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.

中文翻译：

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使用伽马分布对营养需求进行简化的人口数据分析及其在估计育龄妇女铁需求中的应用。

背景

估计营养需求是一项艰巨的任务，尤其是对于像经期女性铁等需求分布不均的营养素。

客观的

使用伽马分布在数学上开发一个简化的人口数据分析来估计营养需求，而不依赖于广泛的数值计算。

方法

设计并求解了用于估计需求的所需方程。文献中铁摄入量和铁损失的现有数据拟合到累积分布曲线，包括伽马分布。使用日本 2003 年至 2007 年的国家健康和营养调查数据，将建议的方法应用于估计女性铁的需求量。

结果

首先引入营养状态的类型2方程：营养状态不足的患病率=Σ（摄入量/需要量<1的个体）/（个体总数）。营养状况不足的流行率由F决定- 具有正实数参数的分布，如果摄入量和需求量具有独立的伽马分布。如果基础铁损和月经铁损具有独立的 gamma 分布，则基础铁损和月经铁损的总和可以很好地近似为 gamma 分布。使用这些关系，可以确定铁需求的近似估计。发现铁的摄入量和损失量可以通过伽马分布很好地近似。基础铁损的变异系数 (CV) 的中值为 34%。还提出了一种新的校正方法，用于在恒定 CV 下对伽马分布的个体内变化进行校正。对于 18-29 岁的女性，估计的中位铁需求量的中位数分别为 8.12 毫克、8.15 毫克和 8.18 毫克，作为精确的数值估计，使用 BETA 的近似估计。Excel 中的 INV 和 Excel 中使用 F.INV 的近似估计。对于 30-49 岁的女性，分别为 9.15 毫克、9.17 毫克和 9.14 毫克。满足 97.7% 女性需求的摄入量为 18-29 岁女性为 14.55 毫克、14.44 毫克和 14.49 毫克，30-49 岁女性为 15.70 毫克、15.77 毫克和 15.60 毫克。

结论

铁需求的近似估计值与精确的数值估计值非常吻合。所提出的方法可用于估算通常需要大量数值计算的经期女性的铁需求量。