Bivariate Dose-Response Modeling and Risk Estimation in Developmental Toxicology

With the recent developments in quantitative risk assessment for noncancer outcomes, dose-response models for developmental toxicity outcomes are being pursued. Among live fetuses, the presence of malformations and reduction in fetal weight are of primary interest. The dose-response relationships are often fit to each of the outcomes separately using appropriate methods to account for clustering due to litter effects. Jointly modeling the outcomes, allowing different relationships with dose while incorporating the correlation between the outcomes and the fetuses, may be more appropriate. We propose modeling the bivariate outcome, malformation (binary) and fetal weight (continuous), where the bivariate correlation and the clustering of fetuses within litters are taken into account. We avoid fully specifying the joint distribution of outcomes within a litter by specifying only the marginal distribution of the bivariate outcome and using generalized estimating equation methodology to account for correlations due to clustering. To characterize joint risk to the fetus for quantitative risk assessment, the bivariate correlation is required and is therefore a focus of inference. Dose-response models and their application to quantitative risk assessment are illustrated using data from a developmental toxicology experiment of ethylene glycol in rats.

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