03/23/2012 02:23 PM
Applied Mathematics & Statistics
We present a Bayesian nonparametric approach to modelling and risk assessment in developmental toxicity studies. The primary objective for this dose-response setting is to quantify the relationship between the level of exposure of pregnant laboratory
animals to a toxic chemical and the probability of prenatal death or a physiological response for viable fetuses. Hence, the data involve clustered categorical responses,
and typically suggest response distributions and dose-response relationships that can
not be captured well by standard parametric approaches. The focus of our modelling approach is on the dose-dependent response distributions, which are represented through a nonparametric trinomial mixture model. The nonparametric mixing is built from a dependent Dirichlet process prior with the dependence of the mixing
distributions governed by the dose level. The key implication of this modelling strategy is flexible inference for both the response distribution as well as for the dose-response curves associated with the different endpoints, including the capacity of the model to capture non-monotonic dose-response relationships. The practical utility of the methodology is illustrated with data from an experiment on the effects of diethylhexalphthalate, a commonly used plasticizing agent.