Estimation of Hazardous Concentrations from Bimodal Species Sensitivity Distributions Using Bayesian Statistics. J. S. Jaworska, Procter & Gamble, Eurocor, Temselaan 100, B-1853 Strombeek-Bever, Belgium; and T. Aldenberg, RIVM, P.O.Box 1, NL-3720 BA Bilthoven, The Netherlands
The sensitivity of biological species for toxicants has been modeled through fitting unimodal statistical distributions to NOEC, or LC50, data sets. Quality objectives can be calculated by estimating percentiles, so-called Hazardous Concentrations, at which a fraction of 5% of the species is affected at the most. For estimating the Fraction Affected at some given or predicted environmental concentration, the method is used inversely by calculating values of the cumulative sensitivity distribution. Since toxicity data sets tend to be small, the estimation of the uncertainty, either through Classical confidence statistics or Bayesian statistics, is an essential part of the assessment process. For pesticides, unimodal distributions may not be appropriate, since many pesticides are developed for certain target species, so that the toxicity data may be distributed in a bimodal or multi-modal way. Using a single mode distribution including data for insensitive species may lead to an overestimation of the risk involved. One way to model bimodality is to employ mixtures of two unimodal distributions. The simplest model involves five parameters: two means, two standard deviations, and a weighting factor. The Bayesian approach is flexible enough to handle the fitting of these bimodal distributions to data sets, as well as to assess the uncertainty of the distribution employed, of its cumulative function and of the percentiles to determine Hazardous Concentrations. Since the mixtures involve a more sensitive group (lowest mean) and a less sensitive group (highest mean), one has at least two options to set Hazardous Concentrations, either as a percentile of the total mixture, or as a percentile of the more sensitive group. This latter option is preferred. For fenitrothion L(E)C50 data (n=42), clearly showing bimodal behavior, it turns out that the several possible options for estimating the median HC5 do not differ much: 0.30 ug/l from the unimodal normal distribution, 0.26 ug/l from the unimodal model for the most sensitive data only, 0.37 ug/l from the bimodal normal mixture, and 0.16 ug/l from the more sensitive group of the bimodal mixture. This is surprising given the fact that the data span a range of 0.021 up to 7000 ug/l. The cause of this apparent insensitivity to the model employed is discussed.
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