Risk assessment via a robust probit model, with application to toxicology

Various frameworks have been suggested for assessing the risk associated wi th continuous toxicity outcomes. The first formulates the affect of exposur e on the adverse effect via a simple normal model and then computes the ris k function using tail probabilities from the standard normal distribution. Because this risk function depends heavily on the assumed model, it may be sensitive to model misspecification. Recently, a semiparametric approach th at utilizes an alternative definition of excess risk has been studied. Unfo rtunately, it is not yet clear how the two approaches relate to one another . In this article, we investigate a semiparametric normal model in which an unknown transformation of the adverse response satisfies the linear model. We demonstrate that this formulation unifies the two existing approaches a nd allows for a coherent risk analysis of dose-response data. In addition e stimation and inference procedures for the unknown transformation in the se miparametric model for the continuous response are developed. These are inc orporated in novel model-checking procedures, including a formal sup-norm t est of the simple normal model. A well-known toxicological study of aconiaz ide, a drug under investigation for treatment of tuberculosis, serves as a case study for the risk assessment methodology.