Sufficient Dimension Reduction for Average Causal Effect Estimation

TL;DR

This paper introduces a method for reducing high-dimensional covariates to a lower-dimensional space that preserves all information necessary for accurate causal effect estimation, improving efficiency and reliability.

Contribution

It provides a theoretical proof for covariate reduction in causal inference and develops a supervised kernel dimension reduction algorithm for practical implementation.

Findings

Effective covariate reduction preserves causal adjustment information.

Algorithm outperforms traditional methods on multiple datasets.

Reduces bias and variance in causal effect estimates.

Abstract

Having a large number of covariates can have a negative impact on the quality of causal effect estimation since confounding adjustment becomes unreliable when the number of covariates is large relative to the samples available. Propensity score is a common way to deal with a large covariate set, but the accuracy of propensity score estimation (normally done by logistic regression) is also challenged by large number of covariates. In this paper, we prove that a large covariate set can be reduced to a lower dimensional representation which captures the complete information for adjustment in causal effect estimation. The theoretical result enables effective data-driven algorithms for causal effect estimation. We develop an algorithm which employs a supervised kernel dimension reduction method to search for a lower dimensional representation for the original covariates, and then utilizes nearest neighbor matching in the reduced covariate space to impute the counterfactual outcomes to avoid large-sized covariate set problem. The proposed algorithm is evaluated on two semi-synthetic and three real-world datasets and the results have demonstrated the effectiveness of the algorithm.