ABSTRACT
This chapter focuses on different models for over-dispersion relative to the binomial distribution, separate from considerations of dose-dependence. Replicated observations at individual doses may indicate over-dispersion. Tests for over-dispersion relative to the Poisson model can be obtained as score tests within mixed Poisson models. The correlated-binomial model was proposed by L. L. Kupper and J. K. Haseman, and independently, as an ‘additive binomial’ generalization of the binomial distribution, by P. M. E. Altham. The main emphasis will be placed on extensions of the binomial distribution, and so the work will be particularly relevant to experiments in which it is litters, rather than individual animals, which are to be regarded as the experimental units. A mixture of two binomials was included in the study by E. P. Smith and D. A. James, which involved fitting the mixture, the beta-binomial and the correlated-binomial models to 48 sets of data from dominant-lethal assays.
