Causal simulation experiments: Lessons from bias amplification

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.