  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.
