Maxway CRT: improving the robustness of the model-X inference

• 成果类型: Article
• 署名作者: Li, Shuangning; Liu, Molei
• 署名单位: Harvard University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad081
• 发表日期: 2024
• 页码: 1441-1470
• 关键词: risk-factors; obesity; knockoffs; therapy; POWER

摘要

The model-X conditional randomisation test (CRT) is a flexible and powerful testing procedure for testing the hypothesis X?Y divide Z. However, it requires perfect knowledge of X divide Z and may lose its validity when there is an error in modelling X divide Z. This problem is even more severe when Z is of high dimensionality. In response to this, we propose the Maxway CRT, which learns the distribution of Y divide Z and uses it to calibrate the resampling distribution of X to gain robustness to the error in modelling X. We prove that the type-I error inflation of the Maxway CRT can be controlled by the learning error for a low-dimensional adjusting model plus the product of learning errors for X divide Z and Y divide Z, interpreted as an 'almost doubly robust' property. Based on this, we develop implementing algorithms of the Maxway CRT in practical scenarios including (surrogate-assisted) semi-supervised learning (SA-SSL) and transfer learning (TL). Through simulations, we demonstrate that the Maxway CRT achieves significantly better type-I error control than existing model-X inference approaches while preserving similar powers. Finally, we apply our methodology to two real examples of SA-SSL and TL.