Estimation of the Parameters of a Clumped Binomial Model via the EM Algorithm

Binary-response data arise in teratology and mutagenicity studies in which each treatment is applied to a group of litters. In a large experiment, a contingency table can be constructed to test the treatment X litter size interaction (see Kastenbaum and Lamphiear 1959). In situations in which there is a clumped category, as in the Kastenbaum and Lamphiear mice-depletion data, a clumped binomial model (Koch et al. 1976) or a clumped beta-binomial model (Paul 1979) can be used to analyze these data. When a clumped binomial model is appropriate, the maximum likelihood estimates of the parameters of the model under the hypothesis of no treatment X litter size interaction, as well as under the hypothesis of the said interaction, can be estimated via the EM algorithm for computing maximum likelihood estimates from incomplete data (Dempster et al. 1977). In this article the EM algorithm is described and used to test treatment X litter size interaction for the Kastenbaum and Lamphiear data and for a set of data given in Luning et al. (1966).