The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a hypothesis testing approach to choosing between two potential treatments for a given individual in the framework of high-dimensional linear models. The methodological novelty lies in the construction of a debiased estimator of the ITE and establishment of its asymptotic normality uniformly for an arbitrary future high-dimensional observation, while the existing methods can only handle certain specific forms of observations. We introduce a testing procedure with the type I error controlled and establish its asymptotic power. The proposed method can be extended to making inference for general linear contrasts, including both the average treatment effect and outcome prediction. We introduce the optimality framework for hypothesis testing from both the minimaxity and adaptivity perspectives and establish the optimality of the proposed procedure. An extension to high-dimensional approximate linear models is also considered. The finite sample performance of the procedure is demonstrated in simulation studies and further illustrated through an analysis of electronic health records data from patients with rheumatoid arthritis.

中文翻译：

---

高维模型中个体化治疗效果的最优统计推断

根据给定患者的资料预测个性化治疗效果 (ITE) 的能力对于个性化医疗至关重要。我们提出了一种假设检验方法，可以在高维线性模型的框架内为给定的个体在两种潜在的治疗方法之间进行选择。方法论的新颖之处在于构建了 ITE 的去偏估计量，并为任意未来的高维观测统一建立了其渐近正态性，而现有方法只能处理某些特定形式的观测。我们引入了一个控制了 I 类错误的测试程序并建立了它的渐近功效。所提出的方法可以扩展到对一般线性对比进行推断，包括平均治疗效果和结果预测。我们从极小极大性和自适应性的角度介绍了假设检验的最优性框架，并建立了所提出程序的最优性。还考虑了对高维近似线性模型的扩展。该程序的有限样本性能在模拟研究中得到证明，并通过对类风湿性关节炎患者的电子健康记录数据的分析得到进一步说明。