We consider a single-index regression model, uniquely constrained to estimate interactions between a set of pretreatment covariates and a treatment variable on their effects on a response variable, in the context of analyzing data from randomized clinical trials. We represent interaction effect terms of the model through a set of treatment-specific flexible link functions on a linear combination of the covariates (a single index), subject to the constraint that the expected value given the covariates equals zero, while leaving the main effects of the covariates unspecified. We show that the proposed semiparametric estimator is consistent for the interaction term of the model, and that the efficiency of the estimator can be improved with an augmentation procedure. The proposed single-index regression provides a flexible and interpretable modeling approach to optimizing individualized treatment rules based on patients' data measured at baseline, as illustrated by simulation examples and an application to data from a depression clinical trial. This article is protected by copyright. All rights reserved.

中文翻译：

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用于估计治疗和协变量之间相互作用的约束单指数回归

我们考虑使用单指数回归模型，在分析随机临床试验数据的背景下，该模型唯一地限制了估计一组治疗前协变量和治疗变量之间的相互作用及其对响应变量的影响。我们通过协变量（单个指数）的线性组合上的一组特定于治疗的灵活链接函数来表示模型的交互效应项，但受到给定协变量的期望值为零的约束，同时保留主效应未指定的协变量。我们表明，所提出的半参数估计器对于模型的交互项是一致的，并且可以通过增强过程来提高估计器的效率。所提出的单指数回归提供了一种灵活且可解释的建模方法，用于根据基线测量的患者数据优化个体化治疗规则，如模拟示例和抑郁症临床试验数据的应用所示。本文受版权保护。版权所有。