Regression Models and Risk Estimation for Mixed Discrete and Continuous Outcomes in Developmental Toxicology

Multivariate dose‐response models have recently been proposed for developmental toxicity data to simultaneously model malformation incidence (a binary outcome), and reductions in fetal weight (a continuous outcome). In this and other applications, the binary outcome often represents a dichotomization of another outcome or a composite of outcomes, which facilitates analysis. For example, in Segment II developmental toxicology studies, multiple malformation types (i.e., external, visceral, skeletal) are evaluated on each fetus; malformation status may also be ordinally measured (e.g., normal, signs of variation, full malformation). A model is proposed is for fetal weight and multiple malformation variables measured on an ordinal scale, where the correlations between the outcomes and between the offspring within a litter are taken into account. Fully specifying the joint distribution of outcomes within a litter is avoided by specifying only the distribution of the multivariate outcome for each fetus and using generalized estimating equation methodology to account for correlations due to litter clustering. The correlations between the outcomes are required to characterize joint risk to the fetus, and are therefore a focus of inference. Dose‐response models and their application to quantitative risk assessment are illustrated using data from a recent developmental toxicology experiment of ethylene oxide in mice.