A Robust Proposal for Heteroscedastic Dose–Response Models with an Application to Interaction Analysis

This article proposes a robust approach to dose–response analysis with inhomogeneous variance observations, as it often arises in practice in the disciplines of toxicology or pharmacology. The motivating problem is a real data set generated by an experimental study where the aim is to decide the nature of the interaction between two chemical agents, that is to say whether it is additive, synergistic or antagonistic. This data set presents nonlinearity, heteroscedasticity and presence of outliers: a very challenging scenario for the analyst. A class of robust estimators for heteroscedastic nonlinear models with fixed design based on a two-step procedure is studied, and their asymptotic distribution is derived under regularity assumptions. Robust confidence intervals of the parameters of interest are deduced from the asymptotic behaviour, which we use to implement a robust version of the graphical tool called isobologram and the associated confidence regions. The robust estimators and their classical relatives are compared through a numerical experiment under different contamination schemes. An application of the methodology is illustrated through the agrochemical data.