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Primary Submission Category: Weighting

Balancing Covariates via Weighted Independence Measures for Continuous Exposures

Authors: Xiao Wu, Trevor Hastie,

Presenting Author: Xiao Wu*

Covariate balance plays a central role in causal inference. In this paper, we study the framework for balancing covariates in observational studies with a continuous exposure. Firstly, we overview two closely related approaches: 1) the modeling approach that maximizes the fit of a propensity model for treatment assignment, and weights by the inverse of the estimated propensity density to achieve covariate balance in large samples; 2) the balancing approach that optimizes certain measures of the covariate balance in finite samples. We propose the use of weighted independent measures to diagnose the degree of covariate balance and to achieve the uniform approximate balance for covariate functions in a reproducing-kernel Hilbert space. We provide theoretical justification that the proposed weighting estimator could achieve minimized biases under certain outcome model specifications. In simulations, the proposed methods outperform existing methods in terms of covariate balance, effective sample sizes, absolute bias, and root mean squared errors.