Total diet study sample compositions uncertainty¶
In MCRA, uncertainty of TDS food sample concentrations is specified through the use of table ConcentrationDistributions. For each subfood, e.g. apple (subfood of TDS food FruitMix), a coefficient of variation, CV, is specified that is derived using the available monitoring samples. Note that monitoring samples may be composite samples. For apple, composite food samples are measured and each sample contains e.g. 12 apples with unit weight 200 g. So monitoring concentrations, \(c_{mi}\), are based on composite samples with a total weight \(w_{mi}\) = 2400 g each.
A TDS food sample is composed of \(w_{i}\) g of food \({i}\) with \({i}\) = 1…k, wi represents the PooledAmount in table TDSFoodSampleCompositions. Then, the concentration of a TDS food sample may be represented as:
with variance:
and \(\mathit{var(c_{i})}\) is the variance of concentrations \(c_{i}\) of food \(i\) with portion sample size \(w_{i}\).
It is expected that increasing the number of units in a composite sample will have a reverse effect on the variation between concentrations. Suppose TDS food FruitMix is composed of 2 x 200 = 400 g apple. The expected variation between portion sizes of 400 g will be larger than between portion sizes of 2400 g:
The variance of the monitoring samples are corrected as follows, calculate:
\(\mathit{var(c_{mi})} = \log (CV_{mi}^2 + 1)\)
\(\mathit{var(c_{i})} = \mathit{var(c_{mi})} \cdot w_{mi} /w_{i}\)
\(CV_{i} = \sqrt{\exp (\mathit{var}(c + i) - 1 )}\)
Specify \(CV_{i}\) in table ConcentrationDistributions.