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 the dose-response relationship, which is depicted by the (conditional) probability of an endpoint 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 benefits of both the discrete nonparametric mixing structure and the overdispersed kernel in delivering coherent uncertainty quantification. Further illustration is provided with different forms of risk assessment, using data from a toxicity experiment on the effects of ethylene glycol.

翻译：本研究针对发育毒性研究中通常表现出显著异质性的聚类序数响应，开发了一种非参数贝叶斯建模框架。此类研究的核心在于考察剂量-反应关系，该关系通过终点事件在不同剂量（毒素）水平下的（条件）概率进行刻画。标准参数化方法受限于响应分布和/或剂量-反应关系的预设形式，在此类场景中难以实现可靠的不确定性量化。我们提出了基于剂量依赖性折棍过程先验的非参数混合模型，利用多项分布的优势比对数表示构建混合核函数。我们进一步拓展了该建模方法，通过引入过度离散核增强混合模型，从而实现对变异性的更优控制。我们通过模拟研究论证了离散非参数混合结构与过度离散核在提供一致不确定性量化方面的优势。最后，利用乙二醇毒性实验数据，通过不同形式的风险评估进一步展示了本方法的实用性。