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To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias by Peng Ding; Luke W. Miratrix is a Mathematics article available to read on EtoBox.

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## 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 th

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Author

Peng Ding; Luke W. Miratrix

Publisher

Walter de Gruyter GmbH

Published

2015

Language

EN

Field

Mathematics (Physical Sciences)