Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.