Treatment Effect Estimation with Collider Bias and Confounding Bias

Baohong Li, Kun Kuang, Ruoxuan Xiong, Fei Wu

Abstract: To answer causal questions from observational data, it is important to consider the mechanisms that determine which data values are observed and which are missing. Prior work has considered the treatment assignment mechanism and proposed methods to remove the confounding bias from the common causes of treatment and outcome. However, there are other issues in sample selection, commonly overlooked in prior work, that can bias the treatment effect estimation, such as the issue of censored outcome as a form of collider bias. In this paper, we propose the novel Selection Controlled CounterFactual Regression (SC-CFR) to simultaneously address confounding and collider bias. Specifically, we first calculate the magnitude of the collider bias of different instances by estimating the selection model and then add a control term to remove the collider bias while learning a balanced representation to remove the confounding bias when estimating the outcome model. Our method is shown to provide unbiased treatment effect estimates from observational data with confounding and collider bias. Extensive empirical results on both synthetic and real-world datasets show that our method consistently outperforms benchmarks when both types of biases exist.

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