The use of a correlated binomial model for the analysis of certain toxicological experiments

In certain toxicological experiments with laboratory animals, the outcome of interest is the occurrence of dead or malformed fetuses in a litter. Previous investigations have shown that the simple one-parameter binomial and Poisson models generally provide poor fits to this type of binary data. In this paper, a type of correlated binomial model is proposed for use in this situation. First, the model is described in detail and is compared to a beta-binomial model proposed by Williams (1975). These two-parameter models are then contrasted for goodness of fit to some real-life data. Finally, numerical examples are given in which likelihood ratio tests based on these models are employed to assess the significance of treatment-control differences.