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Optimal statistical inference for individualized treatment effects in high‐dimensional models
Author(s) -
Cai Tianxi,
Tony Cai T.,
Guo Zijian
Publication year - 2021
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12426
Subject(s) - inference , estimator , computer science , statistical inference , normality , novelty , statistical hypothesis testing , linear model , sample size determination , mathematical optimization , machine learning , mathematics , artificial intelligence , statistics , philosophy , theology
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.