Sensitivity analysis for causal mediation: bridge score, sharp sensitivity bounds, and calibration

TL;DR

This paper develops a new sensitivity analysis framework for causal mediation that uses the bridge score to derive sharp bounds on unmeasured confounding, with calibration methods and Bayesian inference.

Contribution

It introduces the bridge score as a balancing score, derives sharp bounds on confounding, and proposes calibration and Bayesian methods for mediation analysis.

Findings

Bridge score is a balancing score for sequential ignorability.

Sharp bounds on confounding are derived using the bridge score.

Calibration methods improve sensitivity analysis interpretability.

Abstract

Causal mediation analysis decomposes the total treatment effect into a portion operating through a hypothesized mediator and a residual direct portion. Identification of natural direct and indirect effects typically rests on the mediator stage of sequential ignorability, which cannot be empirically verified and requires explicit sensitivity analysis. We introduce the \emph{bridge score}, a low-dimensional vector formed from the two treatment-specific mediator densities at a common mediator value, and show that it is a balancing score for the mediator stage of sequential ignorability. Conditional on the bridge score, we then derive a sharp pointwise envelope on the unidentified mediator-outcome confounding function in terms of two interpretable latent confounding parameters. To make the bound operational for sensitivity analysis, we further introduce two calibration approaches. The first is benchmark calibration against an observed covariate, including a rank-based version that is invariant to monotone re-expressions of the benchmark; the second is residual budget calibration based on residual outcome variation. Finally, we show how the pointwise bound can be operationalized for inference through a scalar functional reduction and a Bayesian g-computation algorithm that propagates all sources of uncertainty into posterior draws of the mediation effect estimates.