A Generalized Multihit Dose-Response Model for Low-Dose Extrapolation

A quantal dose-response model based on a multihit theory of toxic response is presented. When spontaneous background toxic response is included, the model involves three unknown parameters. The maximum likelihood estimators for these three parameters are given as the solution of a nonlinear iterative algorithm. The resulting three-dimensional vector of estimators is shown to be asymptotically strongly consistent, asymptotically unique with probability one, and, when suitably normalized, it has asymptotically a trivariate normal distribution. On the basis of these results, a large-sample goodness-of-fit test is given. The use of this model for low-dose extrapolation is indicated. Application of the results is illustrated using three sets of toxicity data.