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

Ding Peng () and Miratrix Luke W. ()
Additional contact information
Ding Peng: Department of Statistics, Harvard University, Cambridge, MA 02138, USA
Miratrix Luke W.: Department of Statistics, Harvard University, Cambridge, MA 02138, USA

Journal of Causal Inference, 2015, vol. 3, issue 1, 41-57

Abstract: “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.

Keywords: causality; collider; confounding; controversy; covariate (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/jci-2013-0021 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:3:y:2015:i:1:p:41-57:n:1003

DOI: 10.1515/jci-2013-0021

Access Statistics for this article

Journal of Causal Inference is currently edited by Elias Bareinboim, Jin Tian and Iván Díaz

More articles in Journal of Causal Inference from De Gruyter
Bibliographic data for series maintained by Peter Golla ().