Bayesian Nonparametric Risk Assessment in Developmental Toxicity Studies With Ordinal Responses

We develop a nonparametric Bayesian modeling framework for clustered ordinal responses in developmental toxicity studies, which typically exhibit extensive heterogeneity. The primary focus of these studies is to examine dose–response relationships, which are depicted by (conditional) endpoint probabilities across the dose (toxin) levels. Standard parametric approaches, limited in terms of the response distribution and/or the dose–response relationship, hinder reliable uncertainty quantification in this context. We propose nonparametric mixture models that are built from dose‐dependent stick‐breaking process priors, leveraging the continuation‐ratio logits representation of the multinomial distribution to formulate the mixture kernel. We further elaborate the modeling approach, amplifying the mixture models with an overdispersed kernel which offers enhanced control of variability. We conduct a simulation study to demonstrate the uncertainty quantification benefits of both the discrete nonparametric mixing structure and the overdispersed kernel. Further illustration is provided with different forms of risk assessment, using data from a toxicity experiment on the effects of ethylene glycol.