Abstract

A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the main interest lies in the interaction, this approach is not entirely satisfactory because it is prone to (possibly severe) bias when the main exposure effects or the association between outcome and extraneous factors are misspecified. In this talk, I will therefore consider conditional mean models with identity or log link which postulate the statistical interaction in terms of a finite-dimensional parameter, but which are otherwise unspecified. I will show that estimation of the interaction parameter is often not feasible in this model because it would require nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. I will thus consider `multiply robust estimation’, assuming at least one of several working submodels holds. The proposed approach is novel in that it makes use of information on the joint distribution of the exposures conditional on the extraneous factors in making inferences about the interaction parameter of interest. As such, it essentially encompasses a `propensity score’ approach to the estimation of interaction parameters. In the special case of a randomized trial or a family-based genetic study in which the joint exposure distribution is known by design or by Mendelian inheritance, the procedure leads to asymptotically distribution-free tests of the null hypothesis of no interaction on an additive scale. I will illustrate the methods via simulation and the analysis of a randomized follow-up study. This is based on joint work with Tyler VanderWeele (University of Chicago) and James Robins (Harvard University).