This paper introduces a dose-response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size. The maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm. Two methods of low-dose extrapolation are presented, one based on the litter size distribution and the other a conservative method. The resulting procedures are then applied to a teratological data set from the literature.

This paper introduces a dose-response model for toxic quantal response data based on hit theory applied to the dose unit as transformed by a nonlinear kinetic equation. When spontaneous background response is included in the model, the resulting dose-response model has four parameters. The maximum likelihood estimators and their large-sample properties are given. Likelihood ratio tests of interest are developed, including one for whether the model is one-hit in the transformed dose and one to check whether nonlinear kinetics is operative. The use of the model for low-dose extrapolation is presented. Finally, the procedures developed are illustrated on data from three animal carcinogenicity bioassays that show, respectively, concave, linear, and convex dose-response curves in the observed data.

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.

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