Treatment effect estimation with confounder balanced instrumental variable regression

Anpeng Wu, Kun Kuang, Fei Wu

Keywords: treatment effect, unmeasured confounders, instrumental variable, confounder balance, representaion learning

Abstract: This paper considers the challenge of estimating treatment effects from observational data in the presence of unmeasured confounders. A popular way to address this challenge is to utilize an instrumental variable (IV) for two-stage regression, i.e., 2SLS and variants, but they need to assume the additive separability of noise and are limited to the linear setting. Recently, many nonlinear IV regression variants were proposed by regressing the treatment with IVs and confounders in the first stage, leading to confounding bias between the predicted treatment and outcome in the second stage. In this paper, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders with IV regression and reduce the bias from the observed confounders by balancing for treatment effect estimation. Specifically, CB-IV algorithm consists of three main modules: (1) treatment regression: regressing the treatment with IVs and confounders like previous nonlinear IV methods for removing the confounding from unmeasured confounders; (2) confounder balancing: learning a balanced representation of confounders to eliminate the bias induced by the observed confounders (3) outcome regression: regressing the outcome with the predicted treatment and the balanced confounders representation for treatment effect estimation. To the best of our knowledge, this is the first work to combine confounder balancing in IV regression for treatment effect estimation. Moreover, we theoretically prove that CB-IV algorithm is also effective even without the additive separability assumption on noise. Extensive experiments demonstrate that the CB-IV algorithm outperforms the state-of-the-art methods, including IV regression and confounder balancing methods, for treatment effect estimation.

One-sentence Summary: Our algorithm jointly remove the bias from the unmeasured confounders with IV regression and reduce the bias from the observed confounders with balancing for treatment effect estimation without the additive separability assumption.