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in a Group of Menstruating Women The probability approach involves first determining the risk of inadequacy for each individual in the population, and then averaging the individual probabili- ties across the group. For iron, Appendix Tables G-5, G-6, and G-7 give the probability of inadequacy at various intakes. These tables may be used to calcu- late the risk of inadequacy for each individual, and then the estimated preva- lence of inadequacy for a population. In addition, Appendix C of the original report titled, Dietary Reference Intakes: Applications in Dietary Assessment (2000), demonstrates how to carry out the necessary calculations to obtain a prevalence estimate for a group. This case study presents a simplified estimate that could also be deter- mined manually. The estimate is illustrated in Table 6 for a hypothetical group of 1,000 menstruating women not taking oral contraceptives and consuming a 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 59 typical omnivorous diet. The first and second columns of this table are based on information in Appendix Tables G-4 and G-7. Intakes below 4.42 mg/day are assumed to have a 100 percent probability of inadequacy (risk = 1.0). Indi- viduals with intakes above 18.23 mg/day are assumed to have a zero risk of inadequacy. For intakes between these two extremes, the risk of inadequacy is calculated as 100 minus the midpoint of the percentile of requirement. For example, intakes between 4.42 and 4.88 fall between the 2.5 and 5th percentile of requirement. The midpoint is 3.75, and the probability of inadequacy is 100 \u2013 3.75 ª 96.3 percent, or a risk of 0.96. The appropriate risk of inadequacy is then multiplied by the number of women with intakes in that range. In this case study, only one woman had an intake between 4.42 and 4.87 mg/day, so the number of women with inadequate intake is 0.96 (1 ¥ 0.96). In the next range (4.88 mg/day to 5.46 mg/day, or between the 5th and 10th percentiles) there were three women, with an associated number of women with inadequate intake of 2.79 (3 ¥ 0.93). If this is done for each intake range, the total number of women with inadequate intakes can be determined. In this example, 165 of the 1,000 women have inadequate intakes, for an estimated prevalence of inad- TABLE 6 Illustration of the Full Probability Approach to Estimate the Prevalence of Dietary Iron Inadequacy in a Group of 1,000 Menstruating Women (Not Using Oral Contraceptives and Following an Omnivorous Diet) Range of Usual Percentiles of Intake Associated Probability Number of Number of Requirement with Requirement of Women with Women with Distribution Percentiles (mg/day) Inadequacy Intake in Range Inadequate Intake < 2.5 < 4.42 1.0 1 1 2.5\u20135.0 4.42\u20134.88 0.96 1 0.96 5\u201310 4.89\u20135.45 0.93 3 2.79 10\u201320 5.46\u20136.22 0.85 10 8.5 20\u201330 6.23\u20136.87 0.75 15 11.25 30\u201340 6.88\u20137.46 0.65 20 13 40\u201350 7.47\u20138.07 0.55 23 12.65 50\u201360 8.08\u20138.76 0.45 27 12.15 60\u201370 8.77\u20139.63 0.35 50 17.5 70\u201380 9.64\u201310.82 0.25 150 37.5 80\u201390 10.83\u201313.05 0.15 200 30.0 90\u201395 13.06\u201315.49 0.08 175 14 95\u201397.5 15.50\u201318.23 0.04 125 5 > 97.5 > 18.23 0.0 200 0 Total 1,000 165 Copyright © National Academy of Sciences. All rights reserved. Dietary Reference Intakes: The Essential Guide to Nutrient Requirements http://www.nap.edu/catalog/11537.html 60 DRIs: THE ESSENTIAL GUIDE TO NUTRIENT REQUIREMENTS equacy of 16.5 percent. It is important to remember that this approach does not identify the specific women with inadequate intakes, but is rather a statistical calculation of the prevalence of inadequate intakes. Thus, it cannot be used to screen individuals at risk of inadequacy. Note that the prevalence of nutrient inadequacy that is estimated by the full probability approach differs considerably from that estimated by the cut- point method (the proportion with intakes below the EAR). In this example, the EAR (median requirement) is 8.07 mg/day, and only 73 women have in- takes below this amount. Thus, the cut-point method would lead to an esti- mated prevalence of inadequacy of 7.3 percent, which differs considerably from the estimate of 16.5 percent obtained by using the full probability approach. The reason for the discrepancy is that one of the conditions needed for the cut- point approach (a symmetrical requirement distribution) is not true for iron requirements of menstruating women. Case Study Three: Using the EAR Cut-Point Method The EAR cut-point method is illustrated in Figure 10, which shows a hypo- thetical joint distribution of usual intakes and individual requirements for a group of 60 individuals. This example is hypothetical because in practice we almost never have access to accurate data on either usual intakes of individuals or their individual requirements. Figure 10 includes a 45\u221e dashed line labeled \u201cIntake = Requirement.\u201d Individuals who fall to the right of and below this line have usual intakes that exceed their individual requirements (i.e., they have adequate intakes), whereas individuals who fall to the left of and above the line have usual intakes that do not meet their requirements (i.e., they have inad- equate intakes). Determining the prevalence of inadequacy in this hypothetical situation is easy: one simply counts the number of individuals with usual in- takes below their individual requirements. In this example, 13 individuals have intakes to the left of and above the \u201cIntake = Requirement\u201d line, so the group prevalence of inadequacy is 13/60, or 21.7 percent. Figure 10 also shows the EAR (in this example, it is 4 mg/day) on both the requirement axis (the Y axis) and the usual intake axis (X axis). Focusing on the X axis, note that most individuals with usual intakes below the EAR have inad- equate intakes (they are to the left of and above the \u201cIntake = Requirement\u201d line), but that some (who appear in the triangle labeled 1) have usual intakes that exceed their individual requirements. Similarly, although most individuals with usual intakes above the EAR meet their requirements (they are to the right of and below the \u201cIntake = Requirement\u201d line), some (who appear in the tri- angle labeled 2) do not. 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 61 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 2 1 EAR EAR Intake = Requirement Intake < Requirement Re qu ire me nt (m g/d ) Intake > Requirement Usual Intake (mg/d) FIGURE 10 Joint distribution of requirements and usual intakes. Individuals with usual intakes below their individual requirements are found to the left of and above the dashed 45o line labeled Intake = Requirement. When assumptions for the EAR cut-point method are satisfied, this proportion of the group is mathematically similar to the proportion to the left of the vertical EAR line. The assumptions required for use of the EAR cut-point method are satis- fied in this example, as described below: 1. Requirement distribution is approximately symmetrical. In Figure 10, it can be seen that similar proportions of the group have requirements above and below the EAR of 4 mg/day (the number of individuals above the horizontal EAR line is similar to the number of individuals below). 2. Intakes and requirements are independent. Figure 10 shows that indi- viduals with low requirements are just as likely as individuals with high requirements to have high (or low) usual intakes. 3. The usual intake distribution is more variable than the requirement dis- tribution. In