On the application of loss functions in determining assessment factors for ecological risk

Assessment factors have been proposed as a means to extrapolate from data on the concentrations hazardous to a small sample of species to the concentration hazardous to p  % of the species in a given community (HCpHCp). Aldenberg and Jaworska [2000. Uncertainty of the hazardous concentration and fraction affected for normal species sensitivity distributions. Ecotoxicol. Environ. Saf. 46, 1–18] proposed estimators that prescribed universal assessment factors which made use of distributional assumptions associated with species sensitivity distributions. In this paper we maintain those assumptions but introduce loss functions which punish over- and under-estimation. Furthermore, the final loss function is parameterised such that conservatism can be asymmetrically and non-linearly controlled which enables one to better represent the reality of risk assessment scenarios. We describe the loss functions and derive Bayes rules for each. We demonstrate the method by producing a table of universal factors that are independent of the substance being assessed and which can be combined with the toxicity data in order to estimate the HC5. Finally, through an example we illustrate the potential strength of the newly proposed estimators which rationally accounts for the costs of under- and over-estimation to choose an estimator; as opposed to arbitrarily choosing a one-sided lower confidence limit.