Academic

Abstract

In many observational studies, researchers are interested in studying the effects of multiple exposures on the same outcome. Unmeasured confounding is a key challenge in these studies as it may bias the causal effect estimate. To mitigate the confounding bias, we introduce a novel device, called the synthetic instrument, to leverage the information contained in multiple exposures for causal effect identification and estimation. We show that under linear structural equation models, the problem of causal effect estimation can be formulated as an $\ell_0$-penalization problem, and hence can be solved efficiently using off-the-shelf software. Simulations show that our approach outperforms state-of-art methods in both low-dimensional and high-dimensional settings. We further illustrate our method using a mouse obesity dataset.