Bayesian Sensitivity of Causal Inference Estimators under Evidence-Based Priors

2026-05-08

AI Summary

Traditional sensitivity analyses in causal inference often rely on worst-case assumptions that conflict with real-world priors and yield uninformative conclusions. This work proposes the Bayesian Sensitivity Value (BSV), which integrates real-world evidence–informed priors into the s-value framework and employs Bayesian inference with Monte Carlo approximation to quantify the expected sensitivity of causal estimates under perturbations. Applied to an observational study examining the effect of diabetes treatment on body weight, BSV demonstrates that conventional worst-case analyses frequently rest on implausible data-generating mechanisms, thereby offering a more realistic and informative assessment of sensitivity.

Abstract

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.

Problem

• causal inference
• sensitivity analysis
• Bayesian sensitivity
• observational studies
• assumption violations

Innovation

• Bayesian Sensitivity Value
• causal inference
• sensitivity analysis
• evidence-based priors
• s-value