Regression Models for a Bivariate Discrete and Continuous Outcome with Clustering

Abstract

Abstract Developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals and pharmaceutical compounds. Exposure to developmental toxicants typically causes a variety of adverse effects, such as fetal malformations and reduced fetal weight at term. In this article, we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivated by the statistical problems that arise in analyzing data from developmental toxicity studies. We focus on marginal regression models; that is, models in which the marginal expectation of the bivariate response vector is related to a set of covariates by some known link functions. In these models the regression parameters for the marginal expectation are of primary scientific interest, whereas the association between the binary and continuous response is considered to be a nuisance characteristic of the data. We describe a likelihood-based approach, based on the general location model of Olkin and Tate, that yields maximum likelihood estimates of the marginal mean parameters that are robust to misspecification of distributional assumptions. Finally, we describe an extension of this model to allow for clustering, using generalized estimating equations, a multivariate analog of quasi-likelihood. A motivating example, using fetal weight and malformation data from a developmental toxicity study of ethylene glycol in mice, illustrates this methodology.