Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows
This addresses the problem of unobserved confounding for researchers in causal inference, offering a novel method for sensitivity analysis, though it is incremental in building on existing causal graphical models.
The paper tackles sensitivity analysis to unobserved confounding in causal inference by proposing a copula-based normalizing flow method (ρ-GNF) that estimates the average causal effect as a function of a sensitivity parameter ρ, enabling bounds and identification of confounding strength to nullify effects, with experiments on simulated and real-world data demonstrating its benefits.
We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, accounting for various confounding strengths. The output of the $ρ$-GNF is what we term the $ρ_{curve}$, which provides the bounds for the ACE given an interval of assumed $ρ$ values. The $ρ_{curve}$ also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter $ρ$ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method.