This paper explores a methodology for dimension reduction in regression models for a treatment outcome, specifically to capture covariates’ moderating impact on the treatment-outcome association. The motivation behind this stems from the field of precision medicine, where a comprehensive understanding of the interactions between a treatment variable and pretreatment covariates is essential for developing individualized treatment regimes (ITRs). We provide a review of sufficient dimension reduction methods suitable for capturing treatment-covariate interactions and establish connections with linear model-based approaches for the proposed model. Within the framework of single-index regression models, we introduce a sparse estimation method for a dimension reduction vector to tackle the challenges posed by high-dimensional covariate data. Our methods offer insights into dimension reduction techniques specifically for interaction analysis, by providing a semiparametric framework for approximating the minimally sufficient subspace for interactions.

本文探讨了一种治疗结果回归模型降维的方法，特别是为了捕捉协变量对治疗结果关联的调节影响。其背后的动机源于精准医学领域，全面了解治疗变量和治疗前协变量之间的相互作用对于制定个体化治疗方案（ITR）至关重要。我们回顾了适合捕获治疗协变量相互作用的足够的降维方法，并为所提出的模型建立了与基于线性模型的方法的联系。在单指标回归模型的框架内，我们引入了降维向量的稀疏估计方法，以应对高维协变量数据带来的挑战。我们的方法通过提供半参数框架来近似交互的最小足够子空间，从而深入了解专门用于交互分析的降维技术。