Assessment of data sets containing a considerable number of values below the detection limits

Abstract

Using real examples it is demonstrated that the concentrations of non-essential substances in biological systems always follow a statistical log-normal distribution. This is based on the assumption that in a first-order approximation the rate of excretion of the quantity of unwanted molecules or atoms in the biological system is only dependent on their concentration. Applying a natural logarithmic transformation, the resulting log-normal distribution always has a standard deviation of about 1, as shown by statistical analysis of more than 680 clusters of analytical results. Assuming a log-normal distribution with a standard deviation of 1, it is possible to derive factors for the estimation of percentiles, such as the median, even when this percentile is below the detection limit; quantifiable and higher percentiles only must be multiplied by a specific factor. This new method has the advantage that no arbitrary assumptions must be made about artificial parameters such as the numerical treatment of non-detectable analytical data. The assumptions used for the calculation of the factors are justified by proof with experimental data. The applicability of the new method is demonstrated for various contaminants in various plants and animals.