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reported energy intake. Copyright © National Academy of Sciences. All rights reserved. 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, that a given intake will be adequate or inadequate. 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: Copyright © National Academy of Sciences. All rights reserved. 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 ad 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. Copyright © National Academy of Sciences. All rights reserved. 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 ad eq ua cy Risk Curve Usual Intake Distribution 1 2 3 4 5 6 7 8 9 10 11 12 13 Copyright © National Academy of Sciences. All rights reserved. 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 Prevalence of Inadequacy in a Group of 650 Adult Men Ages 19 to 30 Years for a Nutrient with an EAR of 7 mg/day Usual Intake Level Probability of Number of Probability ¥ (mg/day) Inadequacy People Numbera 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