A Single-Index Model With a Surface-Link for Optimizing Individualized Dose Rules

This article focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression. The primary motivation is to estimate an optimal individualized dose rule and individualized treatment effects. To model possibly nonlinear interaction effects between the patients' covariates and a continuous treatment variable, we employ a two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear projection of the covariates. The method is illustrated using two applications as well as simulation experiments. A unique contribution of this work is in the parsimonious (single-index) parameterization specifically defined for the interaction effect term, that can be used to assess the treatment benefit. Supplemental materials for this article are available online.