The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments

Abstract

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 onep arameter binomial and Poisson models generally provide poor fits to this type of binary data. In this paper, a type of correlated binom ial model is proposed for use in this situation. First, the model is described in detail and is shown to have certain theoretical advantages over a beta-binomial model proposed by Williams [8]. These two-parameter models are then contrasted as to 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.

Geometric Science of Information

“…Example 1. Mixture of binomial distributions This example comes from [10] where the authors state that 'simple one-parameter binomial and Poisson models generally provide poor fits to this type of binary data', and therefore it is of interest to look in a 'neighbourhood' of these models. The extended multinomial space is a natural place to define such a 'neighbourhood' and a new computational algorithm defined in §2 is used for inference.…”

Evolution of the Cohort Study

“…Methods for random effects models have been provided for Gaussian outcomes (70), binary outcomes (71), and for event-in-person-years outcomes (72).…”

Computational Information Geometry in Statistics: Mixture Modelling

“…Consider the data discussed in [10] and shown in part in Table 1. Mixture models are of interest scientifically since the data concerns frequency of implanted foetuses in laboratory animals, and it could be expected that there is underlying clustering.…”