High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates

Abstract

Regression adjustment is often used to estimate average treatment effect (ATE) in randomized experiments. Recently, some penalty-based regression adjustment methods have been proposed to handle the high-dimensional problem. However, these existing high-dimensional regression adjustment methods may fail to achieve satisfactory performance when the covariates are highly correlated. In this paper, we propose a novel adjustment estimation method for ATE by combining the semi-standard partial covariance (SPAC) and regression adjustment methods. Under some regularity conditions, the asymptotic normality of our proposed SPAC adjustment ATE estimator is shown. Some simulation studies and an analysis of HER2 breast cancer data are carried out to illustrate the advantage of our proposed SPAC adjustment method in addressing the highly correlated problem of the Rubin causal model.

Keywords

• average treatment effect
• highly correlated covariates
• regression adjustment
• rubin causal model
• semi-standard partial covariance