/day) to be inadequate. The average probability of inadequacy is
calculated by totaling the number of individuals likely to have inadequate in-
takes, and then dividing by the total number of men. (This is mathematically
identical to adding up all the individual probabilities of inadequacy [i.e., 1.0 +
1.0 + 1.0 + . . . + 0 + 0 + 0] and dividing by the total number of men.) In this
example, the group prevalence of inadequacy is approximately 20 percent.
FIGURE 9 Comparison of the risk curve to a usual intake distribution. In this simplified usual
intake distribution, each \u201cbox\u201d represents 10 men aged 19 to 30 years. The prevalence of
inadequate intakes in the group is estimated by determining the probability of inadequacy
associated with each individual usual intake level, and then calculating the average probability.
0
0.2
0.4
0.6
0.8
1.0
1.2
Usual Intake (mg/d)
Pr
ob
ab
ility
of
In
eq
ua
cy
Risk Curve Usual Intake Distribution
1 2 3 4 5 6 7 8 9 10 11 12 13
Dietary Reference Intakes: The Essential Guide to Nutrient Requirements
http://www.nap.edu/catalog/11537.html
58 DRIs: THE ESSENTIAL GUIDE TO NUTRIENT REQUIREMENTS
TABLE 5 Using the Probability Approach to Estimate Group
Ages 19 to 30 Years for a Nutrient with an EAR of 7 mg/day
Usual Intake Level Probability of Number of Probability ¥
2 1.0 10 10
3 1.0 10 10
4 0.97 20 19.4
5 0.90 20 18.0
6 0.73 30 21.9
7 0.50 50 25.0
8 0.27 60 16.2
9 0.10 80 8.0
10 0.03 100 3.0
11 0 100 0
12 0 80 0
13 0 60 0
14 0 30 0
Total 650 131.5
Average probability = probability ¥ number/total
= 131.5/650 = 0.20 (20 percent)
a This represents the number of men expected to have inadequate intakes at each intake
level.
Case Study Two: Using the Probability Approach to
Assess Iron Intakes```