Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding

It is a truth universally acknowledged that an observed association without known mechanism must be in want of a causal estimate. Causal estimates from observational data will be biased in the presence of ‘unobserved confounding’. However, we might hope that the influence of unobserved confounders is weak relative to a ‘large’ estimated effect. The purpose of this paper is to develop Austen plots, a sensitivity analysis tool to aid such judgments by making it easier to reason about potential bias induced by unobserved confounding. We formalize confounding strength in terms of how strongly the unobserved confounding influences treatment assignment and outcome. For a target level of bias, an Austen plot shows the minimum values of treatment and outcome influence required to induce that level of bias. Austen plots generalize the classic sensitivity analysis approach of Imbens [Imb03]. Critically, Austen plots allow any approach for modeling the observed data. We illustrate the tool by assessing biases for several real causal inference problems, using a variety of machine learning approaches for the initial data analysis. Code, demo data, and a tutorial are available at github.com/anishazaveri/austen_plots.