81 research outputs found
To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias
"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.Comment: Journal of Causal Inference 201
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