Estimation of Average Concentration in the Presence of Nondetectable Values

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 standard deviation under a variety of conditions. However, this method is somewhat complex and involves laborious calculations and use of tables. Two simpler alternatives involve the substitution of L/2 and a new proposal of L/2 for each nondetectable value, where L = the limit of detection. The new method was shown to provide more accurate estimation of the mean and standard deviation than the L/2 method when the data are not highly skewed. The L/2 method should be used when the data are highly skewed (geometric standard deviation [GSD] approximately 3.0 or greater)