Exploring extra-binomial variation in teratology data using continuous mixtures

Discrete data from animal teratology experiments are known to exhibit extra-binomial variation. For example, we discuss a dominant lethal assay experiment in which male mice are exposed to various levels of radiation and are then mated to females. The response of interest is the number of resorptions out of the number of implantations. Most statistical work on analyzing such data has focused on modeling response rates as a function of dose of a suspected teratogen (radiation in this case) while accounting for the extra-binomial variability when calculating standard errors of the regression coefficients. Sometimes, however, when an unobserved genetic or exposure variable is suspected, the shape of the mixing distribution is of interest. We propose a mixture of beta-binomials (MBB) family of distributions that includes the non-parametric mixture of binomials model of Laird (1978) as a special case. The MBB family can accommodate a mixing distribution with one or more modes, and we develop a bootstrap test for multimodality. We apply the method to data from a dominant lethal teratology experiment.