A Generative Approach for Treatment Effect Estimation under Collider Bias: From an Out-of-Distribution Perspective

Resulting from non-random sample selection caused by both the treatment and outcome, collider bias poses a unique challenge to treatment effect estimation using observational data whose distribution differs from that of the target population. In this paper, we rethink collider bias from an out-of-distribution (OOD) perspective, considering that the entire data space of the target population consists of two different environments: The observational data selected from the target population belongs to a seen environment labeled with S = 1 and the missing unselected data belongs to another unseen environment labeled with S = 0. Based on this OOD formulation, we utilize small-scale representative data from the entire data space with no environmental labels and propose a novel method, i.e., Coupled Counterfactual Generative Adversarial Model (C 2 GAM), to simultaneously generate the missing S = 0 samples in observational data and the missing S labels in the small-scale representative data. With the help of C 2 GAM, collider bias can be addressed by combining the generated S = 0 samples and the observational data to estimate treatment effects. Extensive experiments on synthetic and real-world data demonstrate that plugging C 2 GAM into existing treatment effect estimators achieves significant performance improvements.