Index: Franks DAmour Feller 2019 - Flexible Sensitivity Analysis Without Observable Implications

Franks DAmour Feller 2019 - Flexible Sensitivity Analysis Without Observable Implications

Routing Summary

This folder fully captures Franks, D’Amour & Feller (2019/2020), Flexible sensitivity analysis for observational studies without observable implications (JASA; arXiv:1809.00399): Tukey’s factorization for causal inference, the copula-invariance theorem for marginal contrasts, logistic selection with exponential-family mixtures, calibration by implicit $R^2$, and the NHANES and JTPA applications. It contains 7 notes plus this index.

• Need the paper on one page or the section-to-note map? → Franks 2019 - Flexible Sensitivity Analysis Without Observable Implications - Overview
• Need why identified sensitivity parameters in latent-confounder models are a problem? → Franks 2019 - Identified Sensitivity Parameters and Latent Confounder Pitfalls
• Need Tukey’s factorization, Conditions 1-2, Theorem 1 or the copula? → Franks 2019 - Tukey Factorization and Marginal Contrast Estimands
• Need the closed-form missing distributions (Props 1-2, Examples 2-4)? → Franks 2019 - Logistic Selection with Exponential Family Mixtures
• Need the meaning of the signs of ${\gamma }_0,{\gamma }_1$ or Proposition 3? → Franks 2019 - Calibrating Sensitivity Parameters
• Need the NHANES or JTPA analyses? → Franks 2019 - NHANES and Job Training Applications
• Need limitations or a PyMC sketch for hidden targeting (E102-E103)? → Franks 2019 - Discussion Limits and Bayesian Sketch

Concept Map

Concept	Note	Type	Depends On	Key Result
Identified vs unidentified sensitivity parameters	Franks 2019 - Identified Sensitivity Parameters and Latent Confounder Pitfalls	concept	Sensitivity Analysis in Observational Studies	latent-class model: data identify the parameters
Tukey factorization	Franks 2019 - Tukey Factorization and Marginal Contrast Estimands	definition	unidentified selection function	$f^{mis}\propto f^{obs}\cdot f(T=1-t
Condition 1 / 2	Franks 2019 - Tukey Factorization and Marginal Contrast Estimands	definition	Eq. 3	integral constraint; outcome overlap
Theorem 1	Franks 2019 - Tukey Factorization and Marginal Contrast Estimands	theorem	Eq. 5	marginal contrasts invariant to the copula
Logistic selection	Franks 2019 - Logistic Selection with Exponential Family Mixtures	definition	Eq. 7	${\gamma }_t$ shifts natural parameter
Props 1-2	Franks 2019 - Logistic Selection with Exponential Family Mixtures	theorem	Eq. 8	closed-form missing distribution (mixtures)
Calibration identity	Franks 2019 - Calibrating Sensitivity Parameters	theorem	implicit $R^2$	$
Sign interpretation	Franks 2019 - Calibrating Sensitivity Parameters	concept	Eq. 7	same-sign: fast ATE change
NHANES / JTPA	Franks 2019 - NHANES and Job Training Applications	example	Props 1-3	ATE $-0.7\to -5.6$ mmHg at $(0.03,0.05)$
Limits, hidden targeting	Franks 2019 - Discussion Limits and Bayesian Sketch	concept	Condition 2	outcome-overlap and tail-dependence caveats

Notes

• Franks 2019 - Flexible Sensitivity Analysis Without Observable Implications - Overview — CONTAINS: research question, contributions, Source Map, E102/E62/E107 links.
• Franks 2019 - Identified Sensitivity Parameters and Latent Confounder Pitfalls — CONTAINS: Sec. 2: setup, estimands, Asm. 1, Eq. 1, Example 1/Fig. 1, snooping and refit costs, related methods.
• Franks 2019 - Tukey Factorization and Marginal Contrast Estimands — CONTAINS: Sec. 3: Eq. 3-6, Conditions 1-2, Def. 1, Thm 1 + proof, Cor. 1.1.
• Franks 2019 - Logistic Selection with Exponential Family Mixtures — CONTAINS: Sec. 4: Eq. 7-14, Props 1-2, Examples 2-4, sign-convention warning, Gaussian tilt check.
• Franks 2019 - Calibrating Sensitivity Parameters — CONTAINS: Sec. 5: Examples 5-7, implicit $R^2$, Prop. 3 + proof, numerical check.
• Franks 2019 - NHANES and Job Training Applications — CONTAINS: Sec. 6, App. B: BART/NHANES, DP-mixture/JTPA, calibration numbers, results.
• Franks 2019 - Discussion Limits and Bayesian Sketch — CONTAINS: Sec. 7: advantages, limits, extensions; PyMC grid sketch; retargeting sign example.

Sources

• Franks DAmour Feller 2019 - Flexible Sensitivity Analysis Without Observable Implications — Franks AM, D’Amour A, Feller A (2019/2020), JASA, arXiv:1809.00399v3; 38 pp. Sole source. (Substituted for McCandless-Gustafson-Levy 2007, which has no open copy found.)

See Also

• Cinelli Hazlett 2020 - Making Sense of Sensitivity - Overview, Imai 2010 - Causal Mediation Analysis - Overview, Rosenman 2020 - Combining Observational and Experimental Datasets - Overview — cluster siblings.
• Unidentified Parameters - Partial Identification and Bayesian Updating — why sensitivity parameters stay prior-driven.
• Sensitivity Analysis in Observational Studies, Propensity Score in Bayesian CI, Chipman 2010 - BART - Overview.