Abstract

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.

摘要

本文侧重于使用单指数回归建模和估计协变量和连续治疗变量之间的相互作用对结果的影响。主要动机是估计最佳个体化剂量规则和个体化治疗效果。为了模拟患者的协变量和连续治疗变量之间可能存在的非线性交互作用，我们在指数治疗域上采用二维惩罚样条回归，其中指数定义为协变量的线性投影。该方法使用两个应用程序以及模拟实验进行说明。这项工作的一个独特贡献是专门为相互作用效应项定义的简约（单指数）参数化，可用于评估治疗效果。