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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.

This paper proposes a method for assessing risk in developmental toxicity studies with exposure prior to implantation. The method proposed in this paper was developed to account for a dose-dependent trend in the number of implantation sites per dam, which is a common problem in studies with exposure prior to implantation. Toxins may have the effect of interfering with the early reproductive process, which can prevent implantation in the uterine wall. An imputation procedure is presented for estimating the number of potential fetuses by sampling from the empirical distribution of the number of implants per litter in the control group. The marginal death outcomes and the joint malformation and survival outcomes for each potential fetus can be estimated using multiple imputation or the chained data augmentation algorithm. Logit models can then be fit and used to estimate the effect of dose on reducing the probability of a normal birth. These models accommodate multiple covariate effects and can be applied to low-dose extrapolation. A simulation study is done to evaluate the properties of model-based estimators of the mean response and the virtually safe dose level (VSD). It was found that both estimates were good approximations of the underlying dose effect. A dominant lethal assay data set (Luning et al., 1966, Mutation Research 3, 444-451) is analyzed, and the results are compared with those of Rai and Van Ryzin.

This paper presents a model-free approach for evaluating teratology and developmental toxicity data involving clustered binary responses. In teratology studies, a major statistical problem arises from the effect of intralitter correlation, or the potential for littermates to respond similarly. Some statistical methods impose strict distributional assumptions to account for extra-binomial variation, while others rely on nonparametric resampling and empirical variance estimation techniques. Quasi-likelihood methods and generalized estimating equations (GEE), which model the marginal mean/variance relationship, also avoid strict distributional assumptions. The proposed approach, often used to analyze complex sample survey data, is based on a first-order Taylor series approximation and a between-cluster variance estimation procedure, yielding consistent variance estimates for binomial-based proportions and regression coefficients from dose-response models. The cluster sample technique, presented here in the context of a logistic dose-response model, incorporates many of the advantages of quasi-likelihood methods, are valid for any underlying nested correlation structure, and are adaptable to a variety of analytical settings. The results of a simulation study show the cluster sample technique to be a viable competitor to GEE methods currently receiving attention.

This paper concerns the impact of litter effects on the inference of dose-response relationships in teratological experiments with binary response. Kupper et al. (1986, Biometrics 42, 85-98) concluded that when intra-litter correlations are dose-dependent, the use of a common intra-litter correlation likelihood based on the beta-binomial distribution could lead to severe bias in estimation of the parameter beta, which characterizes the dose-response relationship. We show here that the problems of bias and coverage probability for beta could still be substantial when one uses the likelihood with heterogeneous intra-litter correlations. We then examine through a simulation study the performance of the quasi-likelihood method (Wedderburn, 1974, Biometrika 61, 439-447) and recommend that this method with a common intra-litter correlation parameter be used when the number of litters is small or modest.