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APPENDIX D Algorithm for Computing the Probability of Intake Inadequacy The probability approach described in this report depends on placement of the observed intake within a normalized distribution of requirements and calculation of the area under the normal distribution to the right of the observed intake. This is done by computing the Z value of the observed intake as: Z = Observed Intake Mean Rea~Ir~m~nt, Standard Deviation of Requirement The statistical tables of the standard normal distri- bution are then consulted to determine the area to the right of Z. This represents the probability that the intake in inadequate for the randomly selected person. An algorithm for use on a computer gives very good agreement with published values of the area under the normal distribution (Abramowitz and Stegun, 1965). The following segment of a computer program illustrates the use of this algorithm. (The program segment is written in Applesoft Basic.) 1510 Z = (A(X)~)J(~ * Cat 1515 IFZ<O THEN Z=ABS(Z): VZ= 1 1520 IEZ~ lOT~NR=O: GOTO 1545 1525 D1 = .0498673470: D2 = .0211410061: D3 = .0032776263: D4 = .0000380036: D5 = .0000488906: D6 = .0000053830 1530 G= 1 +D1 *Z+02 *Z^2+D3 *Z^3+D4*Z^4+D5*Z^S +D6 * Z^6 1535 R=1/~2*G^16) 1540 R = [NT(R * 1000 + 0 5~/1000 1545 IF VZ < >O THEN R= 1 - R: VZ =0 1550 R(X)= R: R=0 127
128 In this program, the following variables have been generated before reaching the above program segment: A(X) is the intake report for nutrient X; NR is the aver- age requirement for nutrient X; and CV is the coeffi- cient of variation of requirement for nutrient X, expressed as a decimal rather than as a percentage. The variables R and R(X) represent the calculated proba- bility that the intake of nutrient X is inadequate to meet the requirement for a person. In the computations in this report, this algorithm has been used with A(X) and R(X) representing the intakes and risks for equal intervals of the population ranked by level of intake (see Appendix A). The values of R(X) have been summed across the population. This yields an estimate of the prevalence of inadequate intakes within the population, which is then divided by the population size. Computer routines are used to estimate requirements on the basis of subject characteristics, to adjust require- ment estimates for the additional needs of pregnancy or lactation, and at the same tome, to adjust variance esti- mates for the new requirement estimate. The program also imputes weight or Energy intake if not provided as input (used in conjunction with derivation of a requirement estimate for some nutrients) and again adjusts the vari- ance of the derived requirement estimate to take into account the variance associated with the imputed value. This program was written for application to a particular person. There are also algorithms for making equivalent adjustments in the analysis of population data rather than individual data if needed. REFERENCE Abramowitz, M., and I. A. Stegun, eds. 1965. Handbook of Mathematical Functions with Fo. =ulas, Graphs, and Mathematical Tables. Applied Mathematics Series No. 55. National Bureau of Standards. U.S. Department of Commerce, Gaithersburg, Maryland.