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Appendix I
Dietary Intake Data and Calculation of the Target Median Intake for Iron

This appendix contains information on how schoolchildren’s dietary intakes compare with Estimated Average Requirements and data and a description of the use of the probability method to calculate the Target Median Intake for iron for adolescent females.

LIST OF TABLES

  • Table I-1 Estimated Average Requirements (EARs) for Schoolchildren and Reported Nutrient Intakes at the 5th Percentile and Median by Age-Grade Group and Gender

  • Table I-2 Iron Intake Distribution for 14–18-Year-Old Female Participants (mg/d)

  • Table I-3 Iron Intake Distribution for 11–13-Year-Old Female Participants (mg/d)

  • Table I-4 Iron Requirement Distribution for 14–18-Year-Old Females (mg/d)

  • Table I-5 Iron Requirement Distribution for 9–13-Year-Old Females (mg/d)

  • Table I-6 Estimated Iron Requirement Distribution for 11–13-Year-Old Females (mg/d)



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Appendix I Dietary Intake Data and Calculation of the Target Median Intake for Iron This appendix contains information on how schoolchildren’s dietary intakes compare with Estimated Average Requirements and data and a description of the use of the probability method to calculate the Target Median Intake for iron for adolescent females. LIST OF TABLES • Table I-1 Estimated Average Requirements (EARs) for Schoolchil- dren and Reported Nutrient Intakes at the 5th Percentile and Median by Age-Grade Group and Gender • Table I-2 Iron Intake Distribution for 14–18-Year-Old Female Par- ticipants (mg/d) • Table I-3 Iron Intake Distribution for 11–13-Year-Old Female Par- ticipants (mg/d) • Table I-4 Iron Requirement Distribution for 14–18-Year-Old Fe- males (mg/d) • Table I-5 Iron Requirement Distribution for 9–13-Year-Old Fe- males (mg/d) • Table I-6 Estimated Iron Requirement Distribution for 11–13- Year-Old Females (mg/d) 

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 SCHOOL MEALS TABLE I-1 Estimated Average Requirements (EARs) for Schoolchildren and Reported Nutrient Intakes at the 5th Percentile and Median by Age- Grade Group and Gender 6–10 years 11–13 years 14–18 years Males Females Males Females Males Females Nutrient (n=295) (n=317) (n=342) (n=342) (n=506) (n=512) Protein (g/kg/d) EAR 0.76 0.76 0.76 0.76 0.73 .71 0.7 0.5 Intake at 5th 1.5 1.5 1.1 0.9 Median Intake 2.4 2.3 1.8 1.4 1.5 1.1 Vitamin A (µg RAE/d) EAR 343 333 445 445 630 485 373 236 280 175 Intake at 5th 352 367 Median Intake 631 614 689 529 635 439 Vitamin C (mg/d) EAR 29 29 39 39 63 56 24 32 19 Intake at 5th 36 48 43 Median Intake 83 90 92 73 90 67 Vitamin E (mg αT/d) EAR 7.2 7.2 9.0 9.0 12.0 12.0 4.9 3.4 4.1 2.6 4.2 2.6 Intake at 5th Median Intake 6.0 5.2 6.5 5.4 7.2 5.3 Thiamin (mg/d) EAR 0.6 0.6 0.7 0.7 1.0 0.9 0.7 Intake at 5th 1.0 1.0 1.2 0.7 1.1 Median Intake 1.6 1.5 1.7 1.4 1.9 1.3 Riboflavin (mg/d) EAR 0.6 0.6 0.8 0.8 1.1 0.9 0.8 Intake at 5th 1.4 1.4 1.6 1.0 1.4 Median Intake 2.3 2.2 2.5 2.0 2.6 1.7 Niacin (mg/d) EAR 7.2 7.2 9.0 9.0 12.0 11.0 9.6 Intake at 5th 13.9 12.9 15.1 10.8 18.1 Median Intake 20.5 19.9 22.5 19.6 27.1 18.2 Vitamin B6 (mg/d) EAR 0.6 0.6 0.8 0.8 1.1 1.0 0.7 Intake at 5th 1.2 1.0 1.2 0.8 1.5 Median Intake 1.7 1.6 1.9 1.6 2.2 1.4 Folate (µg DFE/d) EAR 196 196 250 250 330 330 219 Intake at 5th 310 322 415 228 361 Median Intake 553 536 640 477 647 442 Vitamin B12 (µg/d) EAR 1.2 1.2 1.5 1.5 2.0 2.0 1.4 Intake at 5th 2.5 2.5 3.9 2.0 3.0 Median Intake 5.1 4.6 6.0 4.5 6.1 3.8 Iron (mg/d) 5.7a EAR 4.8 4.7 5.9 7.7 7.9 6.0 Intake at 5th 8.5 8.6 10.9 6.9 10.6 Median Intake 14.6 13.9 16.2 13.3 17.9 11.8

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 APPENDIX I TABLE I-1 Continued 6–10 years 11–13 years 14–18 years Males Females Males Females Males Females Nutrient (n=295) (n=317) (n=342) (n=342) (n=506) (n=512) Magnesium (mg/d) EAR 146 146 200 200 340 300 181 134 182 110 Intake at 5th 165 172 Median Intake 253 236 266 223 291 206 Zinc (mg/d) EAR 5.2 5.2 7.0 7.0 8.5 7.3 5.9 8.0 4.7 Intake at 5th 6.9 6.5 8.7 Median Intake 11.1 10.0 12.4 9.9 14.2 9.1 Phosphorus (mg/d) EAR 665 665 1,055 1,055 1,055 1,055 636 971 597 Intake at 5th 874 917 1082 Median Intake 1,376 1,281 1,483 1,171 1,622 1,087 NOTES: αT = α-tocopherol; d = day; DFE = dietary folate equivalents; g = gram; kg = kilogram; mg = milligrams; n = sample size; RAE = retinol activity equivalents; µg = micrograms. aThe committee used a reference value of 7.5 mg for girls ages 11–13 years, as explained under “Iron Status” in Chapter 3. SOURCES: Weighted tabulations of data from the third School Nutrition Dietary Assess- ment study (SNDA-III) (USDA/FNS, 2007a); adapted from Table VI.16 in Volume II and tables in Appendix J to Volume II. Dietary intake data (24-hour recalls) were collected dur- ing the 2004–2005 school year and do not include intakes from dietary supplements (e.g., multivitamin-multimineral preparations). The personal computer version of the Software for Intake Distribution Estimation (PC-SIDE; ISU, 1997) was used to estimate the usual nutri- ent intake distributions and the percentage of children with usual intakes below the EARs. The EARs used in the analysis were from the DRI reports (IOM, 1997, 1998, 2000a, 2001, 2002/2005). EARs shown for the males and females ages 6–10 years are weighted averages of two DRI age groups. Bolded numbers indicate that intake at the 5th percentile is below the EAR. CALCULATION OF THE TARGET MEDIAN INTAKES FOR IRON The Probability Approach for Calculating the Prevalence of Inadequacy The distribution of iron requirements has been estimated using facto- rial models based on component losses and the deposition of iron. Since it was expected that the distribution was not normal, the distribution was estimated using simulation of a population of 100,000 individuals (IOM, 2000b, p. 569). A consequence of the nonnormality of the requirement distribution is that the Estimated Average Requirement (EAR) cut-point method does not provide a sufficiently accurate estimate of the prevalence of inadequacy, particularly for menstruating women. The recommended al- ternative is to use the probability approach (IOM, 2000b, pp. 205–208). The basic idea underlying the probability approach is most easily

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 SCHOOL MEALS understood in terms of a large population of individuals with known in- takes. For each individual, the probability of inadequacy is calculated from the requirement distribution (i.e., the probability that the requirement is greater than the individual’s intake). These probabilities are averaged over all individuals in the population to give the prevalence of inadequacy. The two inputs for the calculation are the intake distribution and the requirement distribution. Let FR(r) and FI(i) denote the cumulative distri- bution functions for requirement and intake, respectively. The prevalence of inadequacy is the probability that the intake, I, is less than or equal to the requirement, R, that is, P(I ≤ R). In terms of the cumulative distribu- tion functions, we have the following expression for the prevalence of inadequacy: P(I ≤ R) = ∫ P(I ≤ R I = i)dFI (i) = ∫ 1 − FR (i) dFI (i)   Let x1 ≤ x2 ≤ L ≤ xn denote an ordered set of intakes that span the range of the distribution. The probability of inadequacy can be approxi- mated by n − 1  1 − F (x )  + 1 − FR (x j )   P(I ≤ R) ≈ ∑   j +1      F (x ) − F (x )  R  J j +1 2 I I j =1    Intake and Requirement Distributions Calculations using this method were performed for 14–18-year-old females and 11–13-year-old females. The intake distribution was based on National School Lunch participants included in the third School Nutrition Dietary Assessment study. For the 14–18-year-old female participants, the intake distribution is in Table I-2. For the 11–13-year-old female participants, the intake distribution is shown in Table I-3. The requirement distributions for iron are given by IOM (2001). For 14–18-year-old females, the requirement distribution is shown in Table I-4. For 11–13-year-old females, the requirement distribution is not available but the requirement distribution is given for 9–13-year-old females (see Table I-5). Because the 11–13-year-old females will have a higher percentage of menstruating females than the 9–13-year-old females, the iron requirements

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TABLE I-2 Iron Intake Distribution for 14–18-Year-Old Female Participants (mg/d) Percent 0.01 0.025 0.05 0.08 0.10 0.13 0.15 0.18 0.20 0.23 0.25 0.28 0.30 0.33 Intake 5.26 6.13 6.96 7.56 8.05 8.47 8.86 9.22 9.55 9.88 10.2 10.5 10.8 11.1 Percent 0.35 0.375 0.40 0.43 0.45 0.48 0.50 0.53 0.55 0.58 0.60 0.63 0.65 0.68 Intake 11.4 11.7 12.0 12.2 12.5 12.8 13.1 13.4 13.8 14.1 14.4 14.8 15.1 15.5 Percent 0.70 0.725 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.95 0.98 0.99 Intake 15.9 16.3 16.8 17.3 17.8 18.4 19.1 19.9 20.8 22.0 23.6 26.3 29.7 NOTE: mg/d = milligrams/day. TABLE I-3 Iron Intake Distribution for 11–13-Year-Old Female Participants (mg/d) Percent 0.01 0.025 0.05 0.08 0.10 0.13 0.15 0.18 0.20 0.23 0.25 0.28 0.30 0.33 Intake 5.61 6.50 7.37 7.99 8.49 8.93 9.32 9.69 10.0 10.4 10.7 11.0 11.3 11.6 Percent 0.35 0.375 0.40 0.43 0.45 0.48 0.50 0.53 0.55 0.58 0.60 0.63 0.65 0.68 Intake 11.9 12.2 12.5 12.8 13.1 13.4 13.7 14.0 14.3 14.7 15.0 15.3 15.7 16.1 Percent 0.70 0.725 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.95 0.98 0.99 Intake 16.5 16.9 17.4 17.9 18.4 19.0 19.7 20.5 21.4 22.6 24.2 26.9 30.3 NOTE: mg/d = milligrams/day. 

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TABLE I-4 Iron Requirement Distribution for 14–18-Year-Old Females (mg/d) 0 Percentile 0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.975 Requirement 4.63 5.06 5.61 6.31 6.87 7.39 7.91 8.43 9.15 10.03 11.54 13.08 14.8 NOTE: mg/d = milligrams/day. TABLE I-5 Iron Requirement Distribution for 9–13-Year-Old Females (mg/d) Percentile 0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.975 Requirement 3.24 3.6 4.04 4.59 4.98 5.33 5.66 6.0 6.36 6.78 7.38 7.88 8.34 NOTE: mg/d = milligrams/day. TABLE I-6 Estimated Iron Requirement Distribution for 11–13-Year-Old Females (mg/d) Percentile 0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.975 Requirement 4.18 4.61 5.16 5.86 6.42 6.94 7.46 7.98 8.70 9.58 11.1 12.6 14.35 NOTE: mg/d = milligrams/day.

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 APPENDIX I for 11–13-year-old females are higher than those for 9–12-year-old females and the shape of the distribution is likely to be skewed to the right, as is the distribution for 14–18-year-old females. Therefore, an estimated require- ment distribution for 11–13-year-old females was computed by setting the EAR at 7.46 (versus 5.66 for 9–13-year-old females and 7.91 for 14–18- year-old females) and using the shape of the distribution for 14–18-year-old females. Thus, the estimated requirement distribution for 11–13-year-old females was obtained by subtracting 0.45 (7.91–7.46) from each of the per- centiles of the requirement distribution for 14–18-year-old females. Table I-6 presents the resulting distribution. Modeling the Distribution Normal quantile plots indicated that the intake distribution for 14–18- year-old females is skewed to the right. Taking logs and making similar plots suggested that the distributions were fairly close to lognormal but were slightly less skewed. A cubic equation gave a very accurate descrip- tion of the relationship between the normal score and log iron seen in the normal quantile plot for log iron. Therefore, the cumulative distribution for intake was determined by an equation of the form FI (i) = Φ–1 (Constant + A log (i) + B log (i)2 + C log (i)3) where the constant, A, B, and C were estimated by least-squares. This cubic function is used to compute the cumulative distribution for the iron intake distribution needed for the probability approach for calculating the prevalence of inadequacy. The modeled percentiles agreed with reported percentiles exactly when rounded to the reported percentiles. The modeled intake distribution for 14–18-year-old females is FI (i) = Φ −1(–5.898954 + 1.926415log(i) + 0.124009log(i)2 + 0.006763log(i)3 ) l where Φ–1 is the inverse of the normal cumulative distribution function and i is the requirement. The situation was similar for the intake distribution of 11–13-year-old females. The modeled intake distribution is FI (i) = Φ −1(–6.050645 + 1.888511log(i) + 0.148162log(i)2 +0.005342log(i)3 ) l The requirement distributions were somewhat more skewed. The method used for the intake distributions gave similarly accurate fits. For 14–18-year-old females, the modeled requirement distribution is

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 SCHOOL MEALS FR (r) = Φ −1(–2.481062–4.568515log(r) + 4.384396log(r)2 –0.771171log(r)3 ) l For 11–13-year-old females, the modeled requirement distribution is FR (r) = Φ −1(–2.391755–3.901541log(r) + 3.938058log(r)2 --0.698517log(r)3 ) l These approximations for the intake and requirement distributions are very accurate when applied to values within the range of the reported per- centiles. In the calculations used for the Target Median Intakes, the modeled values given above are used for intakes between the 0.5 percentile and the 99.5 percentile (tabled values for intakes are given for the 1.0 percentile and the 99 percentile) and for requirements between the 1.25 percentile and the 98.75 percentile (tabled values for requirements are given for the 2.5 percentile and the 97.5 percentile). For values outside these ranges, the cumulative distributions are set to zero for low values and one for high values. Using the Probability Approach and the Modeled Distributions to Find Target Median Intakes The probability approach was used with the modeled distributions to determine the prevalence of iron inadequacy for 14–18-year-old females and 11–13-year-old females. Alternative intake distributions were assumed to be of the same distributional form but shifted to higher or lower values. Computationally, this was accomplished by adding a constant to the value of i in FI(i). The prevalence of inadequacy was computed for a range of val- ues of the constant and the value corresponding to a 5 percent prevalence of inadequacy was determined. The value represents the shift in the intake distribution needed to achieve a 5 percent prevalence of inadequacy. The Target Median Intake is the median of the shifted distribution. For 14–18-year-old females, the Target Median Intake is 15.92 mg/d; and 11–13-year-old females the Target Median Intake is 15.53 mg/d.