Representing Unmeasured Confounding in Causal Models for Observational Data
*Joseph W Hogan, Brown University
Keywords: sensitivity analysis, treatment effect estimation, matching, design sensitivity
Arguably the most important assumption needed for drawing causal inference from observational data is ‘ignorable treatment assignment’ or ‘no unmeasured confounding,’ which states that, conditionally on a specific set of measured covariates (confounders), potential outcomes are independent of exposure. When the assumption holds, valid inferences about causal effect are possible using a variety of methods.
The no unmeasured confounding condition is untestable, however, which has led to methods for representing unmeasured confounding and quantifying potential biases. We review, compare, and draw connections between two distinct approaches: (1) representing unmeasured confounding using a latent random variable that depends on outcome and exposure; and (2) creating the unobserved potential outcome as the sole unmeasured confounder. Each approach gives rise to methods for sensitivity analysis and bias quantification; these will be illustrated and compared using both simulation and data analysis. We also examine whether and how sensitivity to bias from unmeasured confounding depends on the set of measured confounders being used for adjustment.