Recover Experimental Data with Selection Bias using Counterfactual Logic

TL;DR

This paper develops a causal inference framework using counterfactual logic and SCMs to identify and recover unbiased experimental data affected by selection bias, expanding applicability beyond traditional methods.

Contribution

It introduces graphical and theoretical criteria for recoverability under selection bias and proposes methods to leverage partial observational data for bias correction.

Findings

Criteria for when experimental distributions are unaffected by selection bias

Methods to recover causal effects from biased experimental data

Simulation results demonstrating practical utility

Abstract

Selection bias, arising from the systematic inclusion or exclusion of certain samples, poses a significant challenge to the validity of causal inference. While Bareinboim et al. introduced methods for recovering unbiased observational and interventional distributions from biased data using partial external information, the complexity of the backdoor adjustment and the method's strong reliance on observational data limit its applicability in many practical settings. In this paper, we formally discover the recoverability of $P(Y^*_{x^*})$ under selection bias with experimental data. By explicitly constructing counterfactual worlds via Structural Causal Models (SCMs), we analyze how selection mechanisms in the observational world propagate to the counterfactual domain. We derive a complete set of graphical and theoretical criteria to determine that the experimental distribution remain unaffected by selection bias. Furthermore, we propose principled methods for leveraging partially unbiased observational data to recover $P(Y^*_{x^*})$ from biased experimental datasets. Simulation studies replicating realistic research scenarios demonstrate the practical utility of our approach, offering concrete guidance for mitigating selection bias in applied causal inference.