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

Various frameworks have been suggested for assessing the risk associated with continuous toxicity outcomes. The first formulates the affect of exposure on the adverse effect via a simple normal model and then computes the risk 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 that utilizes an alternative definition of excess risk has been studied. Unfortunately, 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 and allows for a coherent risk analysis of dose-response data. In addition estimation and inference procedures for the unknown transformation in the semiparametric model for the continuous response are developed. These are incorporated in novel model-checking procedures, including a formal sup-norm test of the simple normal model. A well-known toxicological study of aconiazide, a drug under investigation for treatment of tuberculosis, serves as a case study for the risk assessment methodology.