Instrumental variables as bias amplifiers with general outcome and confounding

• https://academic.oup.com/biomet/article/104/2/291/3737784
• P. Ding, T.J. Vanderweele, J. M. Robins

Z bias

It is often believed that the more covariates we condition on, the more plausible this unconfoundedness assumption is. This belief has had a huge impact on practical causal inference, suggesting that we should adjust for all pretreatment covariates. However, when there is unmeasured confounding between the treatment and outcome, estimators adjusting for some pretreatment covariate might have greater bias than estimators that do not adjust for this covariate. This kind of covariate is called a bias amplifier, and includes instrumental variables that are independent of the confounder and affect the outcome only through the treatment.