Independence Weights for Causal Inference with Continuous Treatments

Abstract

Studying causal effects of continuous treatments is important for gaining a deeper understanding of many interventions, policies, or medications, yet researchers are often left with observational studies for doing so. In the observational setting, confounding is a barrier to the estimation of causal effects. Weighting approaches seek to control for confounding by reweighting samples so that confounders are comparable across different treatment values. Yet, for continuous treatments, weighting methods are highly sensitive to model misspecification. In this article we elucidate the key property that makes weights effective in estimating causal quantities involving continuous treatments. We show that to eliminate confounding, weights should make treatment and confounders independent on the weighted scale. We develop a measure that characterizes the degree to which a set of weights induces such independence. Further, we propose a new model-free method for weight estimation by optimizing our measure. We study the theoretical properties of our measure and our weights, and prove that our weights can explicitly mitigate treatment-confounder dependence. The empirical effectiveness of our approach is demonstrated in a suite of challenging numerical experiments, where we find that our weights are quite robust and work well under a broad range of settings. Supplementary materials for this article are available online.

Keywords:

• Balancing weights
• Confounding
• Distance covariance
• Electronic health records
• Observational data

Supplementary Materials

Supplementary Material: The supplementary material contains details for error decompositions of weighted nonparametric estimators, computational details of the proposed method, extended discussion of the existing literature, proofs of the theoretical results, and additional simulation studies. (pdf)

Acknowledgments

We would like to thank the Associate Editor and anonymous referees for their constructive feedback and suggestions Jue Hou for the helpful discussion.

Additional information

Funding

Chen’s effort was partially supported by NSF grant DMS-2054346 and the University of Wisconsin School of Medicine and Public Health from the Wisconsin Partnership Program.