A Single-Index Model With a Surface-Link for Optimizing Individualized Dose Rules
提出一种单指标回归模型，用二维惩罚样条拟合协变量与连续治疗变量的非线性交互效应，以估计最优个体化剂量规则和治疗效果，并通过模拟和实际应用验证。
This paper 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 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) parametrization specifically defined for the interaction effect term.