Can We Know the Iceberg from Its Tip? Censored Distributions in Risk Assessment. M. Butcher, Exponent, Bellevue, WA; T. Barry, Alexandria, VA; and S. Ferson, Applied Biomathematics, Setauket, NY
Data censoring occurs when empirical information about a quantity is limited to knowing only that its value is less than (or greater than) some threshold. Censored distributions commonly arise when observed chemical concentrations contain results that are reported as non-detects. There are several methods available for estimating the underlying distribution from censored data sets. These methods approximate the underlying distribution based on assumptions about the underlying distribution, but their performance degrades as the proportion of non-detects grows to dominate the sample. We describe a method for incorporating all the available data from a censored data set in a risk assessment, without imposing any assumptions on them. We show that even in the cases of highly censored distributions, the information contained in the detected values is still useful, because it is they that contribute to highest dose or exposure. In conjunction with the information known from the censored observations (number of samples and their detection limit), these data may be used to define a probability region, in place of an estimate of a single distribution. The method is sufficiently general to be applied to any source of measurement error, and therefore may be extended to the more difficult cases of multiple detection limits within a data set and the inclusion of uncertainty provided by the analytical laboratory for each concentration. Software for this method is described, and numerical examples involving arsenic in drinking water are provided.
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