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5 The Probability Approach Recognizing the weaknesses of previous efforts to ana- lyze dietary intake, the subcommittee sought an approach that would take into account the variability both in usual nutrient intake among individuals and in their nutrient requirements. To meet this need, it developed and eval- uated a probability approach based on a comparison of two distributions: nutrient requirement and nutrient intake. This method takes into account the likelihood that persons with a particular level of intake would fail to meet their nutrient requirement. The probability of inadequate intake would naturally be very low for those with higher nutrient intakes and would be higher for those with lower nutrient intake. Figure S-1 shows the distribution of protein require- ments among adult men. The probability curve for the in- take has been plotted as a cumulative distribution of requirement. At the lower level of intake, below the lower tail of the original distribution, intake should be inade- quate to meet requirements for everyone. (No persons are believed to have requirements that low.) At the level of the mean requirement, assessing a symmetrical distribution, half the individuals would be expected to have higher needs and half lower. In the upper tail of the distribution, probability of inadequacy approaches zero. (No persons are believed to have requirements this high.) From Figure 5-1, then, a probability of inadequacy can be assigned to any observed level of usual intake. The probability or risk curve is specific to a particular class of people--in this figure, adult men. The application of this concept to protein is discussed in detail in the FAO/WHO/UNU (in press) report on energy and protein requirements. 25

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26 100 80 60 40 20 o it' l I l - - \ \ \ 1 1 J 0 10 20 30 40 50 60 70 PROTE IN INTAKE, g/day FIGURE 5-1. Cumulative distribution of protein requirement expressed as a probability curve. The curve describes the probability, or risk, that an observed intake would be inadequate for a ran- domly selected male, acing a normal diatri- bution of protein requirements. Based on ARC, 1980. In Figure 5-1, the probability of inadequate intake is plotted against the protein intake for an adult male. Beyond approximately 30 g/day, the probability of inade- quate intake decreased rapidly and reaches zero at an intake of about 60 g/day. When applied to the distribu- tion of intakes observed in a population, the curve can be used to generate a prediction or estimate of the prev- alence of inadequate intakes. The approach does not iden- tify those particular individuals who have inadequate intakes, only the proportion of the population. When the approach was applied to iron, Beaton (1974) demonstrated that predictions of the prevalence of inade- quate iron intakes seemed consistent with estimates based on h~matologic data on the proportion of women who might be expected to have increased hemoglobin levels when treated with iron. In that analysis, approximately 7St of women in the sample had intakes less than the Canadian recommended intake of 14 mg/day, but only about 15% were predicted to have intakes below their own requirements (Beaton 1971, 1974) . The approach for iron is discussed

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27 in Appendix ~ and is used with data from the Nationwide Food Consumption Survey (NFCS) later in this section. More recently, the joint FAO/WHO/UNU (in press) com- mittee that studied protein requirements accepted the principles of the probability approach and suggested that it be applied to the interpretation of observed protein intakes. That committee emphasized that the approach can- not easily be applied to energy. In essence, any logis- tically simple approach depends on the assumption that the correlation between intake and requirement is approxi- mately known among similar individuals. On the basis of existing data, this is a reasonable assumption for the nutrients, at least after body weight or other common denominator variables of requirement are taken into account. There is no a priori reason to believe that the _ . person with a low (or high) usual intake will necessarily have a low (or high) requirement. It is possible then to assign a probability of inadequacy to observed intake of nutrients. However, much evidence suggests that usual energy intake and expenditure are closely related in most people (Beaton, 1983; FAO/WHO/UNU, in press). That is, a person with a low energy intake is very likely the person with low energy expenditure. One would have to know the magnitude of this substantial correlation before a prob- ability approach could be applied to energy with any degree of confidence. Obtaining this information would be very dif f icult in the general population. A specific example of the probability approach applied to protein intake is presented in Table 5-1. The adjusted distribution of protein intakes using 1977-1978 NFCS data provided to the subcommittee (Figure 4-2) has been arbi- trarily divided into 11 intake intervals. For each intake interval, the percentage of the total population expected to have inadequate intakes is estimated by multiplying the percentage of the total population in that intake interval (frequency distribution) by the probability of inadequate intake for that interval. When the percentages of inade- quate intake at each level are added together, the sum is 2.2--the estimated prevalence of inadequate protein intakes for that population of adult males (Table 5-1). The probabilities portrayed in Figure 5-1 and tabulated in Table 5-1 were derived from the description of protein requirements provided in the Recommended Dietary Allowances (NRC, 1980). The average protein requirements were stipu-

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28 TABLE 5-1. Predicted Proportion of Adult Males with Protein Intakes Below Their Individual Requirements: An Application of the Proba- bility Approacha Percentage of Estimated Intake Total Popu- Percentage Interval ration with of Total (and Observed In- Probabil- Population Midpoint), take in That ity of with Inade- g/day Intervalb Z ValueC Inadequacy d quate Intake e 24 0.4 -2.85 1.0 0.4 24-28 (26) 0.1 -2.53 0.995 0.1 28-32 (30) 0.2 -1.90 0.97 0.19 32-36 (34) 0.2 -1.27 0.90 0.18 36-40 (38) 0.5 -0.63 0.74 0.37 40-44 (42) 0.9 0 0.5 0.45 44-48 (46) 1.1 +0.63 0.26 0.29 48-52 (50) 1.3 +1.27 0.10 0.13 52-56 (54) 1.8 +1.90 0.03 0.05 56-60 (58) 3.5 +2.53 0.005 0.02 60 91.0f +2.86 0 0 Total 2.2g - aBased on 1977-1978 NFCS data provided to the subcom- mittee. bBased on frequency distribution. cz value = interval midpoint - mean requirement/SD. dProbabilities for each Z value; determined by identi- fying area to right of Z in tables of standard normal dis- tribution. eObtained by multiplying probability of inadequacy by proportion of population in each interval. fPercentages do not add to 100 due to rounding. gPrevalence of inadequate protein intake in this popu- lation of adult males. Obtained by adding the percent- ages for each interval. lated as 0.6 g/kg body weight/day with a coefficient of variation (CV) of 1596. When this was applied to a 70-kg man in the RDA report, the mean requirement was 42 g/day and the SD, 6.3 g/day. Using these parameters and a table of areas under the normal distribution curve, one can derive the proportion of individuals with actual require- ment above a specified level of intake, X. These values

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29 are portrayed in Figure 5-1. This approach was applied to population data by Anderson et al. (1984). The sample analysis in Table 5-1 is based on relatively wide ranges of intake. Through the use of computers, very narrow intervals can be analyzed, thus improving the accu- racy of the estimates. Only 11 intervals were used in Table S-1 because of the constraints of space in this report. The use of such a small number of intake levels is not recommended but is unlikely to cause major error. In its other analyses, the subcommittee analyzed 200 intake intervals. If a parametric approach is used, the actual distributions rather than points on the distribution are analyzed. This approach is examined in Chapter 8 and Appendix C. The approach can be used with any known distribution function. For example, the distribution of menstrual iron losses is a major determinant of iron requirement in females. This distribution approximates the log-normal distribution. By logarithmic transformations of the data on iron intake and use of the logarithmic requirement dis- tribution, a probability approach analogous to the one described above can be applied. Figure S-2 portrays the probability, or risk, curve for inadequate iron intake by menstruating women, derived as described in Appendix B. REQUIREMENT INFORMATION NEEDED FOR THE PROBABILITY APPROACH A knowledge of, or a reasonable assumption about, the mean and shape of the requirement distribution for a par- ticular nutrient is necessary for the probability approach to be applied. As discussed above, the underlying assump- tion of the method is that the correlation between nutrient intake and requirement is low within reasonably homogeneous groups of people. Where this is not true, as for energy, the strength of the correlation must be estimated. For many nutrients, precise descriptions of mean require- ment are not available. Indeed, presumably reliable descrip- tions are available only for protein and vitamin A in adults (NRC, 1980) and for iron in menstruating women (FAD/WHO, 1970; Health and Welfare, Canada, 1983). For other age and physiological groups and for other nutrients, there may be reasonable estimates of the mean requirement, the range of requirements, or perhaps both, but little or no direct knowl-

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30 100 80 60' 40 20 o '1 ~ \ \ \ \ \ \ \ l I I I I ~ 0 2 4 6 8 10 12 14 16 18 IRON INTAKE, mg/day FIGURE 5-2. Probability curve for iron intake in men- struating females. The curve describes the probability, or risk, that an observed level of iron intake would be inadequate to meet the needs of a randomly selected female. This curve is based on the assumption that that menstrual loss follows a log-no~=al distribution. Based on 1977-1978 NFCS data provided to the subcommittee. (Analysis discussed in Appendix B.) edge about the shape of the requirement distribution. In this situation, it is instructive to determine through sensitivity analysis the effect of a particular assumption on the outcome of the analysis. This is done in the next section by testing the effect of changing the mean and the parameters of the requirement distribution on the estimate of prevalence. EFFECT OF REQUIREMENT DISTRIBUTION ON ESTIMATES OF THE PREVALENCE OF INTAKE ADEQUACY Influence of Mean and Standard Deviation of Requirement NFCS data on vitamin C intake of adult men can be used to illustrate how changes in the mean and the variability of the requirement distribution can affect estimates of the prevalence of inadequate intake. To account for changes in the mean requirement, several hypothetical estimates of

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31 the mean requirement of vitamin C are used, ranging from 10 mg/day to 60 mg/day. To explore the effect of changes in variability of requirement on the estimates, standard deviation estimates of 2, 4, 6, 8, and 10 mg/day were used, corresponding to coefficients of variation of 59s, 109, 1S9e, 20%, and 259 where the mean requirement is 40 mg/day. Cable 5-2 presents the results of probability analyses using each standard deviation estimate for each estimate of the mean requirement. TABLE 5-2. Estimated Prevalence of Inadequate Vito n C Intakes by Adult Males: An Illustration of the Sensitivity of the probability Approach to the Mean and Variability of the Requirement Distributiona . . . Estimated Predicted Prevalence of Inadequate Intakes ( % ) D Mean of the by SD of Requirement Requirement SDC SD SD SD SD (mg/day) 2 mg/day 4 mg/day 6 mg/day 8 mg/day 10 mg/day 10 1.4 1.7 2.3 2.9 3.7 15 4.0 4.4 5.0 5.7 6.4 20 8.4 8.6 9.0 9.5 10.2 25 13.5 13.7 14.0 14.4 15.0 30 19.5 19.5 19.7 20.1 20.5 35 25.6 25.8 26.1 26.3 26.5 40 32.8 32.8 32.8 32.9 32.9 45 40.2 39.9 39.7 39.4 39.2 50 46.4 46.2 46.0 45.7 45.3 55 S1.9 51. 9 51. 7 S1 .4 51. 0 60 57.2 57.0 56.8 56.6 56.3 _ "Based on 1977-1978 NFCS data provided to the subc~ttee. bInadeguate in defined as an intake below requirement. CAss~ed standard deviation of the requirement distribu- tion. When mean requirement is held constant and the standard deviation is increased (across rows in Table 5-2), the pre- dicted prevalence estimates do not change substantially. For examples for the estimated mean of 10-mg/day, the prev- alence estimates range from 1. 4% to 3. 7~. For the highest mean of 60 mg/day, the prevalence estimate only changes from 57. 296 to 56. 396 at standard deviations of 2 and 10 mg/day, respectively. However, the prevalence estimates

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32 are greatly affected by changes in the mean requirement, as shown by comparing the estimates down the columns of the table. For a standard deviation of 2 mg/day, the esti- mated prevalence of inadequate intake increases from 1.4% for a requirement of 10 mg/day to 57.2% for a requirement of 60 mg/aay. This is generally true, regardless of the estimated standard deviation. Emus, the prevalence of inadequate intake is sensitive to the mean of the require- ment distribution but is not greatly affected by the vari- ance of the distribution. Influence of the Shape of Requirement Distribution Several nutrients were analyzed by the subcommittee to determine how the shape of the distribution influences prev- alence estimates. These analyses demonstrated that the estimated prevalence is similar whether a normal assumption is used or whether the probability of inadequacy is assumed to increase in a linear manner. In this case, a probabil- ity of O was assigned to the mean requirement +2 SD, and a probability of 1.0 was assigned to -2 SD. The results of these analyses demonstrate empirically that the model is not particularly sensitive to either the variance of the requirement distribution or the shape of the distribution, assuming that the requirement distribu- tion is approximately symmetrical. For all nutrients studied, the variability of the requirement appears to be much smaller than the variability in the observed data on nutrient intake. 'ibis is illustrated in Figure 5-3 in which the probability curve is superimposed on the distri- bution of intakes. Generally, therefore, the errors of overestimation and underestimation of the prevalence of inadequate intake tend to cancel out, and except at the ends of the intake distribution, the model is not sensi- tive to changes in the shape of the requirement distribu- tion, i.e., its symmetry. These empirical findings seem to apply to all the intake distributions examined by the subc~'littee (ascorbic acid, protein, and vitamin A for adult males and females and iron, thiam~n, and thiamin/l,OOO local for adult males), assuming that requirements are distributed symmetrically around the mean. When this condition is present, the simplest empirical approach to estimating the prevalence might be to determine the proportion of the study popula- tion with usual intakes below the mean requirement.

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33 123 11.1 98 z 86 o ~ 74 cat a cat O— 3.7 i 7.\. t2 o USUAL INTAKE 1-DAY INTAKE e e ~ ~ e e RISK OF INADEQUATE INTAKE 0 4080 8160 12240 16320 204 V ITAM I N A I NTAK E, I U/day FIGURE 5-3. One-day and adjusted distributions of vitamin A intake of adult females and superimposed proba- bility curve. Note that the range in varia- tion of requirements is small in comparison to range of intakes. It is assumed that require- ments are normally distributed with a 15% coef- ficient of variation. Based on 1977-1978 NFCS data provided to the subcommittee. Although this procedure will introduce some error into the results, especially when the mean requirement is close to the end of the intake distribution, the error is likely to he within the confidence limits of the estimate. For exam- ple, in the first row of Table 5-2, it would be difficult to assert that 1.4% is different from 3.7%. Conversely, one might say with confidence that both are very low. Thus, the use of any reasonable standard deviation of requirement will improve the estimate of prevalence. The subcommittee also explored the use of the probability approach when the requirement distribution is highly asym- metrical, e.g., for iron requirements of menstruating women. (See Appendix B for the details of this analysis.) The relative shape of the curve is fixed by the known distribu- tion of menstrual iron losses. However, changing the assumption about the upper lout of iron absorption will also change the mean of the requirement distribution. In Table 5-3, prevalence has been estimated with the proba-

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34 bility approach. It has also been estimated by using the logarithmic distribution of iron requirements and estimating the proportion of cases falling below the median require- ment. To change the position of the requirement di~tri- bution in this table, various iron absorption rater have been assumed. Iron absorption among women ingesting typical North-A~erican mixed diets and maintaining iron stores has been estimated to be approximately 20% (FAD/WHO, 1970). Thus, the table compares two approaches to assessment across a family of requirement distributions. When the requirement distribution is asymmetrical about the median, as it is for menstruating women, the propor- tion of persons falling below the median requirement is not a reliable estimate of the prevalence. (See last two col- umns of Table 5-3. ) The full probability approach in manda- tory. The reason for this may be that unlike the vitamin A intake model in Figure 5-3, the range of the iron require- ment distribution encompasses a substantial part of the range of the dietary intake distribution. Because of the asymmetry of the requirement distribution, errors of under- and overest ~ tion on the two sides of the median require- TABLE 5-3 . Comparison of Probability Estimates of the Prevalence of Inadequate Iron Intake and the Proportion of Intakes Falling Below the Mean Requirementa - Estimates Derived Using Median Require- Inferred Estimates Assumed Median Derived f ram Limit of Requirement Probability ment a" Cutoff Absorption (96) (mg/day)b Approach Point (96) 14 9.39 S0.4 44.0 16 8.22 38.7 29.2 18 7.30 29.7 18.2 20 6.57 23.0 12.7 22 5.98 18.0 8.5 24 5.48 14.3 6.1 25 5.26 12.8 5.2 abased on 1977-1978 NFCS data for menstruating women provided to the subcommittee. bIn the requirement distribution model used, the median physiological loss of iron is 1.32 mg/day.

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35 ment would not be expected to cancel each other our. For iron, both the mean and the shape of the requirement dis- tribution are important. For this reason, the simplified empirical approach in which the proportion below the median is used as an estimate of the prevalence of inadequacy can- not be applied to iron intake in menstruating women--or to any other nutrient where there is reason to believe that there is strong asymmetry in the distribution. Impact of the Mode in Which Requirements Are Expressed It is generally accepted that nutrient requirement estimates, and hence approaches to estimating the preva- lence of inadequate intakes, must take into account the physiological variables of age, sex, pregnancy, and lac- tation. However, other variables that affect nutrient requirement should also be taken into account. Current nutrient requirement reports (FAO/WHO/UNU, in press; Health and Welfare, Canada, 1983; NRC, 1980) recog- nize that body weight affects protein requirement. The primary requirement estimate is usually expressed as grams of protein per kilogram of body weight per day. Similarly, energy intake affects thiamin requirements, which are usu- ally stated as mg/l,OOO kcal/day. In addition, at least one report (Health and Welfare, Canada, 1983) recognizes the inf luence of protein intake on vitamin B6 require- ment, which is given as grams of protein intake per day. In those reports, estimates are often applied to a repre- sentat~ve subject to derive an estimate of recommended intake per day, without reference to the original variable that affected the requirement. This practice creates two potential problems. First, the variance of requirement per day may have been underestimated in this derivation. For example, if the variability of requirement for protein per kilogram of body weight has a CV of 15%, and this estimate must be extended to adult men, the variability of their body weights must be considered. The variability of protein requirement per day must be greater than that for protein requirement per kilogram of body weight per day (FAD/WHO/ UNU, in press). There are analogous situations for thiamin and vitamin B6 requirements. To estimate prevalence, this adjustment of variance should be taken into account. How- ever, since the final estimates of prevalence are not seriously affected by the magnitude of the variance of the requirement, this may not be a serious problem.

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36 The second problem is much more important. If the variable of requirement (body weight, energy intake, or protein intake, in the examples cited above) is also asso- ciated with dietary intake of the nutrient, then there will be a spurious correlation between requirement ner dav and intake per day. ~ ~ . , A large man, for example, can be expected to have a higher protein requirement than a mall ma" and is likely also to have a higher total food intake. In addition, protein intake is likely to be larger, result- ing in a correlation between intake and requirement, unless body size is controlled. This contradicts a basic assump- tion underlying the probability approach, i.e., that there is a very low correlation between intake and requirement. The simplest way to avoid this is to express both require- ment and intake in relation to common variables, e,.g., per kilogram of body weight, per 1,000 koal, or per gram of protein intake, as appropriate. The impact of mode of expression on prevalence estimates for thiamin is shown numerically in Table 5-4. The two _ . . estimates of prevalence presented were both derived with the probability approach. One is based on an estimate of thiamin requirement per day. The other is based on an estimate of thiamin requirement per 1,000 kcal/day. Table 5-4 demonstrates that there is a substantial difference between the estimates derived in these two ways because in the second approach correlation between intake and require- ment is avoided and there is recognition that a person with a low thiamin intake may also have a low energy intake and, hence, a low but adequate requirement for thicken. In the ~ ~ - ~ 1980 Recommended Dietary Allowances, the proposed thiamin allowance was expressed as 0.5 mg/1,000 kcal/day (NRC, 1980). The average requirement was not explicitly stated, but the text implies that it is approximately 0.4 mg/l,000 kcal/day, with an implied CV of about 12.5%. In trans- lating these into intakes per day, the It tee on Dietary Allowances assumed an average energy intake of about 3,000 cal/day for the young adult male and derived an RDA of 1.5 mg/day. The imputed average requirement would be approximately 1.2 mg/day. Two different expressions of requirement distributions can be made: 0.4 + 0.05 mg/1,000 koal/day and 1.2 + 0.15 mg/day. The effects of these two requirement estimates on the NFCS data are given in Table 5-4. The Committee on Dietary Allowances suggested that the relationship of thicken requirement to energy intake may not be consistent at levels of energy intake, specifi- cally less than 2,000 kcal/day. The modes of expression given in Table S-4 do not take this RDA into account.

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37 TABLE S-4. Comparison of Two Approaches to the Assessment of Thiam; n Intake for Adult Malesa Mode of Expression of Intake and Requirement Data Percentage of Population Predicted to Have Intakes Below Actual Requirements mg/l, 00 0 koal/day mg/day 3.4 36.9 aBased on data from 1977-1978 NFCS provided to the subcommittee. As illustrated by the analysis of thiamin, when a known variable of requirement can be measured and applied in anal- ysis, it is correct to express both intake and requirement in relation to this variable before applying the probabil- ity approach to assessment, If fully valid prevalence esti- mates are to be obtained. Impact of Criteria for Requirement Estimate As discussed earlier, the criteria that serve as the conceptual framework for the requirement estimate have a sub- stantial effect on estimates of the prevalence of inadequate intake. Two examples illustrate this principle. After exam- ining the literature, an FAD/WHO committee (FAD/WHO, 1970) concluded that an ascorbic acid intake of 10 mg/day was more than minimally adequate to prevent or cure scurvy in adult men. Since the range of requirements for this criterion of adequacy appeared to be 6 to 10 mg/day, one might assume a mean requirement of 8 mg/day and a CV of 15%. The Committee on Dietary Allowances agreed with this estimate of the requirement to prevent scurvy; however, it accepted meta- bolic pool size as the basis for deriving the recommended allowance and suggested that the upper tail of the require- ment range, the recommended intake, was approximately 60 mg/day (NRC, 1980). That c=~ittee's report suggests that the CV of this requirement might be 15% to 20%. Estimates of the requirement distribution for the maintenance of an adequate body pool can be derived as a mean requirement of 45 mg/day with a CV of 15~. Using this logic, one can define two different criteria for vitamin C requirement distribu- tions, and the results obtained with these two different cri- teria can be compared. To explore their impact on the preva-

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38 fence of inadequate intake, these two requirement distribu- tions were applied to NFCS data. The resulting estimates of inadequate intake for vitamin C are shown in Table 5-5. In 1963, a committee (Health and Welfare, Canada, 1964) reviewed the evidence and concluded that a thicken intake of O. 2 mg/1, 000 koal/aay was adequate to prevent clinical signs of beriberi in adults. An FAD/WHO (1967) committee cited evidence suggesting that 0.23 mg/1,000 kcal was higher than the requirement that would prevent any functional aberration for at least 12 weeks. In the United States, the Committee on Dietary Allowances (NRC, 1980) suggested that even lower levels might be ad-equate to prevent beriberi. Making a judgment based on these three estimates, the present subcom- mittee estimated that the average thiamin requirement for the prevention of clinically detectable malfunction is approximately 0.2 mg/1,000 koal per day, with a CV of about 15~. However, none of the committees believed that this requirement was desirable for maintenance of a suitable state of health, and all of them estimated requirements on the basis of metabolic function or implied tissue levels. For examples the Committee on Dietary Allowances (NRC, 1980) recommended an intake of 0.5 mg/1,000 kcal/day but did not specify the underlying requirement distribution. To illus- trate the importance of changes in nutrient requirement, an TABLE 5-5. Prevalence of Inadequate Intake Estimated with Two Different Assumptions About Requirement Distributions of Adult Mena Criterion of Adequacy for Requirement Estimated Prevalence of Inadequate Intakes (I) Ascorbic Acid Thiamine Avoidance of clinically 0.7 0 detectable malfunction Maintenance of tissue 39.6 3.4 levels or metabolic pools - aBased on 1977-1978 NFCS data provided to the subcommittee. bThiamin intakes per 1,000 koal examined. No lower limit was placed on absolute level of thiamin intake.

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39 average requirement of 0.4 mg/day with a CV of approximately 12.59 can be used. The prevalence of inadequate thicken intake was determined for each of there two criteria as given in Table 5-5. As shown in Table 5-5, estimates of the prevalence of inadequate intake depend on the criterion of nutritional adequacy underlying the requirement estimate. Agreement between the dietary assessment and a biochemical or clini- cal anses~ment of the same population depends to a large extent on both the concordance between the underlying con- cepts of adequacy that have been used to net the dietary requirement and the biochemical or clinical criterion. Not surprisingly, current approaches often result in different estimates of the prevalence of inadequate nutrition when the some criterion of adequacy has not been used to establish requirements for dietary intake and criteria for biochemical mea~ur-,nent~. nparinon with Fixed Cutoff Approach In Table 5-6, prevalence estimates derived with the probability approach are compared with those based on the fixed cutoff approach. The bases of the probability esti- mates were presented earlier in this chapter. Four arb4- trary cutoff points, expressed as percentages of the RDA ONE:, 1980), have been used. TABLE 5-6. Comparison of Estimates of the Prevalence of Inadequate Intakes for Adults Using Probabll- ity and Fixed Cutoff Approachesa Prevalence Estimates ( 9e ), by Approach Used Nutrient and Sex Probability Group Approach___ Fixed Cutoff Approach 1009 RDA 8096 RDA 709 RDA 60% RDA _ Protein 2.3 (males ) Vitamin C 39.6 (males ) Iron 23.0 ( females) 6.S 2.4 1.3 0.8 57.5 44.5 36.3 27.1 98.2 91.2 81. 6 62 .5 aApplied to adjusted data from 1977-1978 NFCS provided to the sun; ttee.

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40 It becomes Immediately apparent from the table that a fixed cutoff approach may or may not give estimates of the prevalence of inadequate intakes similar to those generated with the probability approach. However, the cutoff point that produces the similarity is specific to the character- istics of both the requirement distribution and intake dis- tribution. Thus it may or may not be correct. For this reason, analysis of prevalence with cutoff points is not recommended. The possibility of using the mean nutrient requirement as a cutoff point was also considered by the subcommittee. m is would be a possible alternative if the following con- ditions apply: the requirement distribution is reasonably symmetrical, the mean requirement does not fall in the tail of the intake distribution, and the variance of dietary intake is greater than the variance of the requirement for that nutrient. SU=A" When the shape of the distribution of nutrient reguire- ment is known or can be inferred, a probability approach to the assessment of observed nutrient intakes is the most efficient and logical analytical approach. If, as is a reasonable assumption for most nutrients, the requirements are distributed relatively symmetrically about the mean or median, the probability approach is sensitive to the esti- mate of the average requirement. It is, however, rela- tively insensitive to the shape and variance of the require- ment distribution in the assessment of population data.