Treatment Effect Estimation via Differentiated Confounder Balancing and Regression

Abstract

Treatment effect plays an important role on decision making in many fields, such as social marketing, healthcare, and public policy. The key challenge on estimating treatment effect in the wild observational studies is to handle confounding bias induced by imbalance of the confounder distributions between treated and control units. Traditional methods remove confounding bias by re-weighting units with supposedly accurate propensity score estimation under the unconfoundedness assumption. Controlling high-dimensional variables may make the unconfoundedness assumption more plausible, but poses new challenge on accurate propensity score estimation. One strand of recent literature seeks to directly optimize weights to balance confounder distributions, bypassing propensity score estimation. But existing balancing methods fail to do selection and differentiation among the pool of a large number of potential confounders, leading to possible underperformance in many high-dimensional settings. In this article, we propose a data-driven Differentiated Confounder Balancing (DCB) algorithm to jointly select confounders, differentiate weights of confounders and balance confounder distributions for treatment effect estimation in the wild high-dimensional settings. Besides, under some settings with heavy confounding bias, in order to further reduce the bias and variance of estimated treatment effect, we propose a Regression Adjusted Differentiated Confounder Balancing (RA-DCB) algorithm based on our DCB algorithm by incorporating outcome regression adjustment. The synergistic learning algorithms we proposed are more capable of reducing the confounding bias in many observational studies. To validate the effectiveness of our DCB and RA-DCB algorithms, we conduct extensive experiments on both synthetic and real-world datasets. The experimental results clearly demonstrate that our algorithms outperform the state-of-the-art methods. By incorporating regression adjustment, our RA-DCB algorithm achieves more precise estimation on treatment effect than DCB algorithm, especially under the settings with heavy confounding bias. Moreover, we show that the top features ranked by our algorithm generate accurate prediction of online advertising effect.