Independence weights for causal inference with continuous treatments

TL;DR

This paper introduces a new model-free weighting method for causal inference with continuous treatments, focusing on achieving independence between treatment and confounders to reduce bias in observational studies.

Contribution

It develops a novel measure for evaluating weights' effectiveness and proposes an optimization-based approach to estimate weights that promote treatment-confounder independence.

Findings

Weights effectively mitigate treatment-confounder dependence.

Method demonstrates robustness across diverse numerical experiments.

Theoretical analysis confirms the measure's properties and effectiveness.

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 paper 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.