Index: Cinelli Hazlett 2020 - Making Sense of Sensitivity

Cinelli Hazlett 2020 - Making Sense of Sensitivity

Routing Summary

This folder fully captures Cinelli & Hazlett (2020), Making Sense of Sensitivity: Extending Omitted Variable Bias (JRSS-B): the partial-$R^2$ form of the OVB identity, the robustness value $R{V}_q$, the extreme-scenario $R_{Y\sim D|X}^2$, formal bounds from observed covariates, multiple/non-linear confounders, the Darfur application, the failure of informal benchmarking, and a vault synthesis (planted confounders, Bayesian sketch). It contains 9 notes plus this index, covering all tables, figures and supplement derivations.

• Need the paper on one page, headline numbers or the section-to-note map? → Cinelli Hazlett 2020 - Making Sense of Sensitivity - Overview
• Need the classical OVB, impact times imbalance, or raw-coefficient contour plots? → Cinelli Hazlett 2020 - Traditional OVB and Sensitivity Contours
• Need the partial-$R^2$ bias, SE and relative-bias formulas with proof? → Cinelli Hazlett 2020 - Partial R2 Parameterization and Bias Formulas
• Need the robustness value, RV with significance, or the extreme-scenario statistic? → Cinelli Hazlett 2020 - Robustness Value and Extreme Scenarios
• Need to bound a confounder as ’$k$ times as strong as’ an observed covariate? → Cinelli Hazlett 2020 - Bounding Confounder Strength with Observed Covariates
• Need multiple or non-linear confounders? → Cinelli Hazlett 2020 - Multiple and Nonlinear Confounders
• Need the Darfur numbers, Table 1 or contour reading? → Cinelli Hazlett 2020 - Darfur Application and Reporting
• Need why informal benchmarks fail, or comparisons with E-value, Oster and Frank? → Cinelli Hazlett 2020 - Informal Benchmarking Pitfalls and Related Methods
• Need a planted-confounder check or a PyMC prior over confounder strength? → Cinelli Hazlett 2020 - Planted Confounders and Bayesian Sketch

Concept Map

Concept	Note	Type	Depends On	Key Result
Impact times imbalance	Cinelli Hazlett 2020 - Traditional OVB and Sensitivity Contours	definition	Omitted Variables Bias	${\hat{\tau }}_{res}=\hat{\tau }+\hat{\gamma }\hat{\delta }$
OVB in partial $R^2$	Cinelli Hazlett 2020 - Partial R2 Parameterization and Bias Formulas	theorem	impact times imbalance	bias $=\sqrt{R_Y^2{R}_D^2/(1-R_D^2)}\sqrt{df}\text{se}$
Relative bias / bias factor	Cinelli Hazlett 2020 - Partial R2 Parameterization and Bias Formulas	theorem	OVB in partial $R^2$	$BF/
Robustness value	Cinelli Hazlett 2020 - Robustness Value and Extreme Scenarios	definition	relative bias	$R{V}_q=\frac{1}{2}(\sqrt{f_q^4+4f_q^2}-f_q^2)$
Extreme scenario	Cinelli Hazlett 2020 - Robustness Value and Extreme Scenarios	theorem	relative bias	$R^2_{D\sim Z
Formal bounds $k_D,k_Y$	Cinelli Hazlett 2020 - Bounding Confounder Strength with Observed Covariates	theorem	partial $R^2$ bias	$R^2_{D\sim Z
Multiple confounders	Cinelli Hazlett 2020 - Multiple and Nonlinear Confounders	theorem	partial $R^2$ bias	single-confounder formulas are upper bounds
Darfur reporting table	Cinelli Hazlett 2020 - Darfur Application and Reporting	example	RV, bounds	RV 13.9%, $R{V}_{\alpha }$ 7.6%, $R^2_{Y\sim D
Informal benchmark failure	Cinelli Hazlett 2020 - Informal Benchmarking Pitfalls and Related Methods	concept	bounds	0.30 vs $-0.008$ in the Fig. 4 simulation
Planted confounder check	Cinelli Hazlett 2020 - Planted Confounders and Bayesian Sketch	example	all formulas	formula equals actual bias to 15 digits

Notes

• Cinelli Hazlett 2020 - Making Sense of Sensitivity - Overview — CONTAINS: research question, contributions, headline numbers, full Source Map (every section, table, figure, supplement part → note), PyMC example links.
• Cinelli Hazlett 2020 - Traditional OVB and Sensitivity Contours — CONTAINS: Sec. 1-3: Def. OVB (FWL), imbalance vs impact, Fig. 1 contours, Center example, shortcomings of raw coefficients, Python grid.
• Cinelli Hazlett 2020 - Partial R2 Parameterization and Bias Formulas — CONTAINS: Eqs. 7-17: Thm OVB in partial $R^2$ + proof, SE formula, relative bias and bias factor, VRF/VIF decomposition, equivalent parameterisations, worked 1x-3x Female example, Python.
• Cinelli Hazlett 2020 - Robustness Value and Extreme Scenarios — CONTAINS: Eqs. 18-20, 34-48: $R{V}_q$, $R{V}_{q,\alpha }$ derivations, caveat conditions, extreme-scenario theorem, Table 2 bias-factor excerpt, Frank impact counterexample, Python.
• Cinelli Hazlett 2020 - Bounding Confounder Strength with Observed Covariates — CONTAINS: Eqs. 21-22, 49-84: $k_D,k_Y$, tight bounds with $\eta$, simulation verification, total/partial/conditional-on-$D$ variants, feasibility, Python.
• Cinelli Hazlett 2020 - Multiple and Nonlinear Confounders — CONTAINS: Eqs. 23-24: composite $Z^{\ast }$ theorem, df correction, non-linear and misspecification cases, Python check.
• Cinelli Hazlett 2020 - Darfur Application and Reporting — CONTAINS: Sec. 2, 5: model (1)-(2), Table 1, Fig. 2 contour points, Fig. 3 extreme scenarios, Python.
• Cinelli Hazlett 2020 - Informal Benchmarking Pitfalls and Related Methods — CONTAINS: Sec. 6, Supp. C: collider mechanism, Fig. 4/5 reproduction, Frank, E-value, Hosman, Oster, principled-argument caveats.
• Cinelli Hazlett 2020 - Planted Confounders and Bayesian Sketch — CONTAINS: vault synthesis: planting procedure, exact check, PyMC prior over $(R_Y^2,R_D^2)$, marketing reading.

Sources

• Cinelli Hazlett 2020 - Making Sense of Sensitivity — Cinelli C, Hazlett C (2020), JRSS-B 82(1): 39-67; 41 pp. incl. supplement. Sole source.

See Also

• Imai 2010 - Causal Mediation Analysis - Overview, Franks 2019 - Flexible Sensitivity Analysis Without Observable Implications - Overview, Rosenman 2020 - Combining Observational and Experimental Datasets - Overview — siblings in this cluster.
• Omitted Variables Bias, Sensitivity Analysis in Observational Studies, Logic of Regression Adjustment, Gordon et al 2019 - Sensitivity to Unobservables and Bias-Reduction Ratio.