  Recent theoretical work in causal inference has explored an important class
of variables which, when conditioned on, may further amplify existing
unmeasured confounding bias (bias amplification). Despite this theoretical
work, existing simulations of bias amplification in clinical settings have
suggested bias amplification may not be as important in many practical cases as
suggested in the theoretical literature.We resolve this tension by using tools
from the semi-parametric regression literature leading to a general
characterization in terms of the geometry of OLS estimators which allows us to
extend current results to a larger class of DAGs, functional forms, and
distributional assumptions. We further use these results to understand the
limitations of current simulation approaches and to propose a new framework for
performing causal simulation experiments to compare estimators. We then
evaluate the challenges and benefits of extending this simulation approach to
the context of a real clinical data set with a binary treatment, laying the
groundwork for a principled approach to sensitivity analysis for bias
amplification in the presence of unmeasured confounding.
