Estimation for hazardous concentrations based on NOEC toxicity data: an alternative approach

A common task in environmental studies is to determine toxicant concentrations at which a certain proportion (typically 95 per cent) of the biological species is protected. Extrapolation techniques need to be employed for small sample sizes. By definition, our interest focuses on the lower tail of the NOEC (no observed effect concentration) distribution, which is very sensitive to the choice of the underlying distribution. In this paper we investigate the use of the three-parameter Burr Type III distribution because of its flexibility and ease-of-use. The Constrained Maximum Likelihood (CML) method was used to estimate parameters. Collinearity between parameter estimates was overcome by reparameterisation techniques. As an alternative to the computation of adjustment factors, we estimate the lower confidence limits of percentile estimates using the Delta-method. When the NOEC sample sizes are small, we employ Bootstrapping, a computer intensive technique. Our technique is easily extended to mixtures of the three-parameter Burr type III distributions, which can be used to model multimodal distributions.