REGRESSION-MODELS FOR A BIVARIATE DISCRETE AND CONTINUOUS OUTCOME WITH CLUSTERING

Developmental toxicity studies of laboratory animals play a crucial ro le in the testing and regulation of chemicals and pharmaceutical compo unds. Exposure to developmental toxicants typically causes a variety o f adverse effects, such as fetal malformations and reduced fetal weigh t at term. in this article, we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivate d by the statistical problems that arise in analyzing data from develo pmental toxicity studies. We focus on marginal regression models; that is, models in which the marginal expectation of the bivariate respons e vector is related to a set of covariates by some known link function s. In these models the regression parameters for the marginal expectat ion are of primary scientific interest, whereas the association betwee n the binary and continuous response is considered to be a nuisance ch aracteristic of the data. We describe a likelihood-based approach, bas ed on the general location model of Olkin and Tate, that yields maximu m likelihood estimates of the marginal mean parameters that are robust to misspecification of distributional assumptions. Finally, we descri be an extension of this model to allow for clustering, using generaliz ed estimating equations, a multivariate analog of quasi-likelihood. A motivating example, using fetal weight and malformation data from a de velopmental toxicity study of ethylene glycol in mice, illustrates thi s methodology.