A Study on the Impact of Non-confounding Covariates on the Inferential Performance of Methods based on the Potential Outcome Framework

The Potential Outcome Framework (POF) plays a prominent role in the field of causal inference. Most causal inference models based on the POF (CIMs-B-POF) are designed for eliminating confounding bias and default to an underlying assumption of Confounding Covariates. This assumption posits that the covariates consist solely of confounders. However, the assumption of Confounding Covariates is challenging to maintain in practice, particularly when dealing with high-dimensional covariates. While certain methods have been proposed to differentiate the distinct components of covariates prior to conducting causal inference, the consequences of treating non-confounding covariates as confounders remain unclear. This ambiguity poses a potential risk when applying the CIMs-B-POF in practical scenarios. In this paper, we present a unified graphical framework for the CIMs-B-POF, which greatly enhances the comprehension of these models' underlying principles. Using this graphical framework, we quantitatively analyze the extent to which the inference performance of CIMs-B-POF is influenced when incorporating various types of non-confounding covariates, such as instrumental variables, mediators, colliders, and adjustment variables. The key findings are: in the task of eliminating confounding bias, the optimal scenario is for the covariates to exclusively encompass confounders; in the subsequent task of inferring counterfactual outcomes, the adjustment variables contribute to more accurate inferences. Furthermore, extensive experiments conducted on synthetic datasets consistently validate these theoretical conclusions.