Threshold dose-response models in toxicology.

After a brief discussion of the threshold concept in toxicology, we consider models for the estimation of thresholds in the case where the observed response is binary or quantal. A generalization of the four-parameter Tukey-lambda family of distributions is proposed as a useful class of models for threshold estimation. Properties of these models are discussed and the process of model fitting and evaluation is illustrated using a number of data sets. The discussion includes consideration of background or spontaneous response, and comparison with other models. One of these is the linear-plateau or hockey-stick model, which has been used in a number of toxicological studies.