The synthetic instrument: From sparse association to sparse causation

TL;DR

This paper introduces the synthetic instrument, a novel method for estimating sparse causal effects in observational studies with unmeasured confounding, using a new construct that leverages observed exposures directly.

Contribution

It proposes the synthetic instrument approach, enabling causal effect estimation under sparsity assumptions even with unmeasured confounding, and formulates the problem as an $$-penalization problem solvable with existing software.

Findings

Outperforms existing methods in simulations

Effective in both low- and high-dimensional settings

Successfully applied to a mouse obesity dataset

Abstract

In many observational studies, researchers are often interested in studying the effects of multiple exposures on a single outcome. Standard approaches for high-dimensional data such as the lasso assume the associations between the exposures and the outcome are sparse. These methods, however, do not estimate the causal effects in the presence of unmeasured confounding. In this paper, we consider an alternative approach that assumes the causal effects in view are sparse. We show that with sparse causation, the causal effects are identifiable even with unmeasured confounding. At the core of our proposal is a novel device, called the synthetic instrument, that in contrast to standard instrumental variables, can be constructed using the observed exposures directly. 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.