Index: Causal Sensitivity and Mediation

Causal Sensitivity and Mediation

Routing Summary

This cluster covers how robust a causal estimate is to hidden confounding (partial-R² robustness values, Tukey-factorization sensitivity), causal mediation (ACME, sequential ignorability, the unidentified error correlation), shrinking observational estimates toward a few experiments, and keeping answers on identified quantities. It has 5 sub-folders and 32 notes, written to cover the methods used in the PyMC worked examples E35, E62, E101-E103, E107 (examples page). Start from a source overview:

• Cinelli Hazlett 2020: Cinelli Hazlett 2020 - Making Sense of Sensitivity - Overview
• Franks DAmour Feller 2019: Franks 2019 - Flexible Sensitivity Analysis Without Observable Implications - Overview
• Imai Keele Yamamoto 2010: Imai 2010 - Causal Mediation Analysis - Overview
• Rosenman 2020: Rosenman 2020 - Combining Observational and Experimental Datasets - Overview

Sub-topics

• Cinelli Hazlett 2020 - Making Sense of Sensitivity (9 notes) — COVERS: Cinelli & Hazlett (JRSS-B 2020) extend the classical omitted-variable-bias (OVB) formula into a sensitivity toolkit for OLS that needs no model of the confounder or of treatment assignment. Two partial-$R^2$ numbers, the robustness value $R{V}_q$ and the extreme-scenario $R_{Y\sim D|X}^2$, summarise how strong unobserved confounding must be to change a conclusion; a formal bounding…
• Franks DAmour Feller 2019 - Flexible Sensitivity Analysis (7 notes) — COVERS: Franks, D’Amour & Feller (JASA 2020) build a Bayesian-friendly sensitivity analysis for unmeasured confounding from Tukey’s factorization: the missing potential-outcome distribution is the observed one tilted by an unidentified selection function $f(T|Y(t),X)$. Because the observed-data model is fit once and never depends on the sensitivity parameters, the parameters are genuinely…
• Imai Keele Yamamoto 2010 - Causal Mediation Analysis (7 notes) — COVERS: Imai, Keele & Yamamoto (Statistical Science 2010) prove that under a sequential ignorability assumption the average causal mediation effect (ACME) and average natural direct effects are nonparametrically identified, show that the Baron-Kenny product of coefficients ${\beta }_2\gamma$ is a causal ACME under that assumption plus no treatment-mediator interaction, give nonparametric estimators, and…
• Rosenman 2020 - Combining Observational and Experimental Datasets (7 notes) — COVERS: Rosenman, Basse, Owen & Baiocchi (arXiv 2020) combine a small randomised study (unbiased, high-variance estimates ${\hat{\tau }}_r$ of $K$ stratum effects) with a large observational study (${\hat{\tau }}_o$, low-variance but with unknown stratum-level bias $\xi$ from unmeasured confounding). Stein-type shrinkage estimators ${\kappa }_1^{+},{\kappa }_2^{+}$ trade off the two by minimising an unbiased risk estimate,…
• Unidentified Parameters and Question Contracts (concept) (2 notes) — COVERS: Concept notes: Unidentified Parameters - Keeping the Answer on the Question, Unidentified Parameters - Partial Identification and Bayesian Updating

Motivating PyMC examples

E35, E62, E101-E103, E107 — see the worked examples page; each source Overview lists the examples it supports.

Sources

• Cinelli Hazlett 2020 - Making Sense of Sensitivity
• Franks DAmour Feller 2019 - Flexible Sensitivity Analysis Without Observable Implications
• Imai Keele Yamamoto 2010 - Identification Inference and Sensitivity Analysis for Causal Mediation
• Rosenman 2020 - Combining Observational and Experimental Datasets Using Shrinkage Estimators

See Also

• Applied Bayesian Model Families — sibling clusters