Bayesian Sensitivity of Causal Inference Estimators under Evidence-Based Priors
For researchers conducting causal inference from observational data, this provides a more realistic sensitivity analysis framework that incorporates prior knowledge, avoiding overly pessimistic conclusions.
The paper argues that worst-case sensitivity analysis in causal inference can be uninformative or contradict prior knowledge, and proposes the Bayesian Sensitivity Value (BSV) to compute expected sensitivity under evidence-based priors, demonstrating its use in a diabetes treatment study.
Causal inference, especially in observational studies, relies on untestable assumptions about the true data-generating process. Sensitivity analysis helps us determine how robust our conclusions are when we alter these underlying assumptions. Existing frameworks for sensitivity analysis are concerned with worst-case changes in assumptions. In this work, we argue that using such pessimistic criteria can often become uninformative or lead to conclusions contradicting our prior knowledge about the world. To demonstrate this claim, we generalize the recent s-value framework (Gupta & Rothenhäusler, 2023) to estimate the sensitivity of three different common assumptions in causal inference. Empirically, we find that, indeed, worst-case conclusions about sensitivity can rely on unrealistic changes in the data-generating process. To overcome this, we extend the s-value framework with a new sensitivity analysis criterion: Bayesian Sensitivity Value (BSV), which computes the expected sensitivity of an estimate to assumption violations under priors constructed from real-world evidence. We use Monte Carlo approximations to estimate this quantity and illustrate its applicability in an observational study on the effect of diabetes treatments on weight loss.