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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.

Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well‐known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals outperform traditional instrumental variable confidence intervals when invalid instruments are present and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low‐density lipoprotein on globulin levels.