Estimation of Average Concentration in the Presence of Nondetectable Values

TLDR: In this article, the average concentration of a particular contaminant during some period of time, a certain proportion of the collected samples is often reported to be below the limit of detection.

Abstract: In the attempt to estimate the average concentration of a particular contaminant during some period of time, a certain proportion of the collected samples is often reported to be below the limit of detection. The statistical terminology for these results is known as censored data, i.e., nonzero values which cannot be measured but are known to be below some threshold. Samples taken over time are assumed to follow a lognormal distribution. Given this assumption, several techniques are presented for estimation of the average concentration from data containing nondetectable values. The techniques proposed include three methods of estimation with a left-censored lognormal distribution: a maximum likelihood statistical method and two methods involving the limit of detection. Each method is evaluated using computer simulation with respect to the bias associated with estimation of the mean and standard deviation. The maximum likelihood method was shown to produce unbiased estimates of both the mean and s...