ABSTRACT
Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, MA
Harvard School of Public Health, Boston, MA
For the analysis of data from Segment II developmental toxicity designs (Sections 1.2.1 and 2.2, and Chapter 13), focus has recently turned to better handling of the multivariate nature of the response. These studies seek to determine the overall adverse effects of dose on the offspring and it is most often not known a priori how effects will manifest. In developmental toxicity studies with a Segment II design, the uterus of each sacrificed dam is removed and examined for resorptions (very early deaths) and fetal deaths. The viable foetuses are measured for birth weight and length and examined carefully for the presence of different types of malformations. Among viable foetuses, the incidence of any malformation (binary) and reductions in fetal weight (continuous) are typically of primary concern, as both have been found to be sensitive indicators of a toxic effect (U.S. EPA 1991). Often, dose-response relationships are characterized in each of the outcomes
(death, weight, and malformation) separately, using appropriate methods to account for litter effects. Based on the dose-response patterns, the outcome that appears most sensitive to the exposure (called the critical effect) becomes the focus for risk assessment purposes (U.S. EPA 1991, 1995). This approach assumes that protecting against the most sensitive outcome protects against all other adverse outcomes; however there may be a more generalized pattern of effects. An approach that considers the multiple sources of risk and the relationship between them in quantifying an overall risk may be preferable. One approach considers the non-live and live outcomes as conditionally independent, and hence they can be modeled separately (Ryan 1992). Because the live outcomes are correlated (Chen and Gaylor 1992, Ryan, Catalano, Kimmel
and Kimmel 1991), jointly modeling the live outcomes and using the bivariate outcome as a basis for risk assessment may be most appropriate. This motivates the formulation of a joint distribution with mixed continu-
ous and discrete outcomes. The joint model must allow different dose-response functions for each type of outcome and must account for the correlation between them, as well as the correlations that result from clustering. Methods for jointly modeling discrete and continuous outcomes, especially with clustering, are not well established (Regan and Catalano 1999a, 1999b, 2000, Geys, Regan, Catalano and Molenberghs 2001). Without an obvious multivariate distribution incorporating both types of outcomes, specifying a joint distribution of responses within a litter is not straightforward. We discuss several models for jointly modeling discrete and continuous out-
comes in the clustered data setting of developmental toxicity studies (Section 14.1). In Section 14.2, we then discuss the application of the models to quantitative risk assessment.
