Exposure estimation in the presence of nondetectable values: another look

A common problem faced by industrial hygienists is the selection of a valid way of dealing with those samples reported to contain nondetectable values of the contaminant. In 1990, Hornung and Reed compared a maximum likelihood estimation (MLE) statistical method and two methods involving the limit of detection, L. The MLE method was shown to produce unbiased estimates of both the mean and standard deviation under a variety of conditions. That method, however, was complicated, requiring difficult mathematical calculations. Two simpler alternatives involved the substitution of L/2 or L/square root of 2 for each nondetectable value. The L/square root of 2 method was recommended when the data were not highly skewed. Although the MLE method produces the best estimates of the mean and standard deviation of an industrial hygiene data set containing values below the detection limit, it was not practical to recommend this method in 1990. However, with advances in desktop computing in the past decade the MLE method is now easily implemented in commonly available spreadsheet software. This article demonstrates how this method may be implemented using spreadsheet software.