To Adjust or Not to Adjust? Sensitivity Analysis of M -Bias and Butterfly-Bias

Journal of Causal Inference

article

Peng Ding¹  Luke W. Miratrix¹ 

[1] Department of Statistics, Harvard University

关键词: causality;    collider;    confounding;    controversy;    covariate;   

DOI  :  10.1515/jci-2013-0021

来源: De Gruyter

【 摘 要 】

“ M -Bias,” as it is called in the epidemiologic literature, is the bias introduced by conditioning on a pretreatment covariate due to a particular “ M -Structure” between two latent factors, an observed treatment, an outcome, and a “collider.” This potential source of bias, which can occur even when the treatment and the outcome are not confounded, has been a source of considerable controversy. We here present formulae for identifying under which circumstances biases are inflated or reduced. In particular, we show that the magnitude of M -Bias in linear structural equation models tends to be relatively small compared to confounding bias, suggesting that it is generally not a serious concern in many applied settings. These theoretical results are consistent with recent empirical findings from simulation studies. We also generalize the M -Bias setting (1) to allow for the correlation between the latent factors to be nonzero and (2) to allow for the collider to be a confounder between the treatment and the outcome. These results demonstrate that mild deviations from the M -Structure tend to increase confounding bias more rapidly than M -Bias, suggesting that choosing to condition on any given covariate is generally the superior choice. As an application, we re-examine a controversial example between Professors Donald Rubin and Judea Pearl.

【 授权许可】

CC BY