Confidence intervals for causal effects with invalid instruments by using two-stage hard thresholding with voting

• 成果类型: Article
• 署名作者: Guo, Zijian; Kang, Hyunseung; Cai, T. Tony; Small, Dylan S.
• 署名单位: Rutgers University System; Rutgers University New Brunswick; University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12275
• 发表日期: 2018
• 页码: 793-815
• 关键词: mendelian randomization; weak instruments; linear-models; regression; inference; selection; Lasso; identification; variables; epidemiology

摘要

A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called two-stage hard thresholding with voting. The procedure uses two hard thresholding steps to select strong instruments and to generate candidate sets of valid IVs. Voting takes the candidate sets and uses majority and plurality rules to determine the true set of valid IVs. In low dimensions with invalid instruments, our proposal correctly selects valid IVs, consistently estimates the causal effect, produces valid confidence intervals for the causal effect and has oracle optimal width, even if the so-called 50% rule or the majority rule is violated. In high dimensions, we establish nearly identical results without oracle optimality. In simulations, our proposal outperforms traditional and recent methods in the invalid IV literature. We also apply our method to reanalyse the causal effect of education on earnings.