Regression-Based Proximal Causal Inference
arxiv(2024)
摘要
In observational studies, identification of causal effects is threatened by
the potential for unmeasured confounding. Negative controls have become widely
used to evaluate the presence of potential unmeasured confounding thus
enhancing credibility of reported causal effect estimates. Going beyond simply
testing for residual confounding, proximal causal inference (PCI) was recently
developed to debias causal effect estimates subject to confounding by hidden
factors, by leveraging a pair of negative control variables, also known as
treatment and outcome confounding proxies. While formal statistical inference
has been developed for PCI, these methods can be challenging to implement in
practice as they involve solving complex integral equations that are typically
ill-posed. In this paper, we develop a regression-based PCI approach, employing
a two-stage regression via familiar generalized linear models to implement the
PCI framework, which completely obviates the need to solve difficult integral
equations. In the first stage, one fits a generalized linear model (GLM) for
the outcome confounding proxy in terms of the treatment confounding proxy and
the primary treatment. In the second stage, one fits a GLM for the primary
outcome in terms of the primary treatment, using the predicted value of the
first-stage regression model as a regressor which as we establish accounts for
any residual confounding for which the proxies are relevant. The proposed
approach has merit in that (i) it is applicable to continuous, count, and
binary outcomes cases, making it relevant to a wide range of real-world
applications, and (ii) it is easy to implement using off-the-shelf software for
GLMs. We establish the statistical properties of regression-based PCI and
illustrate their performance in both synthetic and real-world empirical
applications.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要