Simplified population data analysis using gamma distribution for nutritional requirements and its application to the estimation of iron requirements for women of child-bearing age.

Background: Estimation of nutritional requirements is a difficult task, especially for nutrients whose requirements have skewed distribution like iron in menstruating women.

Objective: To mathematically develop a simplified population data analysis using gamma distribution for the estimation of nutritional requirements, not depending on extensive numerical calculation.

Methods: The required equations for the estimation of requirements were devised and solved. Existing data of iron intakes and iron losses in literature were fitted to cumulative distribution curves including gamma distribution. The proposed method was applied to the estimation of iron requirements in women using the National Health and Nutrition Survey data from 2003 to 2007 in Japan.

Results: The type 2 equation of nutritional state is first introduced: prevalence of inadequate nutritional state = Σ(individuals with intake/requirement <1)/(total number of individuals). The prevalence of inadequate nutritional status is determined by F-distribution with positive real number parameters, if the intake and the requirement have independent gamma distributions. The sum of basal and menstrual iron losses is well approximated by gamma distribution, if the basal and menstrual iron losses have independent gamma distributions. Using these relationships, an approximate estimate of iron requirements was determined. Iron intakes and losses were found to be well approximated by gamma distribution. The median of the coefficient of variation (CV) of basal iron loss was 34 %. A new correction method for intra-individual variation in gamma distribution under constant CV is presented also. The median of the estimated median iron requirement was 8.12 mg, 8.15 mg and 8.18 mg for women aged 18-29 years, respectively, as the exact numerical estimate, the approximate estimate using BETA.INV in Excel and the approximate estimate using F.INV in Excel. For women aged 30-49 years, it was 9.15 mg, 9.17 mg and 9.14 mg. The intake covering the needs of 97.7 % women was 14.55 mg, 14.44 mg and 14.49 mg for women aged 18-29 years, and 15.70 mg, 15.77 mg and 15.60 mg for women aged 30-49 years.

Conclusion: The approximate estimates of iron requirements agreed well with the exact numerical estimate. The proposed method is useful for the estimation of iron requirements in menstruating women that usually requires extensive numerical calculations.